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.
- 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.
- 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.)
- The probe is a 5-meter radius sphere.
- 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.
- 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?