# Is 75 meters an exceptionally close distance for two satellites to pass at >6,000 m/s?

While researching for this question I ran across something called Celestrak Socrates. I requested the ten closest predicted approaches, and saw distances of closest approach of the order of 100 meters or even less. I recalled this question but this kind of close approach doesn't apply, since I don't think Iridium and OrbComm got together and planned this.

I figured there must be some mistake, so I clicked "Analysis" and got the TLEs for the two spacecraft, Iridium 55 and "OrbComm FM18. I plugged them into Skyfield and sure enough, at about 17 seconds after 2016-12-15 13:14:00 UTC it shows them passing about 100 meters from each other at 6,674 m/s relative velocity. I had to use 1 millisecond time spacing to resolve the event.

Question: Is 75 meters an exceptionally close distance for two satellites to pass at >6,000 m/s? I get the feeling that since this is a "weekly top-10" list, this kind of close approach must be happening frequently. Are these satellite constellations under control to such precision that a ~100 meter miss is routinely acceptable, or did I stumble upon a fluke somehow?

I suppose this will happen even more often if SpaceX put's their first 1,600 satellites at a single altitude/inclination in 32 intersecting planes.

IRIDIUM 55
1 25272U 98019A   16348.53470940  .00000004  00000-0 -55193-5 0  9992
2 25272  86.3948   4.6359 0002006  88.0295 272.1131 14.34219879979454
ORBCOMM FM18
1 25414U 98046B   16347.49264999 -.00000013  00000-0  46447-4 0  9990
2 25414  44.9965  56.3156 0006146 236.8164 123.2093 14.32449704958255


above: Celestrak Socrates screen shot circa 2016-12-13 18:30 UTC

## Wow!!

I went back to the page (about an hour and a half later, I've added estimated times of page loadings before screen shootings) and the predicted distance of closest approach has changed from 0.075 kilometers to 0.113 kilometers, which is precisely the value I get from Skyfield. The TLEs have not changed, gee, what's going on?

update: Figured this out at least. The epoch for the Iridium 55 TLE is 16348.53470940 which is about 12:50 UTC. Clicking the Analysis button around 18:00 UTC seems to have retreived the updated TLE, and not the TLE that was used to generate the display. It could very well be that if I had updated the page at that moment, the new minimum distance 0.113 km would have appeared.

From here:

Methodology

Twice each day, CSSI runs a list of all satellite payloads on orbit against a list of all objects on orbit using the catalog of all unclassified NORAD two-line element sets (TLEs) releasable to the public to look for satellite conjunctions over the next seven days. The reason for limiting the search to conjunctions with payloads is to give satellite operators an opportunity to plan—or obtain planning services—to move their satellites out of harm's way (if their satellite is maneuverable), or to take other appropriate measures. Since there currently is no way of knowing which payloads are still active, all payloads are considered.

above: Celestrak Socrates screen shot circa 2016-12-13 20:12 UTC

No, 75 meters is not exceptionally close — several satellites show predicted passages that close or closer every single week of the year. But it is close enough to potentially appear in the top 10 list of satellite conjunctions for the week:

https://celestrak.org/cgi-bin/searchSOCRATES.pl?IDENT=NAME&NAME_TEXT1=&NAME_TEXT2=&ORDER=MINRANGE&MAX=10

Satellites do routinely pass each other safely with such small margins of error, but the passage can occasionally be dangerous. Since TLE files are rated as being accurate to only a few kilometers, the last I checked, a predicted 100 meter passage could wind up being much more — or much less.

In an incident in 2009, a pair of satellites whose TLEs predicted that they would pass each other by 584 meters failed to do so successfully. A pair of debris fields appeared and were tracked in the positions that the satellites should be in:

You can read a full report about the prediction, and about satellite close passages in general, at CelesTrak:

https://celestrak.org/events/collision.asp

That particular satellite pair had not even made that day’s Top Ten list of close approaches, and — perhaps as a result? — no evasive maneuver was planned to increase the margin of error. In fact, Iridium 33 made safe passage on very many occasions when the margin of error was much less! Quoting the report linked above:

Iridium 33 saw between 10 to 15 times each week when something was predicted to come within 5 km of it—out of the 1,007 to 1,095 such predicted conjunctions for the entire Iridium constellation. Determining that the predicted conjunction for Iridium 33 and Cosmos 2251 was more significant than the many dozens of other Iridium conjunctions for that week is simply not possible using the TLE data.

So, to answer your question: no, the conjunction of 100 meters that you have found is not at all unusual. Again from the report:

close approaches with satellites in Earth orbit are not uncommon events. Over the period examined here, between 11,169 and 11,493 conjunctions were reported each week—over 1,600 times a day.

The system they described to predict close approaches is still operating, and you can visit its web page: SOCRATES, the Satellite Orbital Conjunction Reports Assessing Threatening Encounters in Space. You will find that the encounter of 100 meters you calculated is quite routine. The top encounter at the moment when I click on their “Top 10 Conjunctions by Minimum Range” report shows two satellites predicted to pass only 15 meters from each other!

• Yikes! The report is very helpful. So it seems that the particular values for closest approaches, as predicted on this web page using the publicly released set of TLEs from the Space Surveillance Network (SSN) may not be that meaningful on a case-by-case basis. Even though the displayed precision is 1 meter, and a given conjunction might be of order 100 meters, they might have still been as much as a few kilometers off. And it works both ways, so that a conjunction resulting in a collision might show up as 1 kilometer or more in separation on this page.
– uhoh
Commented Dec 14, 2016 at 15:17
• So in essence, everyone is relying upon luck to keep satellites from hitting each other, because our measurements are too imprecise to do otherwise? Commented Dec 15, 2016 at 1:48
• @aroth TLEs are too imprecise. Other methods of sharing tracking information are not (arguably). Commented Dec 15, 2016 at 2:34
• Huh, if the two satellites collided, why would their debris fields follow the same two orbits that the satellites did? Commented Dec 15, 2016 at 15:37
• @RemcoGerlich The physics of collisions is a big topic — you should probably take the image of the two debris fields and ask that as a separate question, to give people space enough to answer! Commented Dec 15, 2016 at 17:47

Exceptionally rare? No. Uncommon, well, yes. From what I can recall, these happened about once every 10 years per satellite for the constellation of satellites I worked with, at least, prior to doing a collision avoidance maneuver. That of course included debris/ satellite close approaches.

Of course, I note that the two you listed are both live satellites, which makes things a bit more interesting. With live satellites, the two have to coordinate with each other to make sure they don't do the same maneuver at the same time, cancelling each other out. These are a bit rarer, but it seems like it was about one per, say, 50 years per satellite that one of these would happen.

If you look at the same page, there are another pair of satellites, one not active, with a close approach even close, although the predicted approach is further in the future.

I strongly suspect that one or the other of those two satellites will perform a collision avoidance maneuver, and by so doing ensure the distance is at least a couple of km away at that time.

• TLEs shouldn't be used for close approaches. They aren't that accurate. I suspect that they passed their own orbital determinations to Celestrak, who is actually in business to help companies with that kind of stuff, to get a better estimate. But that's another question;-) Commented Dec 13, 2016 at 21:08
• Trust me, with Celestrak there's more going on, especially with 2 active satellites. Commented Dec 13, 2016 at 21:13
• OK, The number jumped after the new TLE was released, and the distance of closest approach agrees within 1 meter of what the TLEs indicate. The numbers on the public web page could be TLE-based and the service they provide to paying customers could be more refined.
– uhoh
Commented Dec 13, 2016 at 21:16
• Ya, see the quote I've added. The operative phrases being "Twice each day" and "...all unclassified NORAD two-line element sets (TLEs) releasable to the public..." We're looking at the free stuff. Paying customers are getting something presumably better.
– uhoh
Commented Dec 13, 2016 at 21:25
• How do they move the satellites (ie, ensure that by moving they do not enter another collision trajectory? Do they simply assume that probability is too small and just avoid the existing problematic close-encounter?) Commented Dec 14, 2016 at 13:34

75 meters isn't all that rare - for the full public catalog there are 75 meter predictions about 2-3 times per day. What you have to consider is the uncertainty in that number. For TLE data, that's 75 meters +- several kilometers.

The 75 meter miss distance is from the nominal position of each object at closest approach. But TLE data has a significant amount of error. For what we're concerned with here - high relative velocity conjunctions - that can be characterized by a position covariance. Think of it as a football shaped ellipsoid surrounding the nominal position which characterizes the position error of the TLE. This is a 3 dimensional Gaussian distribution of the position error. For TLE data this is typically maybe a few hundred meters at the elset epoch (depending on orbit regime, priority, size, drag regime, etc.), and grows with time. Several km of error isn't very unusual.

So again, when you say that the objects will pass within 75 meters of each other, what you really mean is that the centroid of the (potentially very large) position covariance ellipses pass within 75 meters of each other. The actual miss distance could be less, or likely much larger.

In fact, miss distance alone is a notoriously bad indicator of actual collision risk - there are techniques for calculating metrics such as probability of collision, Mahalanobis distance, and others based on the position vectors, uncertainty estimates, conjunction geometry, object sizes, etc.

Here are a few references on probability of collision for space objects. Not sure what I can give you on the error size estimates - I'll take a look later.

Foster, J. L., and Estes, H. S., "A Parametric Analysis of Orbital Debris Collision Probability and Maneuver Rate for Space Vehicles," NASA/JSC-25898, August 1992.

Chan, K., "Collision Probability Analyses for Earth-Orbiting Satellites," Proceedings of the 7th International Space Conference of Pacific Basin Societies, Nagasaki, Japan, July 1997.

Patera, R. P. "General Method for Calculating Satellite Collision Probability," Journal of Guidance, Control, and Dynamics, Vol. 24, No. 4, July-August 2001, pp. 716-722.

• Could you add a few links to supplement the error sizes and list of techniques?
– uhoh
Commented Dec 14, 2016 at 16:53