Could two space ships, traveling at different times, pass through the same space?

Question

This question flows from the recent question Would rocket engine exhaust create pockets of gas in space which could hinder further space exploration? it talks about daily Earth — Moon trips

If we establish shipping lanes in space for these daily deliveries,

Answers there indicate that gas just disperses, so no worries.

There are also 150+ posts about debris that talk about stuff in orbit around Earth and the risk that those items cause. Which is a separate perspective, they are not occupying the same space, the are following the Earth on its journey through space.

On Earth, shipping lanes reach between two locations on land, via sea (or air) and relative to Earth things are fairly static. If a ship passes, a few hours later another ship is likely to travel through the same water and any debris the first ship left behind.

On the Earth — Moon "shipping lane", there is nothing static. The Moon moves around the Earth, the Earth moves around the Sun, the Sun moves around the Milky Way's center, the Milky Way moves around the universe.

Once a ship leaves Earth's atmosphere, is there any possibility of it occupying the same space (relative to the Sun?) as another ship had previously?

A year later, the Earth is kind of the same place, but is it really in the same place?

Answer 1

"Yes", and in fact there are spacecraft that do this all the time in Earth orbit - the geostationary communications satellites. There is only one such orbit, realistically, and therefore, at least to a first order approximation, these spacecraft are in the same space relative to the sun as others. Really you're just asking if it's possible to send two or more spacecraft out on the same orbit, and sure we can, it would just take a crazy amount of planning and timing.

The more general question is "is it possible for a spacecraft to encounter the debris left by another", which is far easier to answer yes to since we see this happen (or nearly happen) a lot - spacecraft need to maneuver around debris or, at the very least, to maneuver to reduce the slim possibility of hitting that debris.

Now, the answer to what appears to be the original question - can one spacecraft travel in exactly the same orbit as another and encounter its debris - is not really. The debris will be travelling with the spacecraft that released it, plus any extra velocity that it obtained during its jettison. Let's assume that this jettison imparts absolutely no further energy. This could happen if, say, a spacecraft gently split apart (it released its Earth Escape Stage, say, very gently) and then maneuvered away for whatever reason. This debris is now on that spacecraft's previous orbit. In order for another spacecraft to encounter it and for that spacecraft to be on the same orbit then the chase craft has to initiate a rendezvous maneuver.

This is because it is possible to send two spacecraft out on the same orbit with appropriate timing, but if you do so then, neglecting orbital perturbations, the two will forever chase each other around the sun. Being on the same orbit means that they one will never catch up, since if it did then it would be on a different orbit. This is more or less what happened with the early Gemini flights, when the astronauts tried to catch the target but kept missing because as they sped up to try to catch the target their orbit changed.

So, in order for this encountering to happen, you'd have to plan for it or be extremely unlucky, where your orbital insertion happened at exactly the wrong time and you insert exactly where and when the debris is passing.