# What is the physical geometry of this apparent "eclipse" of a tiny moon of Asteroid Florence?

Below is a small GIF made from a small subset of images contained in the original 36MB GIF found at https://cneos.jpl.nasa.gov/images/news/florence.p5us.1Hz.s382.sep01.gif as I just found in the Sky and Telescope article Asteroid Florence Has Two Moons.

Although it's tempting to interpret the image as an optical image, I belive this is pulsed-doppler data from the Goldstone Deep Space Network center. I am guessing that one axis is range (delay) and the other is doppler shift.

Still I can't figure out the geometry that would produce an "eclipse" (in this case the moon passing behind the larger asteroid) with it disappearing so "far" from the asteroid.

Could someone help me out here? Is one axis delay (time) and the other doppler shift? One can start with this description but there is more to it than is discussed there.

below: "A radar image shows asteroid 3122 Florence and tiny echoes from its two moons. Here is an animation that shows them more clearly. The direction of the radar illumination (and thus the direction toward Earth) is at the top." From here. NASA / Jet Propulsion Laboratory. This is a small subset of the frames contained in the original 36 MB GIF, and the size has been decreased by a factor of 2 in order to fit in SE's 2 MB limit.

• I'm not exactly sure what you're asking, but I believe this animation should be treated as an image, and the x and y axes have no special meaning?
– user21
Commented Sep 3, 2017 at 13:19
• @barrycarter I don't know what "the x and y axes have no special meaning?" could mean. Axes always have meaning. I found a new JPL/CNEOS link discussing the image and I've added it to the question as well, but apart from saying "it's complicated" they don't characterize the axes. An answer to my question would have to explain what geometry the term "eclipse" is actually referring to.
– uhoh
Commented Sep 3, 2017 at 13:57
• OK, I figured out what you mean, sorry. The inner moon is eclipsed even though there appears to be nothing eclipsing it.
– user21
Commented Sep 3, 2017 at 14:18
• It appears that the "light source" is coming from the top of the image, and the inner moon is falling into the light source's umbra briefly. It would probably look better if we were viewing from the position of the "light source", but that doesn't appear to be the case.
– user21
Commented Sep 3, 2017 at 14:27
• @barrycarter How can this picture show visible light sources if it's a radar image? Commented Sep 3, 2017 at 21:47

The vertical axis is signal delay, and therefore distance from the radar antenna; this is more or less true spatial information. As the caption indicates, delay is increasing from top to bottom in the image.

The horizontal axis is frequency shift (due to the Doppler effect). To the left are signals with a lower frequency relative to what was sent from the radar antenna, i.e. reflections from points moving away from the antenna; to the right, signals with a higher frequency, coming from points moving towards it.¹ This axis is more difficult to interpret.

For a single rigid body, which Florence presumably is, the only way it can have points moving in different directions at the same time is by rotating. On one edge of the body, points that have just come into view of the radar are moving quickly towards it. This relative movement slows down as the points approach the centre of the radar-visible disk; then, they move away increasingly fast until they disappear from view on the opposite edge. (The speed change isn’t linear, which means the body will be somewhat warped on the radar image.)

Only this effect allows the radar to distinguish between points that are at the same distance. If the asteroid wasn’t rotating at all, or if we happened to look exactly onto one of its poles, it would appear only as a thin vertical line in the image. For a rotating body, note that the radar cannot tell to which direction the rotation is: A mirror asteroid rotating the other way would look exactly the same to it.

Now for the moons. They are not rigidly connected to Florence, and apparently not tidally locked to it either, so they will not follow its rotation. With that, the starting point “moving in different directions at the same time = rotation” which worked on the main asteroid breaks down. When one of the moons is moving towards the radar, that tells us exactly nothing about its relative position to Florence; the visualization is misleading in that respect. Therefore, it is absolutely possible for a moon to be straight behind Florence even when it appears to its side in this particular visualization.

Emily Lakdawalla has a nice blog post on this topic, with animated drawings: How radio telescopes get “images” of asteroids

¹ After correcting for the movement of Florence – or the whole Florence-and-moons system – relative to Earth, of course.

• Thank you for the explanation! I think one of us should probably add one or both captions in the question or the answer (as a block quote) for future readers, as general protection against link rot. To double check that I understand, a vertical line down the center (x=0) of the image represents zero velocity (in the Florence system center-of-mass frame)? The lower moon reaches maximum delay and zero relative velocity, and since the inclination of it's orbit is small enough relative to the ecliptic, it passes behind.
– uhoh
Commented Sep 4, 2017 at 1:36
• If the same orbit had a larger inclination with respect to our line-of-sight, the excursions would be reduced in both x and y, and there would be no disappearance? I wonder if saying that the moon is in superior-conjunction with Florence is a better way to describe it, or perhaps an occultation by Florence, rather than "Eclipsed" as labeled in the GIF?
– uhoh
Commented Sep 4, 2017 at 1:42