Gravitational Lensing with Planets

by Paul Gilster on April 26, 2016

As we’ve been talking about the Sun’s gravitational focus, it’s interesting to reflect on the history of its study. Albert Einstein’s thinking about gravitational lensing in astronomy was explicitly addressed in a 1936 paper, but it wasn’t until 1964 that Stanford’s Sydney Liebes produced the mathematics behind lensing at the largest scale, working with the lensing caused by a galaxy between the Earth and a distant quasar. Dennis Walsh, a British astronomer, found the first actual quasar ‘image’ produced in this way back in 1978, with Von Eshleman’s study of the Sun’s lensing the following year including the idea of sending a spacecraft to 550 AU.

SETI was on Eshleman’s mind, for he pondered what could be done at the 21 cm wavelength, the SETI ‘waterhole,’ and so did Frank Drake, who presented a paper on the concept in 1987. If you have a good academic library near you, its holdings of the Journal of the British Interplanetary Society for 1994 will include the proceedings of the Conference on Space Missions and Astrodynamics that Claudio Maccone organized two years earlier. FOCAL was now being considered, though in a mission then called SETISAIL, even though SETI would be only one aspect of its scientific investigations.

FOCAL Beyond Stars

Finding ways to exploit the gravitational lens of the Sun forces us to take into account the Sun’s corona, a problem both Eshleman (Stanford) and Slava Turyshev (JPL) soon addressed. We’d like to get a spacecraft not just to 550 AU, but well beyond it to avoid coronal distortion, taking advantage of the fact that we are not dealing with a focal point but a focal line. Let me quote one of Claudio Maccone’s papers on this (citation at the end of this post):

…a simple, but very important consequence of the above discussion is that all points on the straight line beyond this minimal focal distance are foci too, because the light rays passing by the Sun further than the minimum distance have smaller deflection angles and thus come together at an even greater distance from the Sun.

Thus we have the ability to move well beyond 550 AU, and in fact have no choice but to do so. The Sun’s corona creates what Maccone calls a ‘diverging lens effect’ and opposes the converging effect we associate with a gravitational lens. The result is that the minimum distance the FOCAL craft must reach (here I’m paraphrasing the paper) is higher for lower frequencies (of the source electromagnetic waves crossing the Solar corona) and lower for higher frequencies. Thus at 500 GHz, the focus is about 650 AU. At 160 GHz, the focus is at 763 AU.

But are we limited to using the Sun and, if we build radio ‘bridges’ as discussed yesterday, nearby stars as gravitational lenses? It turns out that planets too can be used for this purpose. In his 2011 study of this idea, which appeared in Acta Astronautica, Maccone produces the needed equations, noting that the ratio of a planet’s radius squared to its mass lets us calculate the distance a spacecraft must reach to take advantage of planetary lensing. From that we have defined what he calls the planet’s focal sphere.

fig01

Image: The complete BELT of focal spheres between 550 and 17,000 AU from the Sun, as created by the gravitational lensing effect of the sun and all planets, here shown to scale. The discovery of this belt of focal spheres is the main result put forward in this paper, together with the computation of the relevant antenna gains. Credit: C. Maccone.

Lensing Moves into the Oort Cloud

The figure above may contain a few surprises. We would expect Jupiter to top the list of planetary lenses, and indeed, its focal sphere is the next out from the Sun at 6100 AU. That’s a useful number to keep in mind, because we may discover that the Sun’s coronal effects are simply too powerful to overcome to produce the needed images. If so, we have a target halfway out to the inner Oort Cloud that we can also use to study the lensing phenomenon.

Beyond this, notice that Neptune, which has a high ratio between the square of its radius and its mass, comes next, at 13,525 AU. Saturn’s focal sphere is 14,425 AU out, and next we find our own Earth, with a focal sphere at 15,375 AU. Our planet makes a better lensing candidate than Uranus because it is the body with the highest density (ratio of mass to volume) in the Solar System. Maccone likes to point out that because we know the Earth’s surface and atmosphere better than that of any other planet, a FOCAL mission using the Earth as a lens would begin with a significant advantage as we try to untangle a lensed image of a distant object.

How would we take advantage of these planetary focal spheres? They extend all the way out to 17,000 AU in the case of Venus. As the figure makes clear, a fast spacecraft departing the Solar System could examine any of them in turn, beginning with observations as the Sun’s coronal effects begin to subside. Noting that a spacecraft enroute to Alpha Centauri would cross all these focal spheres, Maccone muses on the results of such a crossing:

First of all, while the Sun does not move in the Sun-centered reference frame of the Solar system, all the planets do move. This means that they actually sweep a certain area of the sky, as seen from the spacecraft, so that a spacecraft enjoys a sort of moving magnifying lens. How many extrasolar planets would fall inside this moving magnifying lens? Well, we don’t know nowadays, of course, but the over 400 exoplanets found to date [the paper appeared in 2011] are a neat promise that many more such exoplanets could be detected anew by a suitably equipped spacecraft crossing the distances between 550 and 17,000 AU from the Sun thanks to the gravitational lenses of the planets.

Such discoveries would be serendipitous, to say the least, as our Alpha Centauri mission would just be seeing what happened to be in line with the planet being studied as it departed the system. But having Jupiter at 6100 AU and the Earth at 15,375 AU does offer us useful targets for experimentation with the technologies we’ll need to tease images out of a focal sphere encounter. One of the big if’s of Breakthrough Starshot is the construction of operation of the phased laser array. But if it is built and we can achieve velocities of a significant fraction of c, then dedicated missions to explore planetary lensing would be sensible.

Clearly the Sun is our first choice as a gravitational lens not just because of the relative proximity of its minimum focal distance (550 AU) but because the effective gain of the Sun is so much higher than that of Jupiter, and far higher than the low gain we could expect to achieve with the Earth as a gravitational lensing body. Maccone calculates numerical values for the gain at frequencies ranging from the hydrogen line up to the CMB peak at 160 GHz, evaluating each of these for the Sun’s gravitational lens as well as the focal spheres of the various planets. If we want to work with the lensing potential of planets, we’ll need major advances in antenna and imaging technologies to overcome the weak signatures the planets provide.

The paper is Maccone, “A New Belt Beyond Kuiper’s: A Belt of Focal Spheres Between 550 and 17,000 AU for SETI and Science,” Acta Astronautica Vol. 69, Issues 11-12 (December 2011), pp. 939-948 (abstract).

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Alex Tolley April 26, 2016 at 13:47

My calculations suggest that Ceres would have a focal point over 9 ly away.
So it is conceivable that a planet in another star system could use one of the objects in our solar system as a gravitational lens. Which means that theoretically we could do the same, so that we could image a distant star’s solar system using a small wordlet of a star between us and the target. No need to travel long distances, just do the same as we do with galaxies, but on a much finer scale. Theoretically. :)

Paul Gilster April 26, 2016 at 16:54

Wow, talk about doubling down on an idea :-)

Alex Tolley April 26, 2016 at 17:19

While gravitational lensing may work with the sun, what we should bear in mind is that the sun may also distort the planetary lensing should its line of sight start to get close to the light being lensed by the planets. The smaller the wordlet, the more likely the sun will distort the rays, complicating the imaging even further.

However, for data transmission I like the gravity lensing idea a lot, pending experts in this area not throwing up a lot of complications in the communication domain.

Rafik Bourne April 26, 2016 at 18:24

In theory an exoplanet in another solar system may make a good lens – but we still have the problem of glare from the parent star. A better option would be to use a free floating planet/cool brown dwarf as a gravitational lens.

Free floating cool brown dwarfs offer the best near term option for testing gravitational lensing as they have a density greater than Jupiter, for higher magnification gain, but relatively low emissions compared to stars.
WISE 1828+2650 would be a good candidate, 47 light years away, as it emits almost no light at visible wavelengths.
Another candidate would be WISE 0855-0714, at just 7 light years.

A cube-sat scope, dedicated to observing a free floating cool brown dwarf, should be a consideration in testing the gravitational lens concept before we start sending out Starchips.

Tom Pliska April 27, 2016 at 12:53

Brown dwarfs are cool, but there are some closer known white dwarfs. Has anyone done the maths on focal distance around Van Maanen 2 or Sirius B? Though…what kind of corona does a white dwarf have?

Michael May 1, 2016 at 14:53

It should start at around 10 million km for Sirius B, but due to the velocity at which you would be required to orbit it at that distance the image may be highly blurred. As for the corona there should be plenty of ions around due to the temperature to create distortion but a lot calmer and predictable than our Suns.

Mark Zambelli May 6, 2016 at 6:04

Orbiting probably won’t do as the constantly changing image will pass across the detector stupendously fast and there are huge oscillations from offsetting every few tens of metres! Perhaps a sacrificial star-diving scope would do… it could start imaging much further out and fall along a single focal-line-trajectory.

If we can devise a “neutrino-scope” and get it out to between Saturn and Uranus then I wonder what we’d see (the Sun’s core puts that focus a lot nearer). We’ll have electromagnetic FOCAL missions long before that tech arrives though.

Michael May 6, 2016 at 15:29

mmm…as we said the image will be highly blurred, but perhaps two orbiting telescopes, in opposite directions, could cancel out -for a brief moment- the blurring effect. All is not lost however, been a focal line rather than a point the image will be formed along out to infinity with little corona effects at further distances out.

Michael April 27, 2016 at 0:43

An issue with this concept is that although the magnification has gone up due to the effect the light gathering power has dropped substantially. High end brown dwarfs that are cold offer good magnifier properties due to their high densities, red dwarfs as well, I believe PC’s focus line starts at 88 AU and thus could allow communication advantages.

Eniac April 27, 2016 at 13:55

The problem here would be resolving the Einstein Ring. The ring would be extremely small at that distance, and would require an enormous telescope to see. All that for just one pixel of data.

Alex Tolley April 27, 2016 at 15:09

As I said: “theoretically”. I agree that other methods are probably better for imaging. But for data transmission power?

I can’t remember the name of the technique (“ghost imaging”?) where a single pixel detector and a changing random pixel mask can recreate an image from serial pixel intensities. I have simulated it with software and it does work, although the number of pixel values is often larger than the number of pixels in the image mask. It strikes me that perhaps this might work for the gravitational lens telescope for objects that do not move fast, e.g. a star. Planets may be more of a problem as they both rotate and move. It all depends on how fast you can create the serial pixel images.
I’m sure there are many other techniques.

Speaking of imaging, I see there is a new technique to increase resolution of features from multiple images.
Mars’ surface revealed in unprecedented detail

I wonder if there are enough images of Titan (latest post) to improve it’s surface imagery?

Eniac April 27, 2016 at 23:02

Yes, that random pixel mask technique is interesting, but maybe not useful here. For gravitational imaging, a mechanical helical scan seems the better method.

As I recall, for nearby stars, the image is around 1000 times smaller than the original. That means a planet could be scanned quite effectively using a ~10 km rotating tether with some number (including just one) of movable telescopes along its length. Each telescope performs a helical scan as it moves, slowly, up and down the tether. If coordinated properly, the paths interlace into a nice circular picture of the whole planet.

With resolution of the Einstein Ring perimeter and some computational tomography, you can even get more than one pixel’s worth of information from each telescope, as suggested by Landis. This will most likely be mandatory, to overcome the degenerate point spread function that Landis calls focal blur.

Planetary movement is not that much of a problem, it takes only modest acceleration to track it, easily achieved with an ion drive. Not at gram-scale, though. This would need to be a sizable spacecraft, with lots of propellant and a nuclear reactor for power.

Geoffrey A. Landis April 30, 2016 at 11:11

The magnification (or amplification) achieved by a gravitational lens is directly proportional to the angular diameter of the disk of the object that is bending the light.
The angular diameter of Ceres, viewed from nine light years away, is so absurdly small that, while it “theoretically” is a gravitational lens, in practice it is a gravitational lens with no net gain.

Alex Tolley April 30, 2016 at 13:22

Very good point and clearly explains one limitation of using gravitational lensing.
Does this impact the use of lensing to increase relative photon intensity compared to a beam, allowing communication? IOW, does the extended focal line reduce the value of that too, making it a wash compared with other techniques, or is it still a good technique, possibly with small bodies?

Michael May 1, 2016 at 6:03

Is it possible to use an axicon to reform the ring image reducing distortion? We may also have to use a star shade around the edges and in the centre to reduce distortion from the corona but it can be adjustable to suit.

‘R. Schuhart April 26, 2016 at 12:37

http://www.edmundoptics.com/resources/application-notes/optics/an-in-depth-look-at-axicons/

Montie April 26, 2016 at 15:54

So with the Starshot proposal this 550 AU telescope become possible.

Paul Gilster April 26, 2016 at 16:53

We can’t assume that, I’m afraid. There are just too many issues to be resolved. But it’s true that if we were able to build the laser infrastructure for Starshot and move payloads at this velocity, a lot of FOCAL possibilities could be tested.

FrankH April 26, 2016 at 16:12

Using the Sun as a lens produces some serious chromatic aberration! Maybe putting a large convex, active mirror at 550 – 1000 AU could send the focal point back into the inner solar system.

Eniac April 27, 2016 at 15:38

Sure, all it would take is an optically perfect mirror half the diameter of the sun. Solved in principle, what remains is merely an engineering problem. ;-)

Andrew Palfreyman April 27, 2016 at 1:27

I hope the admirable Dr. Maccone has something good to say in response to Dr. Landis’s paper. Or rather, something good to say about grav imaging! He certainly has the ball in his court on this one.

Javier Garcia April 27, 2016 at 8:15

There are a number of reasons for traveling to the stars. But all this enormous efford should have appropiate media coverage. Otherway it wouldnt last.

On the other hand, and I might be naif on this, but I honestly believe the world is running out of good reasons to continue. It is reaching the end of the journey.

We need to buil new “religions”. New ideas full of good purposes and a little bit of fantasy, chalenging adventures that the young ones would be loving to pursuit.

Otherway what kind of world this would be in 100 years time when everything will be already done, down here at Earth?

Jonathan Quinn April 27, 2016 at 15:41

Would it be possible to use Jupiter as a 2nd lens to reduce the focal point distance of the Sun? Or perhaps a number of planets in conjunction with the Sun?

Andrew Palfreyman April 28, 2016 at 2:53

So long as you’re content to restrict yourself to the Sun-Jupiter line, sure. But this isn’t generally useful.

SteveB April 29, 2016 at 11:44

I have sometimes wondered about the possibility of using the Earth’s atmosphere to focus light. I would expect a very blurry focus, but a lot closer than 15,375 AU. Can any useful information be gained this way?

Michael April 30, 2016 at 12:06

Unlikely and as you have stated the image will be distorted and no useful spectroscopy could attained due to the chemical complexity of the Earths atmosphere.

SteveB May 1, 2016 at 15:13

Thanks for your response Michael. It has clarified a number of things in my mind.

Since ground based telescopes do useful spectroscopy on light that passes through the atmosphere, I think the chemical complexity objection doesn’t hold.

The atmosphere intercepts a lot more light than any telescope can directly, but does a poor job of concentrating it on any point behind the Earth. The question is: Will a telescope stationed at behind the Earth collect more light from an object than if it simply looked at that object directly?

Michael May 2, 2016 at 2:08

When we look out in to space straight up there is a lot less air mass than if the light was bent through many hundreds of ‘masses’ of air so spectroscopy would be limited. If the Earth had no atmosphere we would see less than with a bending atmosphere from behind the Earth, but as discussed earlier it will be highly distorted.

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