Gravity Solar Lensing Telescope

[guest70615]

Hi All,

you may have heard about the concept to use light rays bending around the sun due to gravity, to create a giant telescope. This gives a resolution of about 25 km/pixel for exoplanets.

I've had a brief look into the papers and online presentations but no one mentions that sun is not a perfect homogeneous mass. For example the surface is boiling with cells of diameters of thousands of kilometers. This causes time dependant mass distribution. Which causes an additional blur in the image.

What do you guys think, will this blur be bigger than 25 km/pixel?

[laszlo]

We need math to answer that question, for which we need references to the papers and presentations. While we could do a literature search ourselves, is there any chance that we could take advantage of your work and not have to repeat it all ourselves? That is, can you post your links to the papers and presentations that you've found, sort of like a bibliography? Also, at what distance to the exoplanet would we get 25 km/pixel?

That said, my minimally mathematical reasoning by analogy says that it won't be an insoluble problem, if  a problem at all. In spite of its coronal mass ejections and granulations, the Sun is very stable in mass and mass distribution. The convective cells that make up the granulations are a constant phenomenon that is more or less evenly distributed over the entire surface of the Sun. While the material inside the cells is in motion, it's a constant motion like water in a pipeline and none of the material actually leaves the Sun. Since the cells are Bénard cells, each cell has pretty much the same mass distribution as its neighbor so the overall mass distribution is more or less homogeneous. The convective zone is also a low density zone at the outer portion of the Sun (0.7 solar radii and out). Any instability would be swamped by the mass in the much denser lower layers (some 3 to 5 orders of magnitude denser).

Coronal mass ejections and the loss of mass to the fusion reactions are all at least 20 orders of magnitude less than the Sun's mass, so they certainly won't affect individual observations.

As a result, and here is where those references would be handy, I believe that it's valid to treat the Sun as a homogeneous spherical mass because the individual variations are so small and so widespread over the volume of the Sun that they average out. If things like solar seismic waves, granulation, supergranulation, etc. do cause the Sun's mass to wobble enough to affect the telescope, because the Sun is so large it would be a slow instability. Granules last 8 to 20 minutes, seismic waves take 2 to 20 hours to transit the sun, etc. So any blur would be temporally comparable to atmospheric blurring on earth with an optical telescope which can be handled with image stacking and other techniques.

[guest70615]

I first heard about the idea here: https://m.youtube.com/watch?v=4d0EGIt1SPc&t=889s&pp=ygUoUmVhbCBwb3NpYmlsaXR5IG9mIG1hcHB1bmcgYWxpZW4gcGxhbmV0cw%3D%3D

This is the paper mentioned in the video: https://arxiv.org/abs/2206.03037

And one presentation by different people: https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://ntrs.nasa.gov/api/citations/20180003479/downloads/20180003479.pdf&ved=2ahUKEwjdvpPnkcuBAxWNgf0HHfknAh4QFnoECBgQAQ&usg=AOvVaw3GO_6dDI3kBTxKnoYb2gH9

[whitelancer64]

Hi All,

you may have heard about the concept to use light rays bending around the sun due to gravity, to create a giant telescope. This gives a resolution of about 25 km/pixel for exoplanets.

I've had a brief look into the papers and online presentations but no one mentions that sun is not a perfect homogeneous mass. For example the surface is boiling with cells of diameters of thousands of kilometers. This causes time dependant mass distribution. Which causes an additional blur in the image.

What do you guys think, will this blur be bigger than 25 km/pixel?

The nearest focal point of the solar gravitational lens is about 542 AU from the Sun. At that distance, you don't really need to worry about very small surface mass disruptions, it all averages out.

[guest70615]

Thanks for the ideas!

So this website:  https://solarscience.msfc.nasa.gov/interior.shtml says the convective zone is about 200 000 km deep. Those huge convection rolls have different densities in upward compared to downward moving mass. This does not look good.

I thought of asking the paper authors ... but I would not be able to handle the rejection if they do not reply 

[leovinus]

Hi All,

you may have heard about the concept to use light rays bending around the sun due to gravity, to create a giant telescope. This gives a resolution of about 25 km/pixel for exoplanets.

I've had a brief look into the papers and online presentations but no one mentions that sun is not a perfect homogeneous mass. For example the surface is boiling with cells of diameters of thousands of kilometers. This causes time dependant mass distribution. Which causes an additional blur in the image.

What do you guys think, will this blur be bigger than 25 km/pixel?

Not sure, but there was a long, similar discussion in a previous thread Mission to the Gravitational Focus which might have some answers and more background?

[guest70615]

Thanks, though they did not mention the effect of sun's internal structure.

[TheRadicalModerate]

Just FYI, we got into a moderately detailed discussion about SGL on the Starship Extrasolar Missions thread.  IIRC, there are a few papers cited if you're willing to plow through stuff.¹

Note that the farther away you are from the Sun, the light brought into the Einstein ring originates from an angular distance farther away from the Sun's surface.  So if you go farther away than 542 AU, the image will eventually clear the solar atmosphere.  That doesn't necessarily mean that inhomogeneities in the Sun's mass distribution won't cause problems, but my guess is that they'll be less and less severe the farther out you go.

_______________
¹Especially see Landis and Turyshev et al.  The Turyshev paper goes into moderately gory detail on how to de-convolve the signal carried in the Einstein Ring.  Nasty math.

[VSECOTSPE]

Main issues and approaches:

https://arxiv.org/pdf/1604.06351.pdf

[mikelepage]

From what I read of this previously, I thought that a solar gravitational lens wasn't going to be terribly useful, but creating a useful gravity lensing telescope is one of the many outcomes if the Planet 9 primordial black hole hypothesis were true. 

Planet 9 is still predicted to have a semi-major axis of 400-800 AU, so no getting around having to send a craft out that far. But any craft sent there could use an Oberth maneuver to brake into an orbit with relatively small amounts of propellant, and the telescope would be "point-able" in ways that a solar gravitational lens telescope wouldn't be.

Disclaimer: not my field, but attempting BoE math with formulae from here:

Einstein ring radial angle in radians = r/F = (4GM/c2)^1/2 * F^(-1/2)
Assuming a 10 Earth mass black hole (Schwarzschild Radius of ~89mm), the Einstein radius is at 5.6 microradians at 1,000,000km (or 18 microradians at 100,000km).
If I'm reading this right, magnification of the light from a target is proportional to 4 x the Einstein radius / angular diameter of the source.
So for an 12,742km-wide, Earth-sized exoplanet 10 ly away (1.35 * 10^-7 microradians), the light magnification would be roughly 4.1* 10^7 at 1,000,000km from the PBH.

One of the problems the second paper above points out with the solar gravitational lens is that you have to travel so far from the sun for light from the target to be visible above the sun's surface. At >550 AU - the focal length is too long to be useful. Not only is it impractical to point at more than one object, but at 10 ly away, an Earth-sized exoplanet creates an image of a size proportional to f/d. If the telescope is at 630 AU (0.01 light year) from the sun, the image is only 1000x smaller than than the planet (12.742km wide, far bigger than any telescope we could send).

If, on the other hand, we can place the telescope just 1,000,000km away from a primordial black hole, we get a roughly 8 orders of magnitude reduction in image size, so the image of the planet is 1.2m across. For reference, an object in orbit around a 10 Earth mass black hole with a 1,000,000km semi major axis, has an orbit period of ~11.5 days. Still problematic, but it seems more in the ball park of reasonableness (all assuming PBHs actually exist in the first place).

 

[Paul451]

Not only is it impractical to point at more than one object,

A gravitational lens telescope should be thought of as a substitute for an interstellar probe, not as a conventional telescope. One mission, one target. But vastly easier and faster than an actual interstellar probe. And that advantage over interstellar missions remaining no matter how much the technology enabling interstellar probes improves. Better propulsion, power, comms, all improve GL missions as well, so there's never an advantage to interstellar probes until you can do direct sampling of materials, landers, and/or some kind of self-reproducing probe.

That said, you are right that a mini-black-hole telescope would be better in every way. It's just the first step that is the issue:

1) Find a mini-BH...

but at 10 ly away, an Earth-sized exoplanet creates an image of a size proportional to f/d. If the telescope is at 630 AU (0.01 light year) from the sun, the image is only 1000x smaller than than the planet (12.742km wide, far bigger than any telescope we could send).

While the exo-planet's image plane is large, you don't need the probe's imager to be that size in order to take advantage of the GL magnification. You can move the vehicle around the image plane. Similarly the rotation of the planet "scans" it past the spacecraft. A bit like satellites in orbit of Earth, narrow field of view, building up an image over time. (You might use a "push broom" sensor, for that reason.)

You would need to move the spacecraft around the imaging plane in order to track the target as it orbits its own star. (Plus you'd want to be able to explore the rest of the exo-system.) So this ability is baked into the mission requirements.

[You can also have multiple imagers spread around the image plane. And you would for redundancy, since sending a mission that far from the sun would be a tremendous undertaking, there's no reason to skimp on having a single vehicle. Plus different vehicles can focus on different sensors. For eg, radio/MW is very different from optical. And again, with such a mission, you aren't going to be focusing (ha!) on a single type of imager. Shotgun approach.]

Again, it's a substitute for an interstellar probe. Except at 1000th of the distance/time/energy, and with the target exo-system "shrunk" by a 1000 times.

[Barley]

I wonder how you find the target in such a telescope.  Do we know the position of any star with sufficient precision to get it in the field of view?

Prior art is usually to boot strap measurements from a lesser telescope, such as the Hubble guide star catalog.  Jumping many orders of magnitude makes this problematic.

I'm guessing that once you find a star you would want several minor telescopes in the imaging plane to lock on to the limb of the star, in the manner of Hubble Fine Guidance.  Even if the background stars are dense enough, proper motion of your target means you can't lock to them.

TL;DR what is the view finder scope?

[TheRadicalModerate]

I wonder how you find the target in such a telescope.  Do we know the position of any star with sufficient precision to get it in the field of view?

Prior art is usually to boot strap measurements from a lesser telescope, such as the Hubble guide star catalog.  Jumping many orders of magnitude makes this problematic.

I'm guessing that once you find a star you would want several minor telescopes in the imaging plane to lock on to the limb of the star, in the manner of Hubble Fine Guidance.  Even if the background stars are dense enough, proper motion of your target means you can't lock to them.

TL;DR what is the view finder scope?

The problem is more constrained than the problem an optical scope has.  An optical scope only has to use astrometry to fix its pointing in pitch/yaw, and it's relatively independent of position.

With an SGL scope, the telescope "tube" is the position vector between the Sun and the scope, and the target (presumably a planet, orbiting its star, with an angular acceleration) can only be held in the field of view if the position and velocity vectors are accurate.

That implies that the SGL scope has to constantly accelerate back and forth to keep the planet in the FoV.  In addition to that, the Sun's barycenter isn't constant, so the spacecraft's acceleration also has to account for the Sun's wobble.

So you not only need insanely good astrometry, but also unprecedented navigational accuracy for your spacecraft when it's ~600AU away from the sun.  I don't think you can get that with astrometry alone.  I'd imagine that you'd also need something like an all-solar-system GPS system, with birds orbiting at least tens of AU from the Sun.

It's a fun problem.

[lamontagne]

There were at least two talks about gravitational lensing at the IRG 2023 meeting in Montreal.

The talks are here: https://www.youtube.com/@InterstellarResearchGroup/featured

This should help you find authors that write papers on the subject.

[stefan r]

The light collected by a gravity lens focusses on a line rather than a point.  The light coming from a point source appears as ring around the Sun.  A nested set of rings will show light from further points.  If there is variation in the density of the Sun it will also wobble the light from the background by the same magnitude. 

An array of much smaller lenses traveling with the main telescope would be able to measure the wobble. 

A tethered array would be prudent.  We likely want continuos measurement of a planet orbiting a star.  We will want the main lens to circle around so the the focal line orbits the target star. 

The main mission is to use the Sun for focussing visible light.  For only a slight increase in total project cost we can position radio interferometers. We can get an extreme boost in parallax. The sun lens requires an occulting device to block our Sun.  It is not an option to "keep it simple" with only one package.  Tethering them allows for much more maneuver options

[Paul451]

A tethered array would be prudent.  We likely want continuos measurement of a planet orbiting a star.  We will want the main lens to circle around so the the focal line orbits the target star. 
[...]
Tethering them allows for much more maneuver options

The image plane of an exo-planet's orbit, if it's an Earthlike 1AU for eg, is still 300,000km wide. There's no tethered array that is going to cover that. To keep a planet in view over its orbit, you have to move the imagers around the image plane the hard way. Propulsively.

[LMT]

...will this [sun-induced] blur be bigger than 25 km/pixel?

Multipole zonal harmonics seem to be the main factor there; modeled and managed in Turyshev and Toth 2021.

Corona modeling is also important.  Turyshev and Toth 2022.

--

For many purposes, a lunar interferometer "hypertelescope" can be superior to a solar lensing telescope.  Labeyrie 2021.  Relative speed of deployment is certainly one selling point.

The hypertelescope may thus be defined as a many-apertured, and highly dilute, Fizeau interferometer, equipped with a pupil densifier. Properly co-phased, it can provide rich direct images of compact sources, where most light collected from each source resel [resolution element] reaches its sharply peaked interference-limited camera image...

Image:  "Figure 4. Numerically simulated direct image of an exo-Earth at 3pc seen with a 150 km hypertelescope containing 150 apertures of 3 m providing 0.75 microarcsecond resolution for 30 × 30 resels across the planet."

Refs.

Labeyrie, A., 2021. Lunar optical interferometry and hypertelescope for direct imaging at high resolution. Philosophical Transactions of the Royal Society A, 379(2188), p.20190570.

Turyshev, S.G. and Toth, V.T., 2021. Diffraction of electromagnetic waves by an extended gravitational lens. Physical Review D, 103(6), p.064076.

Turyshev, S.G. and Toth, V.T., 2022. Spectrally resolved imaging with the solar gravitational lens. Physical Review D, 106(4), p.044059.

[edzieba]

A 'hypertelescope' (an interferometric array) is unrelated to gravitational lensing.

[Paul451]

A 'hypertelescope' (an interferometric array) is unrelated to gravitational lensing.

I think his point was that the resolution is reputedly on a par with the realistic assessments of the resolving ability of solar grav-lens telescopes. Except be cheaper, quicker, easier, and able to reach more targets. (Although still limited by lunar rotation, electrostatic dust accumulation, etc.)

[grondilu]

no one mentions that sun is not a perfect homogeneous mass.

It may not be homogeneous, but it's likely very spherically symmetrical, considering the Sun is very, very round.

https://www.scientificamerican.com/gallery/well-rounded-sun-stays-nearly-spherical-even-when-it-freaks-out/