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Suppose a spacecraft is on an interplanetary Hohmann transfer trajectory from an inner planet to an outer planet. When the spacecraft finally enters the target planet's sphere of influence, which direction does it typically enter from? From behind the target planet's orbit (i.e. the spacecraft flies into the SOI) or ahead of it (i.e. the planet's SOI moves into the spacecraft's orbit? To clarify, this is a question about the relative motion of the frames of reference of the target planet and the spacecraft, not about which side of the planet the spacecraft ends up in.

I'm developing a simulation of such a transfer trajectory and I just want to know which direction I should expect to see the two meet for debugging purposes only. For simplicity, we can assume the planets and the Hohmann transfer are coplanar.

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    $\begingroup$ @RussellBorogove: I think this question can be seen as one of relative reference frame motion, rather than which side of the planet (a much smaller target) one ends up on. $\endgroup$ – Nathan Tuggy Sep 30 '17 at 23:36
  • $\begingroup$ Oh, I think I see. $\endgroup$ – Russell Borogove Oct 1 '17 at 1:50
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    $\begingroup$ Spending some time with KSP will answer this and similar questions, incidentally. $\endgroup$ – Russell Borogove Oct 1 '17 at 6:21
  • $\begingroup$ Possible duplicate of After a trans-Mars transfer, what is the direction of the rotation of the orbit around Mars? $\endgroup$ – uhoh Oct 1 '17 at 12:01
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    $\begingroup$ @RussellBorogove: Many espouse the virtues of KSP as a good approximation of space flight dynamics, but it is difficult for a novice to separate that which is realistic from what is utter nonsense physically. $\endgroup$ – Paul Oct 1 '17 at 15:42
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When going from an inner to outer body in a Hohmann -- Earth to Mars, for example -- the spacecraft will be nearing the aphelion of its elliptical orbit as it enters the destination SOI, so will be going substantially slower than the outer body. From a fixed solar frame, the spacecraft will be ahead of and inside the planet, and the planet will overtake it from behind. The spacecraft is not going fast enough to have a near-circular orbit, so it would simply fall back to perihelion if not for the gravity of the outer body.

Going from outer to inner, the spacecraft will be near perihelion, going faster than the inner body, overtaking it from behind.

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