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Suppose I am executing an interplanetary rendevous (Hohmann transfer) between two coplanar, perfectly spherical planets, each with circular orbits.

The goal is to execute a hyperbolic escape from a circular parking orbit on planet 1 and arrive from a hyperbolic trajectory into a circular parking orbit on planet 2. Both hyperbolic trajectories are aimed in the direction of each planet's velocity. But due to the hyperbolic trajectory, the spacecraft will exit/enter each planet's sphere of influence some distance $\Delta$ (i.e. the aiming radius) away from the line of orbit.

How can I increase or decrease $\Delta$ while still maintaining the same velocity required to execute the interplanetary transfer? Also, is $\Delta$ is the same both for departure and arrival of the two planets in this ideal case? If not, how can I shape the two aiming radii independently of each other?

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