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Unusual Orbits for Unusual Missions

Our choice of orbits can create scientifically useful space missions that can be operated at lower cost than their more conventional counterparts. How this has been done and the kind of missions it could enable in the future is the subject of James Jason Wentworth’s essay. An amateur astronomer and interstellar travel enthusiast, Wentworth worked at the Miami Space Transit Planetarium and volunteered at the Weintraub Observatory atop the adjacent Miami Museum of Science. Now making his home in Fairbanks (AK), he was the historian for the Poker Flat Research Range sounding rocket launch facility. His space history and advocacy articles have appeared in Quest: The History of Spaceflight magazine and Space News.

by J. Jason Wentworth

In the 1990s, then NASA Administrator Daniel S. Goldin introduced the “Better, Faster, Cheaper” paradigm for space missions. While NASA’s subsequent experiences led many engineers to modify that to “Better, Faster, Cheaper–choose two,” the goal of low cost has remained a primary goal for space mission planners. One way to reduce the cost of a mission is to select a trajectory that requires the least possible change of velocity (called Delta-V by engineers and orbital dynamicists) to achieve the mission’s objectives. This requires less propellant aboard the spacecraft, which results in a smaller and lighter spacecraft, which in turn can usually be lofted by a smaller and less expensive launch vehicle. (Very high-energy missions such as New Horizons are exceptions. In such cases, launching the smallest possible spacecraft merely makes such missions possible within a practical flight duration–even when using the most powerful launch vehicles available–because the velocities required for even the lowest-energy trajectories are so high.)

Another factor that affects the spacecraft’s required amount of onboard propellant is the stability of the mission orbit. If frequent orbital adjustments are necessary for any reason, a larger propellant reserve will be required, which will bump up the probe’s size and mass. The type of spacecraft stabilization system that is used also has an influence on the propellant reserve. A three-axis stabilized probe in orbit around the Moon, the Sun, another planet, or any other body will require more thruster firings (to point its sensors and imaging system at its target body, and to aim its high-gain antenna at Earth) than will a spin-stabilized spacecraft, so the latter can operate for many years using very little propellant for attitude control.

The spin-stabilized Pioneer spacecraft all exhibited this characteristic of very long life. Perhaps the most impressive of the series (besides the Sun-orbiting Pioneer 6 – 9 interplanetary probes, which lasted for multiple decades; two of them may still be functioning) was the Pioneer Venus Orbiter, which returned images of and data on the planet (and Comet Halley) for nearly 14 years, in the hostile thermal and solar radiation environment around Venus. [1] In March of 1986 Pioneer 7 also flew within 12.3 million kilometers (7.6 million miles) of Halley’s Comet and monitored the interaction between the cometary hydrogen tail and the solar wind. It discovered He+ plasma produced by charge exchange of solar wind He++ with neutral cometary material. [2]

venus_pioneer

Image: Orbit attitude of Pioneer Venus 1 between 1978 – 1980 and 1992. Credit: NASA/Ames.

Since the space age began, other trajectories besides the classical Hohmann transfer ellipse have been devised to get satellites and space probes to their destination orbits or worlds. These are used to minimize the necessary Delta-V, or to optimize planet arrival times, or both. Some geosynchronous satellites are now first injected into “super-synchronous” transfer orbits from their initial low-altitude parking orbits, from which they are later maneuvered downward into their 24-hour operational orbits. The Pioneer Venus Orbiter traveled along a similar path to Venus; it was boosted from its parking orbit around the Earth into a solar orbit that initially passed outside the Earth’s orbit about the Sun before curving inward to intercept Venus in its orbit.

Other unusual types of orbits exist, some of which were discovered when asteroids were found to be moving in them, and they are also useful for low-Delta-V (and thus lower cost) space missions. The best-known ones are halo orbits and the tadpole-shaped Lissajous orbits, in which several spacecraft have traveled around the Sun-Earth L1 and L2 Lagrangian points and the Earth-Moon L1 and L2 points.

Enter the Horseshoe Orbit

A more recently-discovered path (which a 2011 Centauri Dreams article, Stable Orbit for a Newly Discovered Companion, discusses) is the horseshoe orbit, which got its name from its shape. [3] A small object in such an orbit goes around the Sun in a normal, low-eccentricity (close to circular) elliptical orbit in the direct (prograde) direction, but since its orbit has nearly the same period and shape as the orbit of a nearby planet (Earth, in the case of the horseshoe-orbiting asteroids discovered to date), gravitational interactions with Earth create the horseshoe path (which occurs only in the Earth-centered reference frame, as the asteroid orbits around the Sun normally). This celestial “dance” works as follows:

As the asteroid is about to pass the Earth in its slightly lower, more rapid orbit, the Earth’s gravity pulls it toward itself; this speeds up the asteroid, which causes it to move farther from the Sun (and thus into a higher orbit), and this then causes the asteroid to slow down, because objects in higher orbits move more slowly. In its higher, slower orbit, the asteroid then begins to drop behind the Earth, slowly “drifting” backwards all the way around the Sun (from the Earth’s perspective–the asteroid is orbiting the Sun in the same direct [prograde] direction as Earth, just more slowly). Many years later, as the asteroid again approaches Earth (from ahead of our planet this time), the Earth’s gravity slows down the asteroid, which causes it to fall into a lower, faster orbit around the Sun. Now moving faster than the Earth (inside Earth’s orbit), the asteroid slowly “drifts” all the way around the Sun again (moving forward this time, from Earth’s perspective), after which it repeats the whole horseshoe orbit cycle again. [4]

Lagrange_Horseshoe_Orbit

Image: A horseshoe orbit, showing possible orbits along gravitational contours. In this image, the Earth (and the whole image with it) is rotating counterclockwise around the Sun. Credit: Wikimedia Commons.

While other asteroids in horseshoe orbits with respect to Earth have been found before, their orbits aren’t long-term stable. Within a certain range of distances, orbital eccentricities, and velocities, however, stable horseshoe orbits are possible, and the asteroid 2010 SO16 (the subject of the Centauri Dreams article in Reference 3) is in one, having possibly followed its current orbit for up to two million years. In addition, it is possible–as 2010 SO16 might have done, as is mentioned in the article–for asteroids (or other objects, such as spacecraft) to librate (migrate) from Lissajous orbits around the Sun-Earth L4 or L5 Lagrangian points into stable horseshoe orbits. Migration from a horseshoe orbit back into a Lissajous orbit might also be possible, and what an unpowered asteroid could do, a self-powered space probe could likely also do–using little propellant.

Another unusual kind of orbit is the quasi-satellite orbit, in which NEAs (Near-Earth Asteroids) have also been discovered. [5] A quasi-satellite is in an orbit around the Sun that has a 1:1 resonance with the orbit of a particular planet. This causes the quasi-satellite to stay close to that planet over many orbital periods. A quasi-satellite’s orbit has the same period as the planet’s orbit, but the quasi-satellite’s orbit has a different–usually greater–eccentricity than the planet’s orbit. As observed from the planet, the quasi-satellite appears to move in an oblong retrograde loop around the planet, although both bodies are orbiting the Sun in direct (prograde) orbits.

Orbital Dynamics and ‘Fuzzy Boundaries’

Pioneer-6-9

Pioneer E (which would have been named Pioneer 10 if it had not been lost in its failed launch on August 27, 1969) was the fifth and last of the series of solar-powered, drum-shaped Sun-monitoring interplanetary probes that began with Pioneer 6 in December of 1965, and Pioneer E was intended to orbit the Sun as a quasi-satellite of Earth. Had it reached its planned solar orbit, Pioneer E (which was launched–and lost–with the TETR C test and training satellite, the intended third “practice” satellite for the Apollo tracking and communications network) would have passed inside and outside the Earth’s orbit, alternately speeding up and slowing down relative to Earth. This would have kept Pioneer E within 16 million kilometers (10 million miles) of Earth during the spacecraft’s design lifetime of from six months to two and one-half years. [6] (It would likely have operated for much longer than two and one-half years, as its sister probes Pioneer 6 – 9 demonstrated.)

Image: Artist’s conception of the Pioneer 6–9 spacecraft. Credit: NASA.

Orbit changes could be done using even less propellant (virtually none, in some cases) by employing Dr. Edward Belbruno’s principle of gravitational “Fuzzy Boundaries,” which involve the physics of chaos. [7, 8, and 9] This was first demonstrated in 1991 after Japan’s first lunar probe, the combined Hiten/Hagoromo spacecraft, ran into difficulties. Launched on January 24, 1990, the craft was injected into a highly-eccentric elliptical Earth orbit that passed beyond the Moon. The tiny Hagoromo lunar orbiter separated from Hiten during its first lunar swing-by and fired its solid propellant retro-rocket as the vehicles passed the Moon; while Hagoromo entered lunar orbit as intended, its radio transmitter failed when its retro-rocket fired (optical telescopic observation from Earth confirmed its entry into lunar orbit), which rendered it scientifically useless. [10] On March 19, 1991, Hiten performed the first-ever aerobraking maneuver, skimming the Earth’s atmosphere to change its orbit.

Having learned of Hagoromo’s transmitter failure, Edward Belbruno approached ISAS (the Institute of Space and Aeronautical Science) and offered to help them get their still-functioning Hiten lunar flyby spacecraft into lunar orbit. The probe, which was in a highly-eccentric Earth orbit, was moving much too fast during its lunar flybys to brake into lunar orbit using its onboard propellant. But by utilizing his “Fuzzy Boundaries” method, which involved using the combined gravity of the Moon and the Earth, on October 2, 1991 Hiten’s flight controllers were able to maneuver the probe into a preliminary, temporary lunar orbit using almost no propellant. After that, Hiten was targeted to fly through the Earth-Moon L4 and L5 points to collect data on any meteoric dust that was thought to possibly have accumulated there (none was detected). On February 15, 1993, Hiten was directed into a permanent lunar orbit, where it remained until it was deliberately crashed on the lunar surface on April 10. [11]

pct_main_hiten

Image: An artist’s conception of the Hiten spacecraft. Credit: JAXA.

A Panoply of Applications

Stable horseshoe solar orbits and quasi-satellite solar orbits–entered and/or exited with the aid of Dr. Belbruno’s “Fuzzy Boundaries” method, making use of planetary as well as solar gravity–would be useful for Pioneer 6 – E type solar monitoring probes, which could observe portions of the Sun that cannot be seen (at any given time) from Earth. They could also, in concert with solar observations from Earth (or from Earth satellites), make stereo observations of solar features at many places along their horseshoe or quasi-satellite orbits. These same solar probes could also, as the Sun-orbiting Pioneer 7 interplanetary probe did, encounter and examine comets that pass through or near their orbits (flybys of asteroids that pass them would also be possible). If necessary, such probes could modify their horseshoe or quasi-satellite orbits (speeding up or slowing down, as needed) in order to make closer flybys of comets and asteroids (and later return to their original orbits) using very little propellant. Or, the probes could utilize solar sail propulsion (a simplified heliogyro sail should work nicely) to make such orbit changes, using no propellant at all.

Another application for horseshoe and quasi-satellite solar orbits would be to place NEO (Near-Earth Object) space telescopes in such orbits, much closer to the Sun than Earth’s distance. These locations would enable the spacecraft to see Earth-crossing NEOs whose orbits keep them mostly inside Earth’s orbit, and objects that could become dangerous to Earth in the future (via gravitational encounters with Venus and/or Mercury) would also be visible to these spacecraft. (To telescopes on or near the Earth, the sunlit sides of these small, often dark-colored objects face away from our planet, making them virtually impossible to see in the Sun’s glare, and Earth-based telescopes could never search for them in a truly dark sky because they would never be far from the Sun.) The B612 Foundation and its aerospace industry partner Ball Aerospace plan to send their NEO-seeking Sentinel space telescope to a Venus-like solar orbit for this reason. [12 and 13]. A horseshoe orbit or a quasi-satellite orbit “threaded around” Venus’ orbit about the Sun could reduce the necessary Delta-V (and thus the spacecraft’s launch vehicle and onboard propellant requirements) by utilizing Venus’ gravity to help establish–and later maintain by itself–either type of orbit for the Sentinel spacecraft.

Sentinel_Space_Telescope_illustration

Image: The Sentinel Space Telescope, being built by the B612 Foundation. Credit: B612Julie (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons.

Closer to home, Earth-centered horseshoe orbits–in which evenly-spaced communication, weather, or Earth resources satellites could “cycle” around the Earth as if on a circular conveyor belt (with two sets of spacecraft, on the inner and outer edges of the “belt”)–could provide global coverage not only of Earth, but they could also serve as communication relays for the lunar farside and for the Earth-Moon L2 point behind the Moon. (For circum-terrestrial horseshoe orbits, the Moon’s gravity would serve the same function that the Earth’s gravity does for Sun-centered horseshoe orbits that are “threaded around” Earth’s orbit about the Sun.) They could also provide close-up lunar observation to monitor time-variant lunar phenomena (the lunar “dustosphere’s” monthly cycling under the influence of Earth’s magnetotail, lunar meteorite impacts during meteor showers, TLP [the luminous Transient Lunar Phenomena], etc.).

wbluesjr

Surprisingly, even low-cost suborbital interplanetary missions are possible. In addition to gathering data on the time-variant phenomena of the interplanetary environment, they could also collect dust, ice, and gas samples from comets that pass relatively close to Earth. NASA’s simple, inexpensive solid propellant Scout satellite launch vehicle, manufactured by LTV (Ling-Temco-Vought) using existing “off-the-shelf” rocket motors, was also used for several high-altitude suborbital probe missions that reached tens of thousands of kilometers into space. [14] (A rocket that ascends to an altitude of one Earth radius or higher is considered a space probe rather than a sounding rocket, because reaching one Earth radius requires a rocket velocity that is equal to Low Earth Orbit [LEO] orbital velocity.) The U.S. Air Force’s Blue Scout vehicles (which were similar to the NASA Scout vehicles for the most part, but were somewhat different because they were produced by a different contractor, the Ford Motor Company’s Aeronutronic Division) also flew numerous probe missions. [15 and 16] One in particular, a Blue Scout Junior launched from Cape Canaveral on August 17, 1961, reached an altitude of 225,000 kilometers (140,000 miles)–more than halfway to the Moon–on a suborbital flight lasting days. Unfortunately, the payload’s transmitter failed during the final (fourth) stage’s burn, rendering the flight scientifically useless. [17 and 18]

Image: The Blue Scout Junior. Credit: Peter Alway/Encyclopedia Astronautica: http://www.astronautix.com/index.html.

In his 1957 book The Making of a Moon: The Story of the Earth Satellite Program (and in its 1958 post-Sputnik revised second edition), Arthur C. Clarke pointed out that by launching suborbital vehicles at velocities approaching Earth’s escape velocity, their payloads could reach altitudes of millions of miles before falling back to Earth. [19] Interestingly, the altitudes achieved begin to increase dramatically at only 35,000 kilometers per hour (22,000 miles per hour), significantly below Earth’s escape velocity. As he wrote: “A rocket launched vertically at 22,000 miles an hour–or four thousand miles an hour faster than a satellite–would reach an altitude of about fifteen thousand miles before gravity checked its speed and it fell back to Earth. Slight further increases in velocity would give altitudes of millions of miles, until at the critical speed of 25,000 miles an hour the rocket never came back at all.”

Such vehicles could be very small–the 7.3-meter (24-foot) long, balloon-launched Project Farside probe rockets of the late 1950s, which reached nearly orbital velocity and rose to altitudes of between 3,200 and 5,000 kilometers (2,000 and 3,100 miles) with 1.4 to 3.3 kilogram (3 to 5 pound) payloads, could have reached the vicinity of the Moon with the addition of a fifth stage, which was proposed. [20] But this proposal was not proceeded with, possibly because the electronics technology of those days likely wouldn’t have enabled such small payloads to return meaningful data from the Moon’s distance (the frequent failures of the Farside vehicles’ payload transmitters also didn’t encourage much confidence in more ambitious ventures). But today a full suite of instruments, an S-band or X-band telemetry transmitter, and their solar cell or battery power supply could be accommodated in payloads of that mass range.

farside

Image: Working on Project Farside. Credit: Parsch, Directory of U.S. Military Rockets and Missiles: http://www.designation-systems.net/dusrm/app4/farside.html.

Existing high-performance multi-stage sounding rockets could, if topped with multiple high-velocity stages, boost heavier payloads to such velocities (similar vehicles have boosted artificial meteors to velocities far in excess of escape velocity, beginning in 1957). [21 and 22] Such “souped-up” sounding rockets, or small–particularly air-launched satellite launch vehicles with additional upper stages, such as Orbital Sciences Corporation’s Pegasus XL and the upcoming Boeing ALASA (Airborne Launch Assist Space Access) system–could loft small suborbital interplanetary probes. [23 and 24] This capability would make possible low-cost, rapid comet sample return missions to “targets of opportunity,” comets such as IRAS-Araki-Alcock and Hyakutake that pass within a few million kilometers of Earth.

pegasus

Image: The Pegasus XL launch vehicle operated by Orbital Sciences Corporation. Credit: NASA.

The recoverable portion of the spacecraft could use a deployable aerogel particle collector that would be housed in a small, blunt re-entry heat shield similar to that of the Pioneer Venus Small Probes or the Japanese Hayabusa and Hayabusa 2 asteroid sample return probes. The expendable section of the spacecraft, which would burn up upon re-entry into the Earth’s atmosphere, would carry fields and particles instruments and an imaging system. At other times, such suborbital probes could collect intact meteoroids from meteor shower streams for return to Earth, and/or they could gather data on the far regions of Earth’s magnetosphere and magnetotail, including their interactions with the solar wind and the solar magnetic field. Since the parent bodies of many meteor shower streams are now known (most originate from comets–a few are from asteroids), suborbital probes would offer inexpensive, frequent, and regular opportunities for collecting samples of these objects.

By substituting subtlety and cleverness for brute force, and by letting some mission targets come to their probes more than vice-versa, many new, scientifically useful, and inexpensive space missions would become practical and affordable. In addition to garnering new knowledge, such missions would also provide more frequent opportunities for young scientists, engineers, and orbital dynamicists to gain hands-on experience in designing and executing deep space missions–experience that would be of great help to them when the time comes to tackle the more ambitious outer solar system and observatory missions that NASA hopes to fly in the coming decades.

——-

References

1. Pioneer Venus Project Information, National Space Science Data Center website: http://nssdc.gsfc.nasa.gov/planetary/pioneer_venus.html

2. Pioneer 6, 7, 8, and 9, Wikipedia article: https://en.wikipedia.org/wiki/Pioneer_6,_7,_8,_and_9

3. Stable Orbit for a Newly Discovered Companion, Centauri Dreams article: https://www.centauri-dreams.org/?p=17484

4. Horseshoe orbit, Wikipedia article: https://en.wikipedia.org/wiki/Horseshoe_orbit

5. Quasi-satellite, Wikipedia article: https://en.wikipedia.org/wiki/Quasi-satellite

6. TRW Space Log, Winter 1969-70, Vol. 9, No. 4, Pioneer E, TETR C entry on pages 40 – 43.
The National Space Science Data Center http://nssdc.gsfc.nasa.gov/ has a Pioneer E mission page at http://nssdc.gsfc.nasa.gov/nmc/spacecraftDisplay.do?id=PIONE.

7. Edward Belbruno, Wikipedia article: https://en.wikipedia.org/wiki/Edward_Belbruno

8. Edward Belbruno : Mathematics, Astrophysics, Aerospace Engineering (Edward Belbruno’s Official Website): www.edbelbruno.com

9. SpaceRoutes.com website: http://www.spaceroutes.com/intro.html

10. Hiten (Muses-A) JAXA webpage: http://www.isas.jaxa.jp/e/enterp/missions/hiten.shtml

11. Hiten, Wikipedia article: https://en.wikipedia.org/wiki/Hiten

12. Sentinel Space Telescope, Wikipedia article: https://en.wikipedia.org/wiki/Sentinel_Space_Telescope

13. Sentinel Mission website (mission overview page): http://sentinelmission.org/sentinel-mission/overview/

14. LTV (Vought) SLV-1 Scout, Designation Systems article: http://www.designation-systems.net/dusrm/app3/lv-1.html

15. Ford RM-89 Blue Scout I, Designation Systems article: http://www.designation-systems.net/dusrm/app1/rm-89.html

16. Ford RM-90 Blue Scout II, Designation Systems article: http://www.designation-systems.net/dusrm/app1/rm-90.html

17. Ford RM-91 Blue Scout Junior, Designation Systems article: http://www.designation-systems.net/dusrm/app1/rm-91.html

18. Blue Scout Jr, Encyclopedia Astronautica article (with launch chronology): http://www.astronautix.com/lvs/bluoutjr.htm

19. The Making of a Moon: The Story of the Earth Satellite Program by Arthur C. Clarke, pages 149 – 150 (First Edition, Published 1957 by Harper & Brothers Publishers, New York, NY, Library of Congress catalog card number: 57-8187 [a post-Sputnik revised edition, the same book with that update, was published in 1958])

20. Aeronutronics Farside, Designation Systems article: http://www.designation-systems.net/dusrm/app4/farside.html

21. Possible Challenge to Sputnik on Unmanned Spaceflight website: http://www.unmannedspaceflight.com/lofiversion/index.php/t1955.html

22. The First Shots Into Interplanetary Space by Professor Fritz Zwicky, California Institute of Technology Library website: http://calteches.library.caltech.edu/181/1/zwicky.pdf

23. Boeing to Design DARPA Airborne Satellite Launch Vehicle, Boeing.com website: http://www.boeing.com/features/2014/03/bds-darpa-contract-03-27-14.page

24. DARPA’s ALASA space launch system from airplane, wordlessTech.com website: http://wordlesstech.com/darpas-alasa-space-launch-system-from-airplane/

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Comments on this entry are closed.

  • Michael October 12, 2015, 22:13

    @Hop David

    ‘Let’s see, 3.1/3.5 = .886. Well, technically 88.6% could be called a fraction. But that’s not the connotation I’m picking up from Benson’s account.’

    In space I would say even a 12% reduction in fuel is quite significant.

    @Paul Gilster

    ‘Charlie, I’ll throw this in: If we found long-haul trajectories that could save fuel, etc. but took a great deal of time, they would doubtless be used not for human missions but for things like robotic re-supply. To a colony on Mars, for example.’

    I would just like to add to your comment Paul in that if a lower energy transfer trajectory was found a supply craft could be sent many years ahead of the main mission which is the human component. A Mars return vehicle could be sent which could be refueled on Mars ready for the arriving astronauts to jump into.

    Sorry Charlie your comment was lost in the blog glare.

  • Michael October 12, 2015, 22:26

    Forgot to add,

    @Hop David

    ‘Hiten had already invested 3.1 km/s to get a high apogee.

    Farquhar’s route is basically a Hohmann path to the moon with a lunar capture burn at perilune and a parking burn at an EML2 apolune. His route from LEO to EML2 totals 3.5 km/s. Let’s see, 3.1/3.5 = .886. Well, technically 88.6% could be called a fraction. But that’s not the connotation I’m picking up from Benson’s account.’

    I am not sure that the Hiten probe was in the ideal trajectory in the first place for a low energy transfer to the moon so the fuel saving could have been better if it started out on that designed trajectory.

  • Paul Gilster October 13, 2015, 8:07

    Dr. Belbruno tells me that he is on travel and too busy to engage in the discussion here, but he regards the ballistic capture transfer to Mars as ‘rigorously proven’ and sends the relevant links. The first we already had, being the preprint on arXiv, but preprints give way to the published paper.

    The original posting on ArXiv:

    http://arxiv.org/abs/1410.8856

    The final paper, which appeared in the refereed journal Celestial Mechanics and Dynamical Astronomy:

    http://link.springer.com/article/10.1007%2Fs10569-015-9605-8#page-1

    The ballistic capture transfer to Mars is also discussed in the proceedings of the 25th Spaceflight Mechanics Meeting in Williamsburg, VA (Jan 11-15, 2015), which appears in Volume 155 of Advances in the Astronautical Sciences.

  • Michael October 13, 2015, 12:33

    I heard via the grape vine that this software for orbital mechanics is very good unfortunately you can only download it with blessing from NASA.

    http://www.nasa.gov/centers/johnson/copernicus/

    Anyone on here with enough clout at NASA can try it out? I am not sure what software Dr Belbruno used but it has got to be close to it, I would love to try it out if I could.

  • Hop David October 13, 2015, 16:15

    I’m not going to pay $40 for Belbruno’s paper.

    Does Belbruno still list ~2 km/s aphelion burns?

    If so, he is flushing 1.3 km/s down the toilet. Far from being a zero delta V route, it costs *more* than entering a capture orbit from an ordinary Hohmann.

    Injection to capture orbits take much less delta V than injection to low circular orbit. A huge Oberth savings can be realized. From an earth to Mars Hohmann, a .7 km/s periaerion burn suffices for capture. See
    http://hopsblog-hop.blogspot.com/2012/06/inflated-delta-vs.html

  • Charlie October 13, 2015, 16:54

    So many extraordinary comments on here that I would like to address the very last one which was posted by Michael. The link that you post that connects to the software (I guess that’s what you meant), is that something in which one can simply plug some parameters into and get out the answers ? Or is it one of these types of software where one has to be fairly intimately familiar with the subject matter before you can proceed to place in the proper parameters ?

    That’s one of the great problems with software even to those that are used by individuals employed by a particular professional group; you often (more often than not) MUST be familiar with the nature of the problem before you can make a decision as to what information to enter to obtain a valid answer. So can you tell me, is this something in which anyone who has a reasonable educational background can employ this particular software ? Or again is something that you must have had a lot of experience with which delves into the detailed nature of the subject material ? Makes a whole lot of difference I can tell you that.

  • Charlie October 13, 2015, 16:59

    Lastly, I should have asked the obvious question, but I forgot about it in the spiel that I put out in the previous question, does Mister Gilster have sufficient clout with NASA to permit some of his readers to download the software ? Could he be asking our behalf as he is more formally a representative of something that represents at least more than just a passing interest in space exploration matters.

  • Paul Gilster October 13, 2015, 20:25

    I could make a request, Charlie, but here is how NASA puts it:

    “The National Aeronautics and Space Act of 1958 and a series of subsequent legislation recognized transfer of federally owned or originated technology to be a national priority and the mission of each Federal agency. The legislation specifically mandates that each Federal agency have a formal technology transfer program, and take an active role in transferring technology to the private sector and state and local governments for the purposes of commercial and other application of the technology for the national benefit. In accordance with NASA’s obligations under mandating legislation, JSC makes Copernicus available free of charge to other NASA centers, government contractors, and universities, under the terms of a US government purpose license. Organizations interested in obtaining Copernicus should contact:
    Technology Transfer and Commercialization Office
    NASA Johnson Space Center
    Phone: 281-483-3809
    E-mail: jsc-techtran@mail.nasa.gov
    For Copernicus-based analysis requests or specific Copernicus modifications that would support your project, please contact Gerald L. Condon (gerald.l.condon@nasa.gov) at the NASA Johnson Space Center.”

    What I’d recommend is that anyone seriously interested in the software write to the address above and make the case. I’ll see if I can find anything else out.

  • Hop David October 13, 2015, 22:03

    Michael, yes 12% is significant. But there is also a time trade off. The fastest 3.1 km/s route from LEO to EML2 I know of is 72 days. The Farquhar Route is 8 or 9 days. Belbruno’s route to the edge of the moon’s Hill Sphere took years.

    “I am not sure that the Hiten probe was in the ideal trajectory in the first place … so the fuel saving could have been better if it started out on that designed trajectory.”

    No. To use solar or lunar tidal influence, you need a high apogee. Which takes 3.1 km/s. That gets you close enough to the moon’s neighborhood where the moon’s gravity can lend a hand.

    Almost all the pages singing the praises of Belbruno’s Hiten route don’t mention that 3.1 km/s. There are many that give the impression of a zero fuel route from LEO to lunar orbit. Which is completely wrong.

    Now regarding trips to Mars…

    Michael, in the paper you linked to, Belbruno mentions going from Sun-Earth Lagrange 2 to sun-Mars Lagrange 1. Both these locations are distant from the planet and confer virtually zero Oberth benefit. For maximum Oberth benefit, you do the burn as deep as possible in the planet’s gravity well.

    If you’re interested I wrote about the Oberth benefit: http://hopsblog-hop.blogspot.com/2013/10/what-about-mr-oberth.html

    If there were no such thing as the Oberth effect, Belbruno’s route might indeed confer savings. But with the Oberth benefit factored in, Belbruno’s route to Mars costs substantially *more* than conventional routes. And it takes a lot longer.

  • Hop David October 13, 2015, 22:41

    I made a spreadsheet where you can type in departure and destination planets. Use can also input altitudes of periapsis and apoapsis for planetary parking orbits. It also gives approximate Hohmann Launch windows:

    http://clowder.net/hop/railroad/Hohmann.xls

    For capture orbits, I usually set periapsis altitude at 300 km and apoapsis altitude at the Sphere of Influence (given to the right of the pink input squares).

  • Michael October 15, 2015, 15:19

    @Hop David

    Without looking more deeply into his paper,$40 is a little steep, I can only surmise that he is using a trajectory that is suited to the low trust of the ion engine. The ion engine is much more efficient than a standard chemical engine and will use less fuel so the numbers will look much better although the journey takes longer to complete. I do believe in these conduits that reduce the amount of energy needed for a transfer by taking favourable alignments of masses and there interactions into consideration but they are not always practical.

    Thanks for the link and spreadsheet, most informative, I not sure if you intended to show the moon as stationary during the trip as the moon would have moved even in the 4-5 days so interception would have occurred earlier.

    http://hopsblog-hop.blogspot.com/2013/10/what-about-mr-oberth.html

  • Hop David October 15, 2015, 19:52

    The free paper makes no mention of low thrust trajectories that I can see.

    People seem to conflate low thrust ion spirals with the ITN. The low thrust spirals actually take more delta V than impulsive burns that exploit the Oberth effect. However the extra delta V is offset by the ion rocket’s higher exhaust velocity.

    The diagram of Farquhar’s trajectory from LEO to EML2 wasn’t drawn by me. It was drawn by Robert Farquhar.
    https://en.wikipedia.org/wiki/Robert_W._Farquhar

    It shows the trajectory in a rotating frame where the earth and moon remain stationary.

  • Michael October 16, 2015, 6:11

    @Hop

    I would have liked to have had an advanced orbital mechanics software package available to compare the two ideas but I don’t.

    Here is the website of Dr Belbruno, you may wish to contact him later and discuss the issues in more depth, please keep us in the picture it is an interesting concept.

    http://www.edbelbruno.com/

    Here is a link to a lecture he gave explaining the idea.

    http://www.maa.org/news/edward-belbruno-on-low-energy-pathways-in-space-chaos-and-random-walks

    And here is the idea applied to Mars.

    http://spaceroutes.com/astrocon/AstroconVTalks/Pergola-AstroconV.pdf

  • Alex Tolley October 17, 2015, 16:47

    I read Belbruno’s popular book on weakly stable orbits and ballistic capture and he is claiming that there ways to traverse the solar system with low fuel requirements, as the orbital paths are chaotic. The evidence for comets and resonant orbit hopping seems quite compelling as an argument. I’m not surprised that the astrogator’s guild are skeptical as the approach is very difficult due to the chaotic nature of these orbits, so they are difficult to plan.

    Belbruno makes a good case that these orbits are good for low thrust vehicles and that the fuel saving substantially increases the payload, even if the fraction of fuel saved is not huge. These orbits are for robotic craft, not crewed vehicles, where time of transit is not critical.

  • Charlie October 17, 2015, 18:38

    Michael – I thank you for your link to the Scientific American article via the Belbruno website link. Scientific American article is able to clear away the cobwebs behind what the proposed ballistic capture idea is about. It strikes me if I understand it correctly, that one is permitted to coast to the apsis point on a path to Mars, and then with Mars arriving in the vicinity of the point it can gently ‘grab hold’ of the craft permitting entry into the Martian sphere of influence. Brilliant, I haven’t seen the paper that was the made available here to get the details but the article in Scientific American appears to clearly convey that idea.

    At the risk of sounding rather like a know it all. I do question that the path to reach the ballistic grab point would seem to be a lot longer than just a few months more by a straight Hohmann transfer. My gut tells me that it would seem to be considerably longer than just the straight six months to get to Mars. This has great deal of importance if I understand that the radiation problems of interplanetary flight are considerably greater than have been estimated to be for human crews. Psychologically, as well as the issue of having sufficiently supplied spacecraft far the journey brings into question as to how useful this type of method might be for manned missions. But again, it depends on how long is defined as how long. The Scientific American article greatly clarified what was the entire problem and it was very well written.

  • Charlie October 17, 2015, 18:43

    @Michael, – forgot to add based upon the article again, that was mentioned in the previous post there seems to be no outstanding reason why this idea could not be applied to ANY planetary encounter that you might wish to make anywhere within the solar system. The only limiting factor would be how much are human crew could endure in the transfer time required to do this procedure; otherwise there seems to be no limitation as to the use of this method as a fuel saving/mass transferring type of mechanism to obtain meaningful interplanetary flights. Perhaps in the distant future. Such methods might also have applicability to capture by distant star systems in which you could minimize the deceleration by allowing a ballistic capture near where the star was expected to be.

  • Hop David October 18, 2015, 0:57

    Alex Tolley wrote “The evidence for comets and resonant orbit hopping seems quite compelling as an argument.”

    Once again — some mass parameters:
    Pluto/Charon 1.043E-01
    Earth/Moon 1.216E-02
    Sun/Jupiter 9.545E-04
    Sun/Saturn 2.856E-04
    Saturn/Titan 2.374E-04
    Jupiter/Ganymede 7.789E-05
    Jupiter/Callisto 5.684E-05
    Sun/Neptune 5.153E-05
    Jupiter/Io 4.700E-05
    Sun/Uranus 4.366E-05
    Jupiter/Europa 2.526E-05
    Saturn/Rhea 4.046E-06
    Sun/Earth 3.039E-06
    Sun/Venus 2.448E-06
    Saturn/Dione 1.935E-06
    Saturn/Tethys 1.091E-06
    Sun/Mars 3.229E-07
    Saturn/Enceladus 1.935E-07
    Sun/Mercury 1.659E-07
    Saturn/Mimas 7.037E-08
    Mars/Phobos 1.682E-08
    Sun/Pluto& Charon 7.149E-09
    Mars/Deimos 2.803E-09
    Sun/Ceres 4.741E-10
    From http://hopsblog-hop.blogspot.com/2015/06/mass-parameter-and-itn.html

    Can Jupiter and Saturn swap comets? Sure. Can the Jupiter’s Galilean moons swap probes? Yes.

    Does this mean we can send stuff from the sun earth L2 to the sun Mars L1? Only with a substantial delta V budget. The sun-earth μ is 3e-6. The sun-Mars μ is 3.3e-7.

    Alex Tolley wrote “I’m not surprised that the astrogator’s guild are skeptical as the approach is very difficult due to the chaotic nature of these orbits, so they are difficult to plan.”

    So show me someone who has planned such an orbit to Mars. The best I’ve seen so far is the Belbruno and Toppotu’s ballistic capture which takes 1.3 km/s *more* than Mars capture from a Hohmann orbit.

    Show me Belbruno’s unicorn and I’ll no longer be a skeptic.

  • Michael October 18, 2015, 2:33

    Alex Tolley October 17, 2015 at 16:47

    ‘I read Belbruno’s popular book on weakly stable orbits and ballistic capture and he is claiming that there ways to traverse the solar system with low fuel requirements, as the orbital paths are chaotic. The evidence for comets and resonant orbit hopping seems quite compelling as an argument.’

    If you look at this Jupiter asteroid clip you can see some asteroids that approach Jupiter have very weird orbits.

    http://star.arm.ac.uk/neos/JupiterResonance/indexflash.html

    @Charlie October 17, 2015 at 18:38

    ‘..It strikes me if I understand it correctly, that one is permitted to coast to the apsis point on a path to Mars, and then with Mars arriving in the vicinity of the point it can gently ‘grab hold’ of the craft permitting entry into the Martian sphere of influence.’

    Yes and it can be applied to many different encounters within the solar system some practical some not.

    ‘At the risk of sounding rather like a know it all. I do question that the path to reach the ballistic grab point would seem to be a lot longer than just a few months more by a straight Hohmann transfer.’

    This longer flight time is well placed for as many have said before robotic probes, if we say send an empty Mars return vehicle to Mars several years ahead using the cost saving of this type of flight and using the Martian air to make fuel it could be ready for when the human crew arrived via a quicker Hohmann transfer process.

    ‘Perhaps in the distant future. Such methods might also have applicability to capture by distant star systems in which you could minimize the deceleration by allowing a ballistic capture near where the star was expected to be.’

    The problem here is that the probe will be going very fast, too fast for a capture.

  • Charlie October 18, 2015, 16:08

    @Michael
    a responder to your comments here and further thoughts on the matter. It occurred to me later that these ballistic captures would have the ability to ‘possibly’ minimize energy requirements as compared to the Hohmann transfer process as you just verified in the above. I would take this to mean that the Hohmann transfer process is no longer considered the ‘minimum’ energy transference process, despite its reign far better than 70 years as the leading contender for minimum energies. This gave me the thought that no longer would we have a situation such as we have recently seen ala a fictional character of Mark Watney in the story ‘ the Martian’ where one would have to wait two years to affect the rescue.

    Rather, even a robotic rescue ship could affect the rescue in less time. You made mention of the fact that it would be in a great deal of situations in the solar system, but not all. Can you elaborate a little further on those that are not accessible to this technique ? Depending upon the type of rescue (or conventional mission) that would be required the ship could carry considerable more amount of propellant to effect an immediate dissent into the orbit of the given planet if time was of the essence, once it had been gently captured by the ballistic capture process.

    To return again to my comment of utilizing it far’s capture by stars in interstellar travel. I wish to reiterate that this might be possible. Still, by a ‘partial deceleration’ carrying some fuel on board are by other means such as interaction with the galactic magnetic field. Do you think that it would be a possibility to perform the same maneuver though if one was to perform a gravity assist very, very close to the target star and if conditions were right, it would permit the vehicle to reach the furthers most ballistic capture point and still enter into a stellar orbit ? It seems that there could be some applicability even given a situation where you would have substantial velocities involved. Again, this would be sharply defined by the mission parameters in the particulars of the situation. Any possibility of agreement here ?

  • Charlie October 18, 2015, 16:14

    Should have said ‘…this might be possible still …’ Instead of ‘this might be possible. Still,’

  • Alex Tolley October 18, 2015, 19:34

    @Charlie – the ballistic capture is useful for the cargo component of a manned mission, when time is not critical. This allows delivery of larger cargoes for each launch and more frequent launch dates. It also allows vehicles with low thrust as the fast orbital insertion burn is not required. This really opens up using electric spacecraft for cargo.

    The longer transit times are bad not only for longer radiation exposure to the crew, but the increased consumables demand probably outweighs any benefit for a crew.

    I would see such maneuvers as emergency only for human crews where fuel is insufficient for a standard Hohmann trajectory and orbital capture.

  • Alex Tolley October 18, 2015, 19:51

    @Hop david “The best I’ve seen so far is the Belbruno and Toppotu’s ballistic capture which takes 1.3 km/s *more* than Mars capture from a Hohmann orbit.”

    But this required a high thrust Oberth maneuver and a high thrust orbital insertion. These are not possible with electric engines, such as ion drives.

    Therefore there is a trade off – Hohmann trajectories with chemical/NTR engines, or some other approach for low thrust electric engines. It is the latter that Belbruno’s approach is for.

    Your mass ratio between bodies argument certainly makes such ballistic trajectories more difficult, but doesn’t negate them, AFAICS. Maybe I’m wrong, but Belbruno seems to argue that any multi-body gravitational interaction offers potential lower energy trajectories, and in special cases, zero energy trajectories, e.g. comets doing “resonant orbit hopping”.

    I don’t even think Belbruno is even suggesting that large energy savings are possible, just that any savings impact potential payload. For the rocket equation, an M1/M0 ration of 11, will allow doubling of M1 with just a 10% energy saving. As ballistic capture doesn’t need high thrust, the choice of engines increases, allowing low thrust engines that have much lower M1/M0 rations, further improving the efficiency of the transport.

    Belbruno himself says that computing these orbits is very hard due to the chaotic nature of the orbits, and therefore it should be surprising that they have not yet been computed. But as computers become ever more powerful, this may not be such a limitation – after all your smartphone is as powerful as a 1970’s Cray supercomputer.

  • Alex Tolley October 18, 2015, 19:58

    As regard star travel, I see ballistic capture as more applicable for comets or asteroids carrying life from star to star, with millions of years to make even short hops. That impacts the panspermia hypothesis, but I don’t see it as useful for even robotic flights as speed is of the essence here, unless the plan is to seed the galaxy with life for the long term – i.e. billions of years.

    If we discovered that Earth is unique in harboring life, I could see this as one way to try to seed the galaxy with life using the lowest energy cost as possible. It would be almost a religious endeavor.

  • Hop David October 19, 2015, 3:16

    An ellipse with a 1 A.U. perihelion (earth’s neighborhood) will be moving 2 to 3 km/s with regard to Mars when in Mars’ neighborhood. Too fast for ballistic capture.

    Which is why Toppotu and Belbruno do a 2 km/s burn at aphelion to circularize the orbit at ~1.5 A.U.

    Upon entering Mars Sphere of Influence, an earth to Mars Hohmann becomes a hyperbolic orbit wrt to Mars. Speed of a hyperbola is sqrt(Vinf^2 + Vesc^2). Close to Mars, escape speed is 4.8 km/s. Vinf is around 2.6 km/s. Sqrt(4.8^2 + 2.6^2) is about 5.5.

    Altitude Mars Sphere of Influence is about 570,000 kilometers. If we can get an apoaerion this high or less, the space craft is captured. The vis-viva equation tells that a 300 km altitude by 57,000 km altitude ellipse is moving 4.79 km/s at periaerion, just a hair below escape.

    Going from 5.5 km/s to 4.8 km/s takes only .7 km/s. .7 km/s to achieve capture.

    Come on. Speed of a hyperbola and the vis viva equation aren’t that hard. A bright high school kid could do this. It doesn’t take a fancy orbital mechanics software to figure out that 2 > .7. And it you’re not going to take the time to learn basic orbital mechanics, you would not be able to use that software in any case.

    Alex, Michael, and Charlie — Artful handwaving can get you an A on a high school English essay. But planning a mission takes math. To credibly defend Belbruno’s ballistic capture, you need math. Your walls of text with no math and no numbers are a waste of time.

  • Michael October 19, 2015, 3:25

    @Charlie October 18, 2015 at 16:08

    ‘It occurred to me later that these ballistic captures would have the ability to ‘possibly’ minimize energy requirements as compared to the Hohmann transfer process as you just verified in the above. I would take this to mean that the Hohmann transfer process is no longer considered the ‘minimum’ energy transference process, despite its reign far better than 70 years as the leading contender for minimum energies.’

    It appears that Dr Belbruno has found a three body algorithm not a two body one to reduce the problem to a more suitable solution which has reduced the energy requirements, sometimes at the expense of time. The three body problem is notoriously difficult, even Sir Newton gave up on it!

    ‘Rather, even a robotic rescue ship could affect the rescue in less time. You made mention of the fact that it would be in a great deal of situations in the solar system, but not all. Can you elaborate a little further on those that are not accessible to this technique ?’

    These tubes of minimum energy may have such long time periods to complete that they are ineffective to the science requirement.

    ‘Depending upon the type of rescue (or conventional mission) that would be required the ship could carry considerable more amount of propellant to effect an immediate dissent into the orbit of the given planet if time was of the essence, once it had been gently captured by the ballistic capture process.’

    It could but it depends on where it is in its orbit when the rescue need arose, there is also the possibility of a rescue vehicle been ready in a slow elliptical orbit around mars sent some years earlier.

    ‘To return again to my comment of utilizing it far’s capture by stars in interstellar travel. I wish to reiterate that this might be possible. Still, by a ‘partial deceleration’ carrying some fuel on board are by other means such as interaction with the galactic magnetic field.

    The galactic magnetic field is quite weak, deceleration using a magsail is achievable using the interstellar medium and target star solar wind, at least a significant reduction in speed. I once thought about allowing the main spacecraft to carry out one last burn still in the direction of the star and drop the magsail probes into the exhaust stream, been charged particles in the exhaust the force will slow down the crafts sharpish, perhaps allowing capture events. The many probes could still use the main craft as a communication centre for transmission back to Earth.

    ‘Do you think that it would be a possibility to perform the same maneuver though if one was to perform a gravity assist very, very close to the target star and if conditions were right, it would permit the vehicle to reach the furthers most ballistic capture point and still enter into a stellar orbit ?’

    As long as you are lower in velocity than the escape velocity of the target star system you will enter into stellar orbit. If there are a few planets in the system then they too could be used to reduce the velocity of the crafts to enable a more suitable orbit in the target star system.

  • Michael October 19, 2015, 10:27

    @Hop David

    ‘Alex, Michael, and Charlie — Artful handwaving can get you an A on a high school English essay. But planning a mission takes math. To credibly defend Belbruno’s ballistic capture, you need math. Your walls of text with no math and no numbers are a waste of time.’

    Dr Belbruno is the person you need to direct your concerns too, not us, if you can prove him wrong you could elevate your standing within the scientific community.

    http://www.edbelbruno.com/

    Complex orbital mechanics is not my field, I do see what he is doing though, he is using a highly efficient engine and found a way to get a more fuel efficient path using it, it may not be time efficient though. If he had used a chemical rocket to do the same route he may have ended up using more fuel than a Hohmann transfer trajectory.

  • Hop David October 19, 2015, 17:33

    “Therefore there is a trade off – Hohmann trajectories with chemical/NTR engines, or some other approach for low thrust electric engines. It is the latter that Belbruno’s approach is for.”

    For convenience I’ll repost the link to Belbruno’s paper:
    http://arxiv.org/pdf/1410.8856v1.pdf

    I can’t see any indication he’s talking about low thrust ion paths. I can see several indications he’s talking about normal high thrust burns, though. From page 13:

    “The time of flight from the Earth to the target point xc. This is needed
    to solve the Lambert problem once the position of the Earth is known.”

    Lambert’s methods are used to find elliptical paths from point A to B. Low thrust ion trajectories are spirals, not ellipses.

    Also from page 13:

    “Moreover, it is expected that the cost for V1 is equivalent to that of a standard Hohmann transfer as the target point is from an angular perspective, not too far from Mars.”

    V1 is the injection burn into the Mars transfer orbit which Belbruno and Toppotu describe as a Hohmann. The Hohman path is an ellipse that relies on high thrust burns.

    In this paper Belbruno has been talking about the ordinary chemical rocket paths to Mars. In which case it is possible to exploit the Oberth benefit and his ballistic capture flushes 1.3 km/s down the toilet.

    Can you give me a cite where Belbruno talks about ballistic Mars capture using ion rockets?

  • Hop David October 20, 2015, 12:18

    Michael wrote:
    “If you look at this Jupiter asteroid clip you can see some asteroids that approach Jupiter have very weird orbits.

    “http://star.arm.ac.uk/neos/JupiterResonance/indexflash.html ”

    You do realize the animation is in a rotating frame? A frame co-rotating with Jupiter and sun.

    If viewed from the usual frame, the Trojan tadpole orbits and the triangular Hilda orbits look like ordinary ellipses.

    Also the ITN exploits L1 and L2. The Trojans dwell in L4 and L5. The Hildas have aphelions at L4, L5 and L3. So these orbits have nothing to do the ITN routes described by Belbruno, Ross, Lo or Marsden.

  • Charlie October 21, 2015, 1:35

    In response to others who have, and on here concerning the capture process when the probe reaches the extreme limits of its path outward from the sun awaiting capture by Mars, led me to a question about the particular dynamics of this process. I have to say up front I have not read his paper in detail, so I am starting from a point of weakness, but I have indeed gave it a once over in a quick fashion so that I can kind of get a feel for what he is saying.

    That out of the way I wish to ask the question of Mister David, I suppose, as well as Michael and that is the question about reaching the most extreme point in the orbit as I just mentioned above. Specifically, I am speaking of the fact that while the probe does not, at its furthest point have a radial component of velocity outward it does in fact have a tangential component to its motion, which will carry the probe back toward the sunward direction. Usually this particular problem of establishing a ‘higher’ orbit, i.e. further from the sun that is, is usually taken care of. I increasing the tangential velocity so that you can maintain the larger orbital radius. At first glance in his paper I believe that he neglected to mention that. Does that lack importance here because of the fact that there is a general capture of the probe from the gravitational attraction the Mars, even if it’s extremely weak ?

    As regarding Mister David’s comment on the following:
    “Therefore there is a trade off – Hohmann trajectories with chemical/NTR engines, or some other approach for low thrust electric engines. It is the latter that Belbruno’s approach is for.”
    I had a question of whether or not in the practical use of these particular orbits to obtain certain objectives whether or not there might be TWO possible engines on board for particular maneuvers that might be needed at particular times. High thrust engines for close encounters, ion engines for needed maintainment of continuous thrust far long-term duration. Any thoughts here on this matters ?

  • Hop David October 21, 2015, 10:48

    Charlie, I believe you are beginning to grasp what I’ve been trying to convey.

    At aphelion (an orbit’s the furthest point from the sun), velocity is completely horizontal with no vertical component. Given a 1 A.U. by 1.52 A.U. ellipse, the aphelion horizontal velocity will be 21.5 km/s. Which is not enough to keep it at 1.52 A.U.. After reaching aphelion it will fall back to a 1 A.U. perihelion (perihelion is the orbit’s closest point to the sun).

    To remain at 1.52 A.U., the spaceship needs to be moving about 24 km/s. This is about the speed Mars travels. 24 – 21.5 = 2.5. Mars arrival Vinfinity is about 2.5 km/s. A Vinf of 2.5 km/s is much too high to permit ballistic capture.

    So Belbruno and Toppotu do a 2 km/s aphelion burn to enter a circular orbit just below Mars. When the spaceship catches up to Mars, ballistic capture is possible.

    Since arrival Mars arrival Vinf is 2.5 km/s, at first glance it looks like Belbruno’s 2 km/s aphelion circularization burn saves .5 km/s

    But a much greater savings can be realized by doing the burn deep in Mars gravity well and exploiting the Oberth benefit. Using the Oberth benefit, Mars capture can be achieved with as little as .7 km/s.

    Regarding ion/chemical hybrids — An ion engine needs a massive power source. See http://hopsblog-hop.blogspot.com/2015/05/the-need-for-better-alpha.html . Compared to ion, chemical has a much lower exhaust velocity and needs a huge mass of propellent for modest delta V. When the ion engine is burning, the chemical portion would be a huge parasitic mass. And vice versa, when the chemical engines are firing, the ion portion would be a huge parasitic mass.

    There is a way to enjoy the best of both chemical and ion engines, I believe. It entails infrastructure at EML2 (Earth Moon Lagrange 2) as well as infrastructure on Deimos and Phobos. I can go into more detail if you’re interested.

  • Charlie October 22, 2015, 1:51

    Mister David you have covered a considerable amount of ground in all the posts that you have put out and I’ve been able to read only just a small fraction of what you’ve written. While I have some agreement on what you been saying and you seem to feel that a high thrust vehicle at closest approach coupled with a low trust drive far general trajectory traversals over long distances might be the ideal solution. I wonder if you have considered the fact that the coupling of these two particular types of propulsion systems could result in a DECREASE of fuel savings in the overall scheme of things.

    It’s very easy to consider these things as a part and parcel of a solution to certain problems. However, oftentimes one technology in’s up costing another technology in a very heavy manner. To whit, a high thrust propulsion system would probably require a very large tankage for fuel, as well as a large type of engine which means that you would end up possibly losing a low energy savings as a result of the high ion engine operating at the rest of the trajectory path. Obviously, these things almost always require some type of trade-off and the very complexity of this scheme is is is in itself, something which would require a can considerable amount of computation to effectively ascertain whether or not this gives a REAL savings in energetics required for the path taken by the vehicle. This is almost completely unanswerable, since it would require considerable amount I’m sure of computer computations to make a final determination. In looking through his paper, he made a mention of the extensive amount of computations that must be done on a cell by cell basis to permit obtaining a certain objective as he slides into a orbit about the planet Mars. So these things are quite a bit up in the air simply because of the enormous number of required unknowns that must be computed and probably are very sensitive to initial conditions. At least that’s my off-the-cuff analysis of the situation.

  • Michael October 22, 2015, 2:31

    @Hop David October 21, 2015 at 10:48

    ‘Regarding ion/chemical hybrids — An ion engine needs a massive power source. See http://hopsblog-hop.blogspot.com/2015/05/the-need-for-better-alpha.html . Compared to ion, chemical has a much lower exhaust velocity and needs a huge mass of propellent for modest delta V. When the ion engine is burning, the chemical portion would be a huge parasitic mass. And vice versa, when the chemical engines are firing, the ion portion would be a huge parasitic mass.’

    There is a way for the hybrid design and that is to eject the ion engine into orbit around Mars before the chemical rocket fires to go for touch down. When the chemical rocket returns to orbit it picks the ion engine up again refuels it and goes on it way again thereby minimising excess mass.

    Have you managed to contacted Dr Belbruno to discuss your findings?

    http://www.edbelbruno.com/

  • Hop David October 22, 2015, 18:33

    Michael wrote: “Have you managed to contact Dr. Belbruno to discuss your findings?”

    Yes. I went to the link you posted, http://www.edbelbruno.com

    I mentioned to him that many people thought Hiten went from LEO to lunar capture using zero delta V. That they didn’t know Hiten had already achieved a high apogee after investing 3.1 km/s.

    I also mentioned to him his 2 km/s aphelion burns for Mars ballistic capture are *more* expensive than .7 Mars capture burns exploiting the Oberth effect.

    I also sent to link to my Potholes on the Interplanetary Super Highway blog entry.

    He replied that of course you must invest 3 km/s to get out of LEO. That his savings were only at the lunar capture part of the mission. And that my misreading of his papers indicates my blog’s not worth reading.

    I replied that I wasn’t talking about his papers but the misleading spin in pop sci articles and claims made by his fans.

    He said he had no issues with misleading pop sci coverage.

    I replied of course he didn’t, the misleading coverage casts him in a favorable light.

    So far Belbruno hasn’t commented on 2 km/s aphelion burns for Mars ballistic capture vs .7 km/s Mars capture burns using the Oberth effect.

  • Hop David October 22, 2015, 18:43

    Charlie wrote “To whit, a high thrust propulsion system would probably require a very large tankage for fuel, as well as a large type of engine which means that you would end up possibly losing a low energy savings as a result of the high ion engine operating at the rest of the trajectory path.”

    Which is more or less what I said. From my Oct. 21, 2015, 10:48 comment: “Regarding ion/chemical hybrids — … When the ion engine is burning, the chemical portion would be a huge parasitic mass. And vice versa, when the chemical engines are firing, the ion portion would be a huge parasitic mass.”

  • Charlie October 23, 2015, 0:22

    I wish to be certain with both Hop and Michael that I am not attempting to dispute or belittle anyone here on this website. I am not in a position to state that there was an argument between myself or anyone else, primarily because I merely jumped here in the middle of all this and didn’t read everything that was written here, word for word. I have at best a tenuous connection as I mentioned previously with this subject matter through reading probably almost a decade ago now an article that appeared in ‘Discover’ Science Magazine concerning a Minimal Transfer Path to the Moon by a Former JPL Scientist. My assumption here is that this fellow is also the same individual who was highlighted in the magazine.

    My only statement here that I can start of dwell on is the fact that I question as to whether or not these particular trajectory paths will yield as much of the savings as it is hoped that it would. From what I can gather from all these particular back and forth between the interested parties is that this method may be useful for unmanned cargo ships, but it would hold little or no interest for manned missions to any of the planets in the solar system. As I stated previously, there could be psychological barriers to people who are on long paths and longtime trajectories (unless of course were talking about some kind of animation process for passengers) and what is almost inescapable now from the standpoint of harming long-term presence in space by humans is the almost very, very difficult problem of shielding people from radiation. I’m aware that it was written a few months ago about a water shielded craft that would tend to use the hydrogen water to perform shielding. However, how good is that if you traded greater amounts of shielding far longer turned exposure in the vacuum of space simply because your voyage now takes a considerably greater amount of time because you wish to save fuel ? I’m always very much of the doubter on a lot of things because I have been exposed to this business for going on now six decades and a often take with a grain of salt what is said. It’s always good to be skeptical because we know that the good things will take care of themselves.

  • Michael October 23, 2015, 0:23

    @Hop David October 22, 2015 at 18:33

    ‘Michael wrote: “Have you managed to contact Dr. Belbruno to discuss your findings?”

    Yes. I went to the link you posted’

    At least it cleared up a few things.

    ‘I mentioned to him that many people thought Hiten went from LEO to lunar capture using zero delta V. That they didn’t know Hiten had already achieved a high apogee after investing 3.1 km/s. I also mentioned to him his 2 km/s aphelion burns for Mars ballistic capture are *more* expensive than .7 Mars capture burns exploiting the Oberth effect.

    He replied that of course you must invest 3 km/s to get out of LEO. That his savings were only at the lunar capture part of the mission. And that my misreading of his papers indicates my blog’s not worth reading.’

    He was a little harsh by not reading it, I found it quite informative, thanks for it.

    ‘I replied that I wasn’t talking about his papers but the misleading spin in pop sci articles and claims made by his fans. He said he had no issues with misleading pop sci coverage.

    I replied of course he didn’t, the misleading coverage casts him in a favorable light.’

    He can’t be expected to control what is said in the media can he now, look what happened to KIC 8462852, the media thinks it is a full blown Alien civilisation!

    ‘So far Belbruno hasn’t commented on 2 km/s aphelion burns for Mars ballistic capture vs .7 km/s Mars capture burns using the Oberth effect.’

    I believe that the Oberth effect is worthwhile with minimising time and energy of a chemical system. I have always believed he meet a low thrust engine which made use of the more efficient ion engine. Ion engines as you know can’t preform the deep gravity well burn as it does not have the power so he found a mathematical solution to make best use of the ion engine, its high efficiency. He has stated that it is best suited to missions that are not time sensitive, you must admit that the fuel/payload ratio is very good. Ion engines can be useful in getting out of the LEO (3km/s delta v) as well, much better than a chemical engine, just not as fast.

    He is a colourful character that is for sure.

  • Hop David October 24, 2015, 1:19

    Charlie wrote “From what I can gather from all these particular back and forth between the interested parties is that this method may be useful for unmanned cargo ships,”

    Not even that, in my opinion (in the case of Mars). In the case of delivering stuff to Earth Moon Lagrange 2, there is an ~.4 km/s savings for long duration cargo routes.

    “Ion engines as you know can’t preform the deep gravity well burn as it does not have the power so he found a mathematical solution to make best use of the ion engine, its high efficiency.”

    True low thrust ion engines have a hard time exploiting the Oberth effect.
    ll the stuff I’ve seen Belbruno talk about seems to be assuming high thrust, chemical engines. If you know of a paper where he discuss ion, please let me know.

    There are a wide range of scenarios possible with ion trajectories. I’m not sure what acceleration you’re thinking of, flight path angles, etc.

    If it’s a very small acceleration, the flight path will remain close to zero (that is, nearly horizontal. See http://space.stackexchange.com/questions/8420/general-guidelines-for-modeling-a-low-thrust-ion-spiral

    In this case the ship will approach Mars along a nearly parallel trajectory to Mars’ heliocentric orbit. The trajectory will be near parabolic with regard to Mars. Being in a lower orbit, the ship is moving faster than Mars. When the ship is coming up on Mars from behind, Mars will pull the ship forward, pulling it to a higher orbit.

    To achieve capture without sailing by, it seems to me the craft would have to match the smaller black orbit in this illustration: http://4.bp.blogspot.com/-rhZknNnNrC4/VSGaywiBB4I/AAAAAAAAA6Y/slTL6HRJSp8/s1600/SML1and2.jpg

    And it would have to match the orbit at the right time so that the ship reaches the aphelion in the neighborhood of Mars. (capture has to be in the right time as well as the right place.)

    The orbit pictured in the link above has a perihelion much higher than 1 A.U.. Since the ship has already invested enough delta V to achieve a near Mars orbit, the arrival Vinfinity is much lower than the usual 2.5 km/s. I would venture to say the ballistic capture gives .2 or .3 km/s savings.

    An ion engine can have a wide range of exhaust speeds. Let’s say 30 km/s.

    Exp(.3/30)-1 = ~.01. So maybe the Mars ballistic catch would enable a 1% increase in payload mass. In the case of ion engines that can’t enjoy an Oberth benefit.

  • Charlie October 24, 2015, 15:08

    As I am was saying before I believe from the scientific American article that the craft arrived ahead of the planet Mars, and that being the case there comes the difficulty in my mind of the fact that if the craft has reached the highest point in its orbit from Earth, then at that point, you must either fire the engines to retain the higher orbit (i.e. the orbital radius of Mars) or you must be close enough to Mars to provide gravitational capture.

    I heard that that idea of coming up behind Mars’s so as to chase the planet would be the route that would be LEAST successful because of the fact that the craft would undergo an unnecessary acceleration toward the planet, which would necessitate using fuel to slow it down for capture. I a noted that you stated that some combination of orbital motion would in unique set of circumstances provide capture, but I haven’t studied any of this.

    You keep mentioning here in your repeat replies that there would be an Oberth benefit; in a very brief number of words, what is it that you been trying to say in all your postings concerning the use of this particular close planet maneuver ? I’m afraid I have not been able to follow what it is you been trying to prove in your arguments, but I’m interested enough to ask if you could briefly give a synopsis of what it is that you been trying to convey to us on whatever idea you are arguing for or against. I’m afraid in all the flurry of what’s been said.I’ve lost the central idea as to what you are for or against concerning this scientist’s idea that has been bandied about here. Could you provide a brief summary of your ideas so that I could get a fix on what you’re talking about, please?

  • Charlie October 24, 2015, 15:13

    I just wanted to add that quoting a blizzard of numbers on various kilometers per second velocity changes doesn’t convey the central idea of what you’re trying to say for me that doesn’t clarify the central idea of your arguments. So in just words. I wanted to get your basic idea of what you trying to convey

  • Hop David October 24, 2015, 23:55

    “I heard that that idea of coming up behind Mars’s so as to chase the planet would be the route that would be LEAST successful because of the fact that the craft would undergo an unnecessary acceleration toward the planet, which would necessitate using fuel to slow it down for capture. ”

    Check this screen capture from Belbruno’s paper:
    http://3.bp.blogspot.com/-obvjUJo6Y_g/VSGinQLYPGI/AAAAAAAAA6o/1yRQSqIqRrE/s1600/BelbrunoMarsHohmann.png

    The burn to circularize at aphelion is done at Xc. Note that at the time of the burn Mars is ahead of Xc. Lower orbits move faster and after the burn at Xc, the space ship catches up with Mars.

    “…(snip)… in a very brief number of words, …(snip)”

    Just two numbers: 2 km/s and .7 km/s

    2 km/s is the burn Belbruno does at Xc.

    .7 km/s gets you Mars capture if you’re deep in Mars’ gravity well.

    Belbruno’s 2 km/s burn is greater than a .7 km/s capture burn done close to Mars. So far as delta V goes, Belbruno’s ballistic capture is very wasteful.

  • Hop David October 25, 2015, 0:04

    “I just wanted to add that quoting a blizzard of numbers on various kilometers per second velocity changes doesn’t convey the central idea of what you’re trying to say for me that doesn’t clarify the central idea of your arguments. So in just words. I wanted to get your basic idea of what you trying to convey”

    We’re talking about orbits and you don’t want to use numbers or kilometers per second?

    (scratching my head…)

    Belbruno’s orbit is a big St. Bernard dog turd. Ordinary capture is a tiny chihuahua turd. Big dog turds are nastier than little dog turds.

  • Charlie October 25, 2015, 16:58

    The request about your answers on your ideas concerning this man’s mathematical works was not I’m afraid answered here by your most recent reply. You obviously don’t feel that ‘Belbruno’s orbit ‘ is a very viable option from what you are telling me; do I have that correct ?

    When I was speaking about the use of numbers to justify your ideas. I was merely commenting to the fact that I don’t know the particulars behind what you base your numbers on. Therefore numbers to me at this point are rather useless as a means of comparison if I don’t understand the fundamental idea behind what you’re trying to convey. That’s why I was commenting to the fact that I don’t understand the use of mathematical values as a way to buttress your argument. I was looking rather at the broader picture of what you were trying to convey in all that you were saying. I hope that clarifies my position here. I take it that based upon what you have said that there is NO value whatsoever in his ideas. I’m not quite sure yet WHY they are completely useless to you because I can see some value if the conditions were right that might allow a gentle capture by a target body.

    But apparently you do feel otherwise; do you wish to explain further in words (not numbers, please) your objections to this particular orbital mechanism. That’s the real reason why I was asking for a bit more detailed WORDY answer rather than a large number of numbers.

  • Charlie October 25, 2015, 17:07

    “The burn to circularize at aphelion is done at Xc. Note that at the time of the burn Mars is ahead of Xc. Lower orbits move faster and after the burn at Xc, the space ship catches up with Mars.

    “…(snip)… in a very brief number of words, …(snip)”

    Just two numbers: 2 km/s and .7 km/s

    2 km/s is the burn Belbruno does at Xc.

    .7 km/s gets you Mars capture if you’re deep in Mars’ gravity well.

    Belbruno’s 2 km/s burn is greater than a .7 km/s capture burn done close to Mars. So far as delta V goes, Belbruno’s ballistic capture is very wasteful.”

    OK, got that. Again, I did not read the paper in detail so the numbers that you’ve given me while obviously have a magnitude difference doesn’t quite tell me where they came from or exactly the particulars behind them. But would you believe that perhaps a gravity assist very close to the planetary body Mars (are perhaps any other body that would be a target) MIGHT, JUST MIGHT present the fuel savings.

    I have to say that I did scan his paper, and there is a spiraling in mechanism that he uses to permit capture, but whether or not this is a savings in fuel I’m unable to state with any definitiveness. It only fair analysis would be to completely delve into his paper, and at this time, I’m not willing to do that.

  • Michael October 26, 2015, 10:13

    Ok, lets say he wastes 1.3km/s delta V not doing a Hoffman. AN ion drive is much more efficient than a chemical engine, where he needs extra delta V energy not using an Hoffman he lowered it (overall) getting there by the ion drive and therefore a much greater payload.

    ‘Belbruno’s orbit is a big St. Bernard dog turd. Ordinary capture is a tiny chihuahua turd. Big dog turds are nastier than little dog turds.’

    I would prefer if you used his title, Dr Belbruno, he appears to have achieved more than you academically.

  • Hop David October 26, 2015, 12:56

    Charlie, regarding word explanations of where the numbers come from…

    Belbruno’s paper mentions ~2 km/s burns at Xc.

    I say .7 km/s at Mars arrival can capture.

    You want an explanation of where my .7 km/s capture burn comes from? You will have to invest some effort. In case you’re inclined make that investment, I will give you a few strings to Google:
    vis viva equation
    hyperbolic orbit
    Oberth effect
    V infinity or Vinf

    Charlie, in my reply to Michael I will be using equations and numbers. The rest of this reply isn’t directed to you.

    Michael,
    Hohmann, not Hoffman. And up until the ballistic capture path reaches Mars, it is an ellipse. Not a spiral.

    The ballistic path to Mars capture is a nearly circular orbit just below Mars but grazing Mars’ Hill Sphere at aphelion. It’s almost all the way there. Whether you invest the delta V via chemical or ion engines, the delta V still must be invested.

    If there’s no Oberth benefit, the delta V between Mars and earth heliocentric orbits is in the neighborhood of 6 km/s. An ion spiral from a 1 A.U. circular orbit to the ballistic path will take maybe 5.7 km/s. Maybe a .3 km/s savings.

    The fraction of spacecraft that is devoted to propellent relies on an exponent: end mass/starting mass = e^(delta V/exhaust velocity) – 1.

    Let’s look at that exponent, delta V/exhaust velocity. An ion engine has enormous exhaust velocity. In my examples I’ve been using an exhaust velocity of 30 km/s. .3/30 is .01. Euler’s number e raised to the .01 power is about 1.01.

    So when you have this enormous exhaust velocity, .3 km/s is an inconsequential savings, on the order of 1 percent.

  • Michael October 26, 2015, 15:20

    @Hop

    Something is not right?

    ‘The fraction of spacecraft that is devoted to propellent relies on an exponent: end mass/starting mass = e^(delta V/exhaust velocity) – 1. ‘

    Shouldn’t it be

    m(fuel) = m(finish) (e^(Vd/Ve) – 1)

    So 0.3km/s @ 30km/s

    I get fuel required at 0.5 % of mass which is very good!

  • Charlie October 26, 2015, 16:42

    At this juncture here and willing to vacate the field and handed over to David and Michael for their respective viewpoints. Mister David I’m a familiar with the equations that you are speaking about. I’ve invested quite a bit of time in this subject matter and I am familiar with the applications of these ideas to orbital mechanics. I can only assume hear from what you said and what Michael has said that you are concerning yourselves in an argument about whether or not the Hohmann transfer path will yield a less appreciable investment of Delta V into a Mars orbit versus say the application of what we call here a ballistic capture.

    Once again, I haven’t read everyone’s arguments in detail because of the exhausting amount of effort he would be required to tease through the entire line of reasoning by the large number of contributors. I was somewhat astounded when you stated the following:

    “If there’s no Oberth benefit, the delta V between Mars and earth heliocentric orbits is in the neighborhood of 6 km/s. An ion spiral from a 1 A.U. circular orbit to the ballistic path will take maybe 5.7 km/s. Maybe a .3 km/s savings.”

    A “1 A.U. circular orbit to the ballistic path”, were you MEANING to say , ‘ 1 A.U. circular orbit ‘. A 1 A.U. circular orbit?! Are you suggesting that the vehicle to be captured by Mars should be 100,000,000 miles from the planet and spiral in ? Perhaps you made an error there. I don’t know. I thought that the professor who wrote the paper was talking about a distance somewhere in the ardor of 1,000,000 miles, that seems far more likely. Returning to the capture process. I suppose that David you mean that you would rather have a ion engine to perform a capture add a savings compared to igniting an engine at closest approach to the planet Mars – is that which your reasoning is about ? Again, I have to say that the merits of either approach would probably be highly computationally dependent and perhaps unanswerable by either person using just simple mathematics. Just a thought.

  • Hop David October 26, 2015, 23:56

    A few vocabulary words:

    Heliocentric – sun centered.
    Aphelion – A heliocentric orbit’s most distant point from the sun.
    Sun Mars Lagrange 1 (SML1) – A Lagrange neck between sun and Mars. It’s quite close to Mars, relatively speaking.

    For ion craft that can’t enjoy an Oberth benefit, we’re talking about travel from one heliocentric orbit to another. There are 3 heliocentric orbits in question here:

    1 A.U. circular heliocentric orbit. In other words, earth orbit. An object in circular orbit 1 A.U. from the sun moves about 30 kilometers/second with regard to the sun.

    1.52 A.U. circular heliocentric orbit. Mars orbit. An object this far from the sun moves about 24 km/s.

    Ignoring the Oberth effect, it takes 6 km/s to get from a 1 A.U. circular orbit to a 1.52 A.U. circular orbit.

    Now let us talk about a 3rd heliocentric orbit — the ballistic capture path. This path isn’t much different from Mars’ orbit. At aphelion this orbit passes through Sun Mars Lagrange (SML1). At aphelion it matches the velocity of SML1, thus allowing Mars capture.

    The ballistic capture orbit is very little different from Mars. It takes 5.7 km/s to go from Earth to the ballistic capture path.

    A pic comparing the scenarios:
    http://clowder.net/hop/TMI/BallisticPathToMars.jpg
    Left is labeling the 3 orbits. Middle is earth to Mars path. Right is earth to ballistic capture path.

    .3 km/s isn’t the delta V budget for getting from Mars to Earth. It’s the *savings*. And when you’re using ion engines with a 30 km/s exhaust velocity, that savings gives you an extra 1% extra payload mass.

  • Michael October 27, 2015, 14:37

    @Hop

    ‘0.3 km/s isn’t the delta V budget for getting from Mars to Earth. It’s the *savings*. And when you’re using ion engines with a 30 km/s exhaust velocity, that savings gives you an extra 1% extra payload mass.’

    I would not just switch the ion engine just for orbital insertion now would I!
    The ion engine would be used from start -LEO to LMO, that works out to be a BIG mass saving meaning more payload because the engine is much more efficient than a chemical one.

  • Hop David October 27, 2015, 15:42

    Michael,Don’t credit Belbruno with any advantages Ion engines confer. He did not invent ion engines.

    The mass savings comes from an ion engine’s high exhaust velocity. Not a lower delta V route exploiting the weak stability boundaries from SML1.

    An ion engine route not using ballistic capture is 6 km/s (from a 1 A.U. circular heliocentric orbit to a 1.52 A.U. heliocentric orbit)

    An ion engine route using ballistic capture is 5.7 km/s (from a 1 A.U. circular heliocentric orbit to the ballistic capture path)

    The savings is .3 km/s. When your exhaust velocity is 30 km/s, a .3 km/s savings is practically nothing.