Update, June 2021. This month, Starlink released an update to their mobile app that produces an image similar to what I was trying here. Hopefully some day they talk publicly about the feature, so I can lean how far off I was on implementation details.
The Starlink app, whether on a mobile device, or in a web browser, will tell you in which direction the dish regularly finds something blocking its view of the satellites. I've had it in my head for a while that it should be able to do more than this. I think it should be able to give you a silhouette of any obstructions.
As a satellite passes through the sky above the dish, the "beam" connecting the two follows it, sweeping across the scene (Figure 0). The dish repeatedly pings the satellite as this happens, and records how many pings succeeded in each second. When the view is clear, all, or nearly all, pings succeed. When there's something in the way all, or nearly all, pings fail. In theory, if the dish stays connected to the same satellite for the whole pass, we end up with a "scan line" N samples (= N seconds) long, that records a no-or-low ping drop rate when nothing is in the way, and a high-or-total ping drop rate when something is in the way.
One line isn't going to paint much of a picture. But, the satellite is going to pass overhead every 91 to 108 minutes. The earth also rotates while this happens, so on the next pass, the satellite will be either lower in the western sky, or higher in the eastern sky. On that pass, we'll get a scan of a different line.
But 91 minutes is a long time for the earth to rotate. That's farther than one time zone's width, nearly 23º of longitude. Since the beam is tight, we'll have a wide band between the two scans in which we know nothing. However, each satellite shares an orbit with 20 or more other satellites. If they're evenly spaced, that means the next satellite should start its pass only about 4-minutes after the previous one. That's conveniently only about 1º of longitude. If the dish reconnects to the next satellite in an orbital reliably at a regular interval, we should get 20-ish scan lines before the first satellite comes around again.
But are 1º longitude scanlines enough? Before we get into the math, let's look at some data. I've created a few simple scripts to download, aggregate, and render the data that Starlink's dish collects. With over 81 hours of data in hand - 293,183 samples - I can make Safari complain about how much memory my viewer is using … er, I mean I can poke around to see what Dishy sees.
In Figure 1, I've plotted ping drops attributed to obstructions at one second per 4x4-pixel rectangle. Solid red is 100% drop, and the lighter the shade the less was dropped, with white (or clear/black for those viewing with different backgrounds) being no drops. There are 600 samples, or 10 minutes, per line. It doesn't look like much beyond noise, so let's play around.
Figure 2 is the signal-to-noise ratio data instead. White/clear means signal was full (9), solid grey means signal was absent (0), with gradations in between. Still mostly noise, except for the obvious column effect. Those columns are 15 samples wide. So something happens every 15 seconds. It's not clear what - it could just be an artifact of their sample recording strategy - but that's as good of a place to start as any for a potential sync frequency.
So let's drop down to our guesstimated 4 minutes between satellite frequency. With 240 seconds per row (Figure 3) … mostly everything still looks like noise. Let's start by guessing that the period between satellites is longer.
I clicked through one second increments for a quite a while, watching noise roll by. Then something started to coalesce. At 330 seconds (5.5 minutes) per row (Figure 4), I see two patterns. One is four wide, scattered, red stripes running from the upper right to the lower left. The other is many small red stripes crossing the wide stripes at right angles. Given that this persists over the whole time range, I don't think it's just me seeing form in randomness.
Advancing to 332 seconds per stripe (Figure 5) causes the small red stripes to pull together into small vertical stacks. Especially in the later data, some of these blobs seem to fill out quite a bit, encouraging me to see … something.
But here I'm fairly stuck. Doubling or halving the stripe size causes the blobs to reform into other blobs, as expected given their periodicity. But nothing pops out as obviously, "That's a tree!" I experimented with viewing SNR data instead. It does "fill in" a bit more, but still doesn't resolve into recognizable shapes.
It's time to turn to math. I think there are two important questions:
- How much sky is covered in a second? That is, what span does the width of a pixel cover?
- How much sky is skipped between satellite passes? That is, how far apart should two pixels be vertically?
If I draw the situation to scale (Figure 6), with the diameter of the earth being 12742km, and the satellites being 340 to 1150km above that - giving them orbital diameters of 13082 to 13892km, there's really not enough room to draw in my geometry! So I'll have to zoom in.
We can start estimating how big our pixels are by comparing
similar triangles. The satellites moving between 7.28 and 7.70
km/s. If we're looking strait overhead, for our purposes at these
relative distances (340 to 1150km), we can consider that 7km to be
a straight line, even though it does have a very slight curve. In
that case, we can just use scale the triangle formed by the line
from us to the satellites T=0 position and the line from us to its
T=1sec position, into our scene (Figure 7). If the scene objects
are 20m (0.02km) away, then the width of one second at that object
0.02km * 7.7km / 340km = 0.00045km, or just under
half a meter. Compared to the higher, slower orbit, it's
0.00012km, or 12cm. At 12 to 45cm, we're not going to see
individual tree branches. Resolution will actually get a bit
better when the satellite isn't directly overhead, because it will
be further away and so the perceived angle of change will be
smaller. But for the moment, let's assume we don't do better than
half that size.
On to estimating the distance between scan lines. Wikipedia states that there are 22 satellites per plane. If these are evenly spaced around the orbit, we should see one every 4.14 to 4.91 minutes (248.18 to 294.55 seconds). If the earth rotates once every 23hr56m4s, then that's 1.038º to 1.231º. At the equator, that's 115.42 to 136.881km. I'm just above the 45th parallel, where the earth's circumference is only 28337km, so the change in distance here is only 81.705km to 96.897km. If we change our frame of reference, and consider the satellite orbital to have moved instead of the earth, we can use the same math we did last time. To estimate, this distance (81km/satellite) is approximately one order of magnitude larger than the last ones (7km/s), so we can just multiply everything by ten. Thus, our scan lines should be 1.2m to 4.5m apart.
At 12 x 120cm per sample, we're not going to be producing photographs. At 45 x 450cm, I doubt we're going to recognize anything beyond, "Yes, there are things above the horizon in that direction." Let's see if anything at all compares.
What parameters should we use to generate our comparison scan? If we're seeing satellites pass in 4.14 minute (91 minutes / 22 satellites) intervals, we should guess that a scan line will be about 248 seconds. If they're passing every 4.91 minutes, we should guess about 295 seconds. Given the aliasing that integer math will introduce, the fact that 4.14 and 4.91 are kind of the minimum and maximum, and that the satellites won't sit at exactly those altitudes, it's probably worth scanning from about 240sec to 300sec, to see what pops up. I see what look like interesting bands show up at 247, 252, 258, and 295 at least. Maybe I'm catching satellites at a band between the extremes?
But then why was 330-332 the sweet spot in our pre-math plot? Maybe I'm just indulging in numerology, but 330 = 22 * 15. Twenty-two is the number of satellites in an orbital, and 15 is the width of the columns we saw in the SNR plot. Could it be that satellites are not evenly spaced through 360º of an orbital, but are instead always 5.5 minutes (330 seconds) behind each other? If that were the case, the orbital would "wrap" its tails past each other. That seems odd, because you'd end up with a relative "clump" of satellites in the overlap, so maybe there's a better explanation for the coincidence.
In any case, I'm going to forge on with an example from the 332-sample stripe, because its blobs look the strongest of any to me. Let's also redraw it with the boxes ten times as tall as they are wide, since that's what I calculated to be the relationship between one satellite's samples and the next satellite's samples. If I overlay one of those clumps on the northward view I shared in my last post, does it line up at all?
I've stared at this for far too long now, and I have to say that this feels worse than the numerology I indulged in a moment ago. I'm starting to worry I've become the main character of the movie Pi, searching for patterns in the randomness. If there's something here, it needs a lot more knowledge about satellite choice and position to make it work. Even if I adjusted the rendering to account for the correct curve of the satellite's path and the camera's perspective, the data is too rough to make it obvious where it lines up.
With some basic information like which satellite the dish was connected to for that sample, and the database of satellite positions, I'm pretty sure it would be possible to throw these rectangles into an augmented-reality scene. Would it be worth it? Probably not, except for the fun of doing it. The obstruction diagram in the Starlink app (Figure 9) divides the horizon into twelve segments. If it shows red in one 30º segment, it's the tall thing you can see in that segment that is causing the obstruction. This additional data may be able to narrow within the segment, but if there are multiple tall things in that segment, they're probably all obstructions.
So, while this was a fun experiment, this is probably where it stops for me. If you'd like to explore your own data, the code I used is in my starlink-ping-loss-viewer repo on github. The data used to to generate these visualizations is also available there, in the 1.0 release. Let me know if you find anything interesting!
… and just one more thing before I sign off. Following up on the topic of my past notes about short, frequent Starlink outages. Figure 10 is a rendering of my obstruction (red) and beta (blue) downtime over this data. I've limited rendering to only d=1 cases, where all pings were lost for the whole second, since this seems to be the metric that the Starlink app uses for labeling time down. One rectangle per second, 10 minutes per row. The top row begins in the early afternoon on February 9, and the bottom row ends just before midnight on February 12, US central time.
 Many thanks to u/softwaresaur, a moderator of the Starlink subreddit for pointing out that routing is far more complex, since active cells are covered by 2 to 6 planes of satellites, so it's likely unrealistic to connect to several satellites in the same plane in a row. ⤣
 From the same source, routing information is planned on 15 second intervals. At the very least, this means that the antenna array likely finely readjusts its aim every 15 seconds, whether or not it changes the satellite it's pointing at. ⤣
 Again from the same source, while 22 satellites per plane was the plan, 20 active satellites per plane was the reality, though this has now been adjusted to 18. That fits the cycle observation better, as 18 satellites at a 91-108 minute orbit is 5 to 6 minutes between satellites. ⤣ ⤣ ⤣
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