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A man M and a satellite S of comparable mass (say 5M) are revolving round the earth in a fixed orbit.

Now what will happen if man gives a strong jerk to the satellite in opposite direction to their tangential velocity?

Will both objects change their orbital radii as velocity of M and S would have increased and decreased respectively?

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Their orbit point in the place where push happened will stay the same.

Their orbit point at the opposite side of where the push happened will differ. The one that moves faster will move to a higher orbit. The one that moves slower will move to the lower orbit.

Orbits dont have to be circular. They rarely are. Orbits best described with two points, the closest to the thing they orbit, periapsis, and the furthest from the thing they orbit, apoapsis.

Their orbit time will differ. Higher orbit will take longer time to make a full round, and will seem to lag behind. Even if it was moving faster initially, right after the push. This is why orbit mechanics is so unintuitive. You need to slow down, to go to a lower orbit, to catch up with an object that is ahead of you in a similar orbir.

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  • $\begingroup$ Since their combined center of mass would remain in the original orbit (right?), does that imply some synchronicity between the two orbits, where they have to cross the common point at the same time each orbit? $\endgroup$ Feb 9, 2022 at 13:51
  • $\begingroup$ @JohnAlexiou no, their center of mass will change its orbir. There is no synchronicity. They can meet at some point again in the same spot, after many turns. for a 10 m/s push and 8000 km/s orbit it will be on the order of a thousand turns. And in about 500 turns their center of mass will be inside the earth, as their orbital phase will differ by 180*. $\endgroup$ Feb 9, 2022 at 13:54
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    $\begingroup$ Also I strongly suggest Kerbal space programm. Not only you get to witness exploding rockets, but also learn orbital mechanics meanwhile $\endgroup$ Feb 9, 2022 at 13:58
  • $\begingroup$ But how? There would need to be an external force to change the orbit of the center of mass if you consider the satelite+person as a system. Were talking about Newton's 3rd law between the two objects, and that should not change the orbit of the center of mass. $\endgroup$ Feb 9, 2022 at 19:45
  • $\begingroup$ @JohnAlexiou well, it changes the orbit. Probably that law doesnt work with orbits. $\endgroup$ Feb 9, 2022 at 19:58

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