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What tools and techniques are used to calculate as well as to ensure a collision free trajectory when space junk as well as real live useful satellites are so numerous? While the chances of hitting a given object are of course low, there are so many of them!

Probably some degree of planning can be done ahead of time, but since the moment of launch is sometimes unpredictable within a launch window and all of them are moving so fast, would this collision avoidance procedure have to be revised on almost a second-by-second timescale?

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    $\begingroup$ The roadster is going to avoid space junk by not being in orbit around the Earth. Answers to the more general question might be found in space.stackexchange.com/questions/21265/…. $\endgroup$ – JCRM Feb 20 '18 at 8:47
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    $\begingroup$ @Hobbes that question is how they avoid creating space junk; I think the question is asking how they avoid colliding with it $\endgroup$ – JCRM Feb 20 '18 at 9:53
  • $\begingroup$ I've also voted to close in order to speed up the cycle of an adjustment to the post to make it clearer that (probably) the OP is asking about how to avoid collisions with space junk, rather than how to avoid making it, followed by potentially re-opening the improved version. $\endgroup$ – uhoh Feb 20 '18 at 9:59
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    $\begingroup$ guys, question has been edited with more readability.. $\endgroup$ – armaghan Feb 20 '18 at 16:17
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    $\begingroup$ @uhoh, thanx, it makes the point. $\endgroup$ – armaghan Feb 20 '18 at 17:23
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Currently, NORAD and others use large radar arrays to keep track of objects. Simplified trajectories are what appear in the common TLE databases.

Conjunction analysis is done by propagating the trajectories of these objects. There are many types of model used here, but broadly speaking they model the conjunction of large error boxes (ellipsoidal or rectangular) around each object. These are typically many kilometers across. Many of the propagation models are proprietary.

There is a gap from launch conjunction (airspace / FAA) to space conjunction - there is a lag from when an object "appears" in space, until it appears on radar and its trajectory is tracked and propagated. For more detail, see here for example.

When there is the potential for conjunction, NORAD / JSpOC / SpaceTrack send notifications to individual satellite operators warning them of this, in the hope that they plan collision avoidance manoeuvres. Each operator will have their own tolerance of risk, and as in the case of the Iridium-Cosmos collision, their risk appetite was too large. I recall that Iridium were receiving 400 messages per day or per week indicating potential collisions.

Operators are likely to perform routine orbital manoeuvres at times that are less convenient, just to avoid debris. That way, the avoidance doesn't "cost" them anything apart from some rescheduling of planned operational manoeuvres. This is one of the main reasons the debris problem is getting worse - no-one has a financial incentive to do anything about it.

Yes, there are a lot of objects in orbit, but space is also very very large. LEO is about $10^{12} km^3$, so the overall density of objects and thus the probability of any collisions is overall "low" - it's definitely higher than I would like to personally see but is apparently acceptable to satellite operators.

Density of debris in LEO

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  • $\begingroup$ wow that was fast, thank you, and welcome to Space! $\endgroup$ – uhoh Oct 25 '18 at 10:24
  • $\begingroup$ Excellent graphic. How long would it take aproximately for the peak at 800 km to move down to 400 km per drag induced orbit decay? $\endgroup$ – Uwe Oct 25 '18 at 13:39
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    $\begingroup$ Depending on the area-to-mass ratio, lifetime at 800km is hundreds to thousands of years. $\endgroup$ – Diamond Oct 25 '18 at 14:30
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    $\begingroup$ This is the number density - the number in each box of 1km on each side. It means that you need a 10^8km^3 box, on average, to enclose a piece of debris at 1400-1500km. $\endgroup$ – Diamond Oct 26 '18 at 14:28
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    $\begingroup$ Understood - but for LEO it's a fair measure due to the velocities and repeat track periods - this chart is specifically for LEO. $\endgroup$ – Diamond Oct 26 '18 at 16:19
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While the length of a launch window varies, launches within the window typically occur at discrete times - typically "launch on minute" or "launch on second". Often a common earth-relative trajectory is used for the entire window (or subsections thereof), and rotated to the correct inertial trajectory for each expected discrete launch time.

Once you have the collection of trajectories for the discrete launch times within the launch window, you can do a relatively standard conjunction screening analysis against the catalog - as long as your algorithm can handle powered flight ephemeris. Some algorithms make assumptions in the screening process that are incompatible with powered flight. The results of this analysis can be used to close portions of the launch window as posing to high a collision risk. For US military launches, the CA analysis is typically done at intervals prior to launch. I don't think any of the commercial launches do this screening.

And their is some reason to be skeptical of the value of this screening. Typical launch covariances are so large that, in combination with the covariances of on-orbit LEO objects predicted 10s of hours to days in advance - you aren't likely to get actionable results except for the largest on-orbit objects. Such as ISS, which is handled somewhat differently anyway.

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