# What determines if a star tracker blends two stars that are close to each other?

If two stars are very close to each other, a star tracker could identify the pair as a single star, with a magnitude and position different from both stars. This obviously impairs the software's ability to determine which star it's looking at. My question is, how could one figure out if a tracker will distinguish between two stars or blend them together? It must be related to both the distance and the magnitude of each star (as well as the tracker accuracy).

My understanding of a star tracker is as follows (please correct if I'm wrong). The tracker records pixel values within a FOV, then it defocuses the image and uses some numerical method to pinpoint where the star centroids are, as well as what their magnitudes are. How could I find out whether this process will identify two stars separately or together, based on star magnitude and distance? Some sort of generic equation like

stars are blended if:

$M_1*M_2*d_{12}^2 > B$

is true,

where $M_1$ is the visual magnitude of star 1, $M_2$ is the visual magnitude of star 2, $d_{12}$ is the angular distance between the two stars, and $B$ is some constant (please note I completely made this equation up, but I imagine if there is an answer to this question it might take a similar form).

I'm not looking for a concrete answer, rather an educated guess as to how to determine if it's likely two stars will be blended. Thanks!

• Usually, the tracker will know its last known location and there is an IMU as well. from there, you calculate a guesstimate of the position and then use stars you know to be safe from overlapping to get the actual fix. There are documents from the Apollo era that list the available fix stars and when which were used to get a fix on the position, as well as the procedures of choosing them. I'll see if I find a link. – Polygnome Jun 1 '17 at 18:26
• The reason I'm asking this question is because I want to know what the star catalog will look like. If the catalog has two stars very close to each other, the tracker might read them as one star. Then, when it looks for what it's looking at in the catalog, it won't find a match. I want to know how to make a catalog that makes two close stars into a single star, in order to compensate for the tracker picking them up as one. If that makes any sense. – Arthur Dent Jun 1 '17 at 18:54
• The catalogue is made in such a way so that no two stars are too close to each other. The spacecraft roughly knows where it is. Even if in its current position there are two stars that might blend together, it simply chooses to use another set of stars to get a fix. Its really not all that difficult. I'm still scouring my links, but If I remember correctly the apollo catalogue had 90+ stars, and you only need 3 for a fix. Its both in the transscripts of Apollo 10 and 13 (and probably others) and in the flight manuals. Its late, I'll post info tomorrow after getting some sleep ;) – Polygnome Jun 1 '17 at 19:13
• The gist is: there really aren't any bright objects in the sky we have not yet catalogued. – Polygnome Jun 1 '17 at 19:15
• Outlier removal is potentially dangerous but essential. A star tracker will start with the brightest stars since they are the fewest and will lead to a quick unambiguous coarse alignment, then work its way down in brightness until enough stars are captured and their centroids established to perform a sufficiently precise fit. There will always be "flyer" rejection since images are affected by cosmic rays, potential co-orbital debris, other random debris, unexpected minor planets, etc. If something is an outlier in the fit, it will likely be jettisoned from the data and the fit performed again. – uhoh Jun 2 '17 at 7:19

## 1 Answer

Modern star trackers are intentionally a bit out of focus. This spreads the light from a single star (which would otherwise resolve to a single pixel) across multiple pixels. Close binaries are similarly spread across multiple pixels. This is a feature rather than a misfeature.

What about stars that happen to appear to be close by one another, resulting in a misshaped blob? The solution is simple: Don't put those confusing objects in the star tracker's star catalog. There are always going to be objects in the field of view that are not in the field of view that are not in the catalog. These range from the wide binaries, apparent binaries, planets, asteroids, chunks of unburnt fuel, and pixels that have been fried due to radiation effects.

Modern star trackers don't look at just one object. They instead look for triangles that unambiguously match some triangle of stars in the star tracker's star catalog, which is typically in the tens of thousands. Multiple triangles are even better.

This is part of why star trackers operating in "Lost In Space" mode take multiple seconds to arrive at a solution. The solution has to be statistically unambiguous. A star tracker in a fictional (think Star Wars) asteroid field won't work because there are too many bright objects in the field of view that aren't in the catalog. A star tracker with a commercial quality CCD array won't work because too many of the pixels in the array will have been fried.

A modern star tracker in a star cluster also won't work. That is not our problem. When humanity reaches the stage where navigation in a star cluster does become a issue, those future star trackers will most likely look at quasars.

• So basically there isn't a standard equation for determining if a blob is really two blobs, because it's never done? That's a shame. I'm trying to make a catalog that actually does include blended stars, so I wanted to see if someone had done this before. I'll do some more research on this myself, but if no one has a better answer in a few days I'll accept yours. Also, the "triangles" isn't exactly always the case. The angular distance between two stars can also be used to match stars. There are a variety of algorithms that can be used to identify stars. – Arthur Dent Jun 5 '17 at 13:45