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After centuries of careful search and travel, some intrepid extraterrestrial explorers have finally found another inhabited world! Elated with their discovery and exhausted after their long journey, they swing into a high orbit around Earth and start running their scans. Thankfully their vessel is very hard for our primitive telescopes to detect, so they aren't worried about any interference from the surface until they're well and ready to reach out to us.

However, might their chief apprehension be an accidental high-impact collision with one of our 934,000 orbiting objects over 1cm in length?

When we send things into orbit, we obviously have a big leg up in that we've already catalogued the orbital trajectories of our satellites. We currently track over 22,300 total orbiting objects.

Assumptions:

  1. It would be difficult for these aliens to gain that same level of knowledge from their high orbit, because of the small size and high speed of all of the objects. Let's say they can only detect the largest 20% of our 22,300 tracked orbiting bodies initially.
  2. They need to send a stealth probe down into a low Earth orbit for 3 weeks to complete their scans. This is the most crowded area (63% of satellites operate here, and we can assume that's the distribution of junk as well.)
  3. The probe is a 5-meter radius sphere.
  4. The aliens do not possess any handwavium-powered shields or unobtanium-plated armor, so a collision with even a small orbiting body could be disastrous.
  5. The alien's method of interstellar travel effectively avoids space debris, but that technology cannot be used in orbit.

If the probe remained in a random low-Earth orbit for three weeks, what are the odds that it would collide with an object over 1cm in length?

BONUS 1: Is there an optimal orbit to minimize the chance of these collisions, given their initial level of knowledge of our orbital patterns?

BONUS 2: Assume further that in this low orbit they can detect an additional 44,000 orbiting objects every day, and adjust the probe's orbit accordingly at the end of each day. By the end of 3 weeks they know where nearly all of our 934,000 dangerous objects are. Exactly how much does this effect the probe's overall survival chance?

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    $\begingroup$ The probabilty of a collision will be approximately the same as the International Space Station. It survives well in orbit. An alien probe could do as well. High-impact collisions will be a standard problem for interstellar travellers. They will possess more than adequate technology to deal with the problem. They won't even notice it was a problem. A spacecraft will face worst high-impact collisions inflight, so in Earth orbit will be trivial. $\endgroup$ – a4android Feb 20 at 21:29
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    $\begingroup$ Wouldn't you say though that the ISS is benefiting from our own orbital planning? After all, we're not going to put a satellite into orbit that is going to crash into our own space station. And if we're tracking debris that will collide with the station, we can do something about it. These aliens have a lot less intel. $\endgroup$ – WhittlesJr Feb 20 at 21:34
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    $\begingroup$ The odds are astronomical... $\endgroup$ – Harper - Reinstate Monica Feb 21 at 14:33
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    $\begingroup$ @a4android No doubt any alien species capable of reaching us would have tracking tech superior to ours, but we've been carefully observing and tracking space debris for decades and they only just got here and don't have access to our stored databases yet. It might take a little time for them to get as complete a picture as we have of what's up there. $\endgroup$ – Darrel Hoffman Feb 21 at 14:56
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    $\begingroup$ @user3482749 While there is no stealth in space. The probe only has to have extremely low-reflectance, be dark coloured, have high radar absorbance, and only improved radar stealth to avoid BMEWS detection. Its remaining detection problem will be infrared due to heat loss. Most IR telescopes are astronomical and are unlikely to notice an orbiting heat source. If they did, it would be discarded as an annoying satellite. The fact no-one is looking for alien probes in orbit is their best stealth. $\endgroup$ – a4android Feb 22 at 0:13
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Luckily for your intrepid explorers, the odds are infinitesimal.

According to this study, the chances of something twice as large as your probe hitting another object with a cross section larger than 1 cm is between 1:100 and 1:1000 over a ten year period. Insofar as an ideal altitude (bonus #1), figures 4.2 and 4.3 in that same study seem to indicate that an altitude below 200 km would be best. After that, between 1200 and 1400 km has the lowest chance of collision. (Most satellites operate between 500 and 1000 km.) These are very simplified estimates, though; the article has more details on various considerations.

This article corroborates that altitudes of 800-1000 km are the most congested. It also gets into micrometeoroid data.

Note the odds go up quickly the smaller the cross section you’re concerned about. It might hit one or two objects in the mm range, but in the lowest altitudes even the odds of that are tiny. But after a three week period (bonus #2), they should be able to avoid just about anything as large as a grain of sand, if they wanted to.

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    $\begingroup$ Interesting data! I noticed that the first study is from 1995. I believe that the amount of debris has grown substantially since then. $\endgroup$ – WhittlesJr Feb 20 at 21:44
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    $\begingroup$ @WhittlesJr: The point is that debris cannot survive for long on low Earth orbit; atmospheric drag will deorbit it in a matter of months. (That's why space stations need periodic altitude boosts, and deorbit quite quickly at end of life.) $\endgroup$ – AlexP Feb 20 at 21:47
  • $\begingroup$ @WhittlesJr Correct. The second article is from 2019 and estimates >1 cm at 300,000 objects. In any case, over a period of a few days, the odds won't significantly change, and the ideal altitudes are the same. $\endgroup$ – Dan Feb 20 at 21:47
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    $\begingroup$ @AlexP Thanks for highlighting this. It's largely why there's a big drop-off at the lowest altitudes. $\endgroup$ – Dan Feb 20 at 21:52
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I would say that if the alien race is advanced enough for Interstellar travel than they would have the capabilities to detect granular sized objects at a decent safe distance. They needed to be able to detect these if they were traveling at any amount of a relativistic speed otherwise a grain of sand could have destroyed their ship.

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  • $\begingroup$ Welcome to Worldbuilding user72655, a sensible answer. An alien interstellar spacecraft would also have countermeasures to destroy matter on a collision course. $\endgroup$ – a4android Feb 20 at 21:22
  • $\begingroup$ I'm guessing that the concentration of dangerous objects is probably much more dense in Earth's orbit than in interstellar space. I'm looking for an answer that maintains the assumptions I listed. $\endgroup$ – WhittlesJr Feb 20 at 21:22
  • $\begingroup$ @WhittlesJr There are some problems I'm seeing with the assumptions you list. First, as user72655 pointed out, if the alien spaceship travels through normal space at any appreciable fraction of lightspeed, they absolutely MUST be able to detect and deal with very small objects. Interstellar space is definitely not empty, and even something as small as a 5-meter probe is going to run into a LOT of stuff while flying across those many lightyears. HOWEVER, if the alien ship uses some form of hyperspace/subspace/wormhole/etc. to travel between stars, you might be able to get around that problem. $\endgroup$ – Lawton Feb 20 at 21:33
  • $\begingroup$ I'm really mostly interested in the question of the probabilities, so I'll add an assumption like that. $\endgroup$ – WhittlesJr Feb 20 at 21:35
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The odds are very, very, very low. For reference, the International Space Station (110 meters long, currently) has lived in low Earth orbit for over 20 years and there have been no significant collisions. The ISS is subject to micro-strikes all the time, as can be seen on this equipment which flew on the ISS for 19 years. But these are essentially grains of sand.

The ISS does have the benefit of Earth-based tracking of debris, and does occasionally maneuver to avoid potential obstacles. But the odds are still very low even if they did not do that. The ISS has to re-boost itself periodically anyway, so maneuvering to avoid obstacles is essentially free.

Your assumption 2 is wrong. Low Earth orbit is cleaner than higher orbits, and this is one of the reasons we put things there. The reason is that there's still enough atmosphere in low Earth orbit to produce significant drag, so any debris left there will eventually de-orbit on its own (in maybe 6-24 months, depending on initial conditions). When LEO satellites reach the end of their useful life they are either de-orbited, or boosted into a higher stable orbit where they are unlikely to cause problems in the future.

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  • $\begingroup$ I'll grant that LEO might not be the most congested area, but it's seemingly not clean by any means: en.wikipedia.org/wiki/Low_Earth_orbit#Space_debris $\endgroup$ – WhittlesJr Feb 21 at 15:24
  • $\begingroup$ @WhittlesJr First, LEO describes a large range of altitudes. You're talking about very low LEO- 200-300km. That's a very different regime than 500-2000km. Second, yes, about half of all debris is in LEO, but that's higher LEO and not lower LEO where you're talking about. See for example: swfound.org/media/99971/wright-space-debris_situation.pdf $\endgroup$ – David Feb 21 at 15:54
  • $\begingroup$ I did not specify an altitude. I asked what would happen if the probe entered "a random low Earth orbit." Granted, the optimal decision seems to be to orbit as low as possible, but that pertains to my bonus question and not the primary question. $\endgroup$ – WhittlesJr Feb 21 at 16:01
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Regarding your first bonus point, of minimising the chances of collision (and hoping my shaky Kerbal-based understanding of orbital mechanics is correct):

If two objects are orbiting at the same altitude and the same inclination, then they'll be moving at the same velocity. So their relative velocity will be zero, and they'll never collide as long as they maintain their orbits. The risk would be of something in a higher orbit losing altitude due to atmospheric drag (and thus gaining relative velocity) and potentially colliding with a lower object.

If they're at different inclinations, there would also be the risk of collision at the points where their orbits intersect.

So your safest orbit would seem to be just high enough that drag isn't a factor, and at the same inclination as the majority of objects orbiting at that altitude. Assuming that altitude isn't too high for your probe's instruments. At which point your potential collisions are other objects at the same altitude but a different inclination.

The problem with that is, if that turns out to be equatorial, then that's not going to be much help for your probe scanning the entire planet, since it's always going to be over the equator. The optimal inclination is obviously going to depend on how long you have to scan the planet and how far either side of the probe's path it can scan on each pass.

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    $\begingroup$ Other than geostationary satellites, they mostly aren't equatorial, as they need to cover more of the surface. Also, anyone who can cross interstellar distances probably doesn't need to worry about a bit of drag on their temporary orbit. They could just orbit lower than would be useful for a satellite, where most of the debris would have already decayed and re-entered. $\endgroup$ – Robin Bennett Feb 21 at 13:42
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    $\begingroup$ They could have the same altitude and inclination but be orbiting in opposite directions! $\endgroup$ – Matthew Feb 21 at 13:43
  • $\begingroup$ @RobinBennett Fair point, although I was thinking more of getting hit by local satellites rather than the drag being a factor for the probe. $\endgroup$ – Mohirl Feb 21 at 16:14
  • $\begingroup$ @Matthew Would the inclination not be 180 apart if they're going in opposite directions? But yes, you definitely don't want to do that! $\endgroup$ – Mohirl Feb 21 at 16:14
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    $\begingroup$ One assumes that alien standard orbits involve orbiting along the same direction as the planet rotates for the same reasons we do. It's more fuel-efficient for rockets, and after you upgrade to super-tech alien thrusters you simply retain the convention for the sake of your older hardware and then later as a matter of tradition and convenience. $\endgroup$ – Ruadhan Feb 21 at 16:29

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