Parallel orbits around the Earth - effectively?

edit: For the purposes of this exercise, one could consider using three or four identical spacecraft, and using the "best two out of three (or four)" for interferometry at any given moment.

In 1994, STS-59 and STS-68 flew Spaceborne Imaging Radar, a type of Synthetic Aperture Radar (SAR). SAR is a type of interferometric radar where phase information (relative to the onboard local oscillator) is recorded and the interference phenomena is calculated/simulated offline during analysis. Instead of multiple antennas, multiple data sets are recorded with the shuttle or spacecraft in different but nearby positions in its orbit.

Two sequential measurements milliseconds apart provides the separation in the orbital track direction, but near-coincidental ground-track orbits separated by long periods of time are necessary to get displacements in the perpendicular direction.

So in 2000 STS-99 was launched with the Shuttle Radar Topography Mission. By extending a second antenna 60 meters away from the shuttle perpendicular to the orbit track, interference in this direction could be implemented with conventional interferometry, while the SAR-like data analysis was still used for the orbit direction. below: from here.

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Without the mechanical extension, if the 2nd antenna was at the same altitude as the shuttle and moving parallel, it would collide with the shuttle in one quarter of an orbit. This is because their orbital planes would intersect. Conventional parallel orbits around a spherically symmetric body do not exist. (Let's leave discussion of exotic orbits around cigar-shaped bodies to other questions.)

As an exercise, what kinds of orbital solutions exist if the extension scaffolding were not used? Suppose it wiggled too much for a hypothetical next generation shorter wavelength system, or that a longer baseline was desired. Suppose also you could use more than one antenna.

Question: What orbital "tricks" could be used to provide at least one antenna orbiting roughly parallel to a primary spacecraft at any time? The separation does not have to be constant, it just needs to be known/predictable, and should keep working for a few weeks at least.

note: Now that we have independently flying antennas, an additional unit could fly ahead of the primary without problem. That may or may not eliminate the need for SAR analysis, there may be other benefits such as the much large effective baselines. Also, assume optical links between spacecraft, so no more coaxial cables.

below: "Space Shuttle Radar Topography Mission Canister, Antenna" from the Smithsonian National Air and Space Museum A20040261000d20.

• How about just put the antenna in the same orbit ahead or behind? Separation distance will remain constant (with very small stationkeeping corrections) and direction will be consistent in the surface-relative rotating frame. – Russell Borogove Jun 19 '17 at 4:59
• 2D imaging needs data in both directions. I've tried to cover this in the question; the boom is an improvement over stitching data from different passes. – uhoh Jun 19 '17 at 5:02
• Does it matter if that second antenna moves a bit, as long as it's location relative to the shuttle were known very well? – Steve Jun 19 '17 at 16:14
• @Steve for the purposes of my current question on orbital techniques, nope!. "The separation does not have to be constant, it just needs to be known/predictable..." In a real radar mapping application that will also be true to some extent, but it may depend on the rate and/or frequency spectrum of the relative motion. But that would be a different question. For this question let's assume all satellites have a suite of navigational instrumentation, including some combination of relative GPS, sensitive accelerometers/gyros, and laser interferometers between each pair of spacecraft. – uhoh Jun 20 '17 at 2:22
• "Conventional parallel orbits around a spherically symmetric body do not exist." An unconventional solution is a continuously powered orbit. Rockets run out of fuel, but a solar sail does not. C.R. McInnes discusses offset orbits in his text "Solar Sailing". I constructed an example but could not get the drawing to post with the text. – MBM Dec 7 '17 at 18:38

You could use a main satellite with 2 subsidiaries. The subsidiaries use orbits with the same shape as the main orbit, but in a plane that has a slight angle relative to the main (plus a minimal difference in altitude to prevent collisions). The point where sub 1 crosses the main's orbit should be 90 degrees away from where sub 2 crosses the main's orbit.

With 2 subs, you always have one that is more than half the maximum distance away from the main.

If you are looking perpendicular to the orbital plane, instead of radially outward, you can have your secondary sensor at a lower orbit by your chosen distance d. It will drift ahead of the craft by about 3 pi d for every orbit. For LEO it only moves ahead by about a tenth of a second per orbit. So the images from the secondary sensor slightly earlier so that the positions in orbit match up.

For 7000km orbit you have ~100 orbits per week. With 60m separation that is 7.5 seconds of separation per week. You could always compensate with correction burns between measurements or launching a new sensor once the first is to far away. probably the ideal configuration though would be a tidally locked tether, but that does not satisfy the question.

The obvious con to this configuration is that you get a more limited view of the sky.

• I'll give this some though, it's a great idea! The problem is that a radial separation might not provide any high-resolution transverse information interferometrically. It's normally the separation perpendicular to the direction of the beams that allows the interferometry to work. I'll look into it. I really like the method you describe in your comment - can you double check the math and if it works, maybe consider adding it here or as a 2nd answer? – uhoh Dec 1 '17 at 0:40
• As far as I can tell, having a radial offset does not help here. A small radial displacement (tens of meters) at 400,000 meters produces an almost identical reflected signal. This is why the displacement shown in the question is cross-track (sideways). – uhoh Dec 6 '17 at 0:49
• I think you are misunderstanding my suggestion. In the original version all four points are within the same sphere and thus your 'bore sight' is radially outward. In my suggested configuration, the four points are within the same orbital plane, thus your 'bore sight' is perpendicular to the orbital plane or equivalently parallel to the axis of rotation. Hence why I mentioned the more limited view of the sky since along the entire orbit the telescope is limited to the same two vectors instead of swinging around by 360 degrees. – Lex Dec 6 '17 at 19:47
• You are still missing what I am trying to say. I can't think of any way to communicate it better without diagrams which would be very hard to draw free hand, so I think I am giving up. It looks like the other answer answered things satisfactorily so understanding this answer isn't as important anyways. – Lex Dec 8 '17 at 16:00
• Sorry, this whole confusion was my mistake then, I was thinking of Synthetic-Aperture Radio Telescopes instead. – Lex Dec 10 '17 at 7:26