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Relativistic Effects on Solar Sails

It’s a long way from the back of an envelope to a deployed spacecraft, which is one reason why scientists write papers in journals and gather at conferences. Such venues are where ideas get shaken out, problems identified and solutions proposed. We sometimes talk about realistic technologies like solar sails as if all that remained were to build them, but as Roman Kezerashvili demonstrated at the recent conference in Aosta, there is a range of problems that we are only beginning to consider.

Kezerashvili (City University of New York), working with colleague Justin Vazquez-Poritz, has identified a significant area of concern for mission concepts that pass close by the Sun. Often called ‘Sundiver’ missions (a Gregory Benford coinage, if memory serves), these sails would be so constructed as to survive an extremely close solar pass. Perhaps protected behind an occulter until periherlion, the sail would then be unfurled to receive the full force of the Sun’s photons at extremely close range.

How close? No previous mission has ventured closer than 0.3 AU to the Sun. But Kezerashvili points to one recent study that showed deploying a sail at 0.1 AU could produce accelerations sufficient to reach 200 AU in 2.5 years, the Sun’s gravitational focus at 550 AU in 6.5 years, and the inner Oort Cloud at 2550 AU in thirty years.

Close passes work. We need highly reflective, low density sail materials that are extremely heat tolerant to withstand the conditions they will encounter, but there is no reason to think these are unattainable in the future. Kezerashvili believes that perihelion distances may be reduced as low as 0.05 AU – 0.1 AU as we develop the needed materials.


Image: From the recent Aosta conference, a snapshot taken in the Italian Alps. Left to right: Giovanni Vulpetti, Roman Kezerashvili, and Justin Vazquez-Poritz. Photograph courtesy of Roman Kezerashvili.

All of which is good news, but the problem that now emerges is one of navigation. Any time we venture so close to the Sun, we have to take account of General Relativity. The sail may be in close proximity to the Sun for only a short period of time, but this is also the period when the outward acceleration due to Solar radiation pressure is the greatest. The results of applying these calculations are stunning — our sail could be taken well off-course.

From the paper:

“…we consider a number of general relativistic effects on the escape trajectories of solar sails. For missions as far as 2,550 AU, these effects can deflect a sail by as much as one million kilometers. We distinguish between the effects of spacetime curvature and special relativistic kinematic effects. We also find that frame dragging due to the slow rotation of the Sun can deflect a solar sail by more than one thousand kilometers.”

For deep space purposes, this strikes me as the most significant result to come out of the Aosta sessions. Without the kind of trenchant analysis Kezerashvili and Vazques-Poritz offered up in two papers at the conference, a seemingly workable mission concept would have lacked a fundamental navigation solution. The duo examined as well more exotic factors such as the slowing of the passage of time near the Sun due to relativistic effects. An observer on Earth at 1 AU measures about 31 more seconds per year than an observer at 0.01 AU, leading to a redshift in the wavelength of sunlight whose effects on the optimum thickness of the sail turn out to be negligible.

Some relativistic effects are minor, then, but some are not. Indeed, we see the effects of General Relativity play out in terms of crusing velocity. Kezerashvili and Vazques-Poritz look at the motion of a sail from 0.01 AU outwards, one whose cruising velocity is 480 kilometers per second. With the effects of curved spacetime in mind, the radial component of its velocity turns out to be faster than what we would expect under a purely Newtonian approximation by about 1.65 meters per second. This is a difference, the authors note, that “…remains constant throughout most of the voyage and therefore has a cumulative effect.”

General Relativity, then, is a significant consideration in making a Sundiver mission a reality. Spacetime curvature can cause large deflections depending on our targets, but in any scenario, precision demands a full accounting of each of these variables. Not long ago we discussed the options for a fast mission to Haumea, an orbiter that was also discussed at Aosta. Obviously, the effects Kezerashvili and Vazques-Poritz studied would bear upon the navigational inputs for any sail mission to Haumea using a close solar pass.

The paper is R. Ya. Kezerashvili and J. F. Vazques-Poritz, “Escape Trajectories of Solar Sails and General Relativity,” (accepted for publication at Physics Letters Bpreprint available). Orbital issues relating General Relativity to solar probes are discussed in the same authors’ “Solar Radiation Pressure and Deviations from Keplerian Orbits,” Physics Letters B 675 (2009), pp. 18-21 (abstract).


Comments on this entry are closed.

  • tacitus September 23, 2009, 14:15

    Of course, having to take General Relativity into account when navigating a spacecraft is nothing new. The Mercury-bound Messenger mission routinely includes the effects of GR in its trajectory calculations:


    While the effects are minor compared with a sun-diver mission, they accumulate over the years of the mission, and are large enough disrupt the precision flyby imaging of Mercury if not taken into account.

  • Carl September 23, 2009, 15:10

    At deployment of the sail, instruments could acquire reference objects and begin the course corrections. The first such Sundiver mission would have to pioneer the relativistic effects of its close solar flight. The on-board navigation would have to continuously deal with the deviations until ‘regular’ astrogation techniques work reliably. These data might be useful for subsequent Sundiver missions.

    This reminded me of Isaac Asimov’s novel Nemesis. It dealt with a light-velocity drive which accumulated significant flight path error, which the characters had to quickly learn to take into account.

  • NS September 23, 2009, 17:38

    Presumably missions to the heliopause/near interstellar space or the Oort Cloud would be somewhat error-tolerant? I hope I live to see one of those — the currently proposed Innovative Interstellar Explorer mission wouldn’t get out to 200 a.u. until I’m 88 years old. Just sayin’…

  • Carl September 23, 2009, 18:22

    MESSENGER was able to accurately maneuver by solar radiation pressure while adjusting the angle of its panel arrays: http://messenger.jhuapl.edu/news_room/details.php?id=102 The technique works predictably at Mercury’s distance from the sun. A small probe could be engineered for a near-sun flyby which could test conditions deeper in the gravity well. Smaller panels, not a full solar sail, designed to steer the craft by the intense environment would be sufficient to yield data for subsequent attempts. Such a mission would test the concept while investigating sun-space. There is Solar Probe+ intended to investigate the sun close-up; if its funding is intact its movements can be interesting: http://science.nasa.gov/headlines/y2008/10jun_solarprobe.htm?list1065474

  • NS September 24, 2009, 1:46

    An amazing mission, Carl. Looks like it’s still a go:


  • Tulse September 24, 2009, 9:59

    Is there somewhere that discusses the sundiver concept in more detail? Googling doesn’t seem to give much on that approach specifically.

  • Paul Titze September 24, 2009, 10:32
  • Administrator September 24, 2009, 13:02

    Tulse writes:

    Is there somewhere that discusses the sundiver concept in more detail? Googling doesn’t seem to give much on that approach specifically.

    Here are a couple of articles from the archives that may be of use:


    But first, do this one:


    And be aware of the Matloff, Johnson and Vulpetti volume Solar Sails: A New Approach to Interplanetary Travel, which gets into it a bit. That one has made its way into numerous libraries by now and should be available. As I recall, Greg Matloff also discusses sundiver missions in his Deep Space Probes book.

  • inquire September 25, 2009, 1:43

    If navigation is an issue, why assume that there is only one form of propulsion? If we have the technological capability to construct a solar sail and payload that can survive such a close approach to the sun, why not simply treat the solar-sail propulsion as the ‘first stage’ which would be jettisoned when it’s effectiveness is sufficiently diminished? At which point the ‘second stage’ ion or VASIMIR propulsion would kick in to accelerate/decelerate/navigate the payload to the appropriate location. Being off course is hardly a problem if you have the means for effective course correction.

  • Frank Taylor September 25, 2009, 7:20

    As an earth-based ocean sailor the concept of calculating relativistic effects to sailing is just awesome! The whole idea of interstellar travel by sail has always seemed the ultimate blend of ancient (on human scales) mariner history, and futuristic technological achievement. By far one of my favorite notions going from science fiction to future science fact. Relativistic effects to sailing?! Cool!

  • wazza September 25, 2009, 10:00

    Sundiver is the name of a David Brin novel (the craft in question used a refrigerating laser rather than a solar sail, which had the added effect of making the inside of the craft a shirtsleeve environment).

  • Tulse September 25, 2009, 10:54

    Being off course is hardly a problem if you have the means for effective course correction.

    It is if you’re moving at relativistic speeds, and have to rely on a much less effective propulsion system for course correction. If you’re shot out of a cannon, you don’t want to have to rely on a can of compressed air to make trajectory adjustments.

  • Duncan Ivry September 26, 2009, 10:51

    Frank Taylor: “As an earth-based ocean sailor the concept of calculating relativistic effects to sailing is just awesome!”

    We experience the same relativistic effects here around earth regularly every day.

    Earth-based ocean sailors — and other people — can use, and many already do use, the Global Positioning System (GPS). Because its sattelites move rather close to earth, their movement is influenced in such a way by earth’s gravity, that relativistic effects have to be taken into account, in order to calculate positions on earth, based on GPS data, correctly. Space is pulled around by a rotating mass, the nearer the more. And be aware of gravity being a geometrical feature of space-time since Einstein.

  • Administrator September 26, 2009, 13:53

    Frank Taylor wrote:

    As an earth-based ocean sailor the concept of calculating relativistic effects to sailing is just awesome! The whole idea of interstellar travel by sail has always seemed the ultimate blend of ancient (on human scales) mariner history, and futuristic technological achievement.

    I’m with you, Frank, but I haven’t done the amount of sailing you have, that’s for sure. Travel by sail does seem to resonate with our history and touch a deep, almost mythic chord with our experience. I was amazed to see how much of an effect General Relativity would have at ‘Sundiver’ mission distances. We’ll have more on this topic in the not so distant future.

  • tom January 23, 2013, 21:36

    Interesting. How much ‘acceleration’ could be attained by such maneuvers? If would be funny if the Sun was key to interstellar ‘relativistic’ voyages? I don’t actually believe you can go into the years 1966-1968 via this technique (a.k.a Star Trek ‘The Lightspeed Breakaway’)
    Could you actually build a craft that could Contour below the ‘Photoshpere’ of our Sun & slingshot into deepspace at 90% or more of ‘lightspeed’?
    If you had deadly accuracy, you could ‘bankshot’ around the Sun and 10 minutes later ‘devastate’ an enemy on the daylight side of Earth?
    I’m no ‘warhawk’, but Strategic Weapons Programs involving hypervelocity ‘kinetic kill’ units aren’t that hard to fund?