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After a spacecraft reaches orbit and jettisons its last stage, that stage would be in the same orbit too. What are methods to avoid this, or isn't it cared about?

In case of the Space Shuttle, the External Tank was jettisoned at an orbit that intersected with the mesosphere, so that the ET would reenter while the shuttle ascended on its own engines to a higher orbit. In the Apollo moon flights the third stage actually flew together with the CSM and impacted the Moon eventually (only the Apollo 12 stage entered solar orbit somehow). Did the 2nd stage of the Titan II GLV orbit together with the Gemini, and does that of Falcon 9 orbit with the Dragon spacecraft? Did the Atlas orbit with the Mercury?

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Yes the uppermost stage is in a similar orbit to the satellite, assuming that neither the satellite nor the rocket stage apply any further propulsion.

However similar is not identical.

For a satellite deployment at 400km altitude, a "jettison" speed of just half a meter per second (prograde or retrograde to the orbit) will cause the satellite and rocket to drift apart by 22 km per orbit.

By the time the two could possibly meet up again, the differential drag on the two would have further separated the two objects, and they will never meet again.

However as a general rule, space launch operators do try to remove the rocket from orbit where possible, either with an actual propulsive burn or even just by venting residual propellant thus imparting a few meters per second of thrust. Similarly just about all satellites that are more than just cubesats will have their own propulsion, and also scoot off to their final orbit following deployment.

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  • $\begingroup$ What about the Inspiration4 upper stage? Did it reenter before the Crew Dragon? $\endgroup$
    – user43968
    Sep 19, 2021 at 10:45
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    $\begingroup$ @Giovanni well, It's no longer showing on any of the sat trackers, so presumably it has already splashed down. When SpaceX does do a planned disposal of a second stage, that usually happens within an orbit or two of payload delivery. (the SpaceX second stage has very limited on-orbit loiter ability.) $\endgroup$
    – CuteKItty_pleaseStopBArking
    Sep 19, 2021 at 11:01
  • $\begingroup$ Your numbers seem to be wrong. 0.5 m/s for 92.5 minutes are 0.5 * 92.5 * 60 = 2.775 km. 22 km with 0.5 m/s take 12 hours and 13 minutes 20 seconds. $\endgroup$
    – Uwe
    Sep 19, 2021 at 11:23
  • $\begingroup$ @uwe That is not how orbital mechanics work. Go, calculate how much a slowdown of 0.5m/s alters the period of a satellite, and just how far the sat moves in the time difference between those two orbits. $\endgroup$
    – CuteKItty_pleaseStopBArking
    Sep 19, 2021 at 21:06

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