A spacecraft arrives at the completion of a Hohmann transfer trajectory from ear

Question

A spacecraft arrives at the completion of a Hohmann transfer trajectory from earth. Using the patched conic technique, calculate the actual minimum Delta v magnitude needed to tangentially enter a posigrade elliptic 150 km times 6200 km (altitude) orbit about Mars. Assume all orbits are coplanar. Determine the required angle at the center of Mars between the point where the orbital insertion bum takes place and the Mars-sun line. Determine the required aiming radius at Mars in units of Mars radii. Sketch the geometry as viewed from Mars. In your sketch, show Mars, the Mars-sun line, the direction to the sun, the aiming radius, the incoming trajectory, the final elliptic orbit about Mars, and precisely locate the point where the orbital insertion burn occurs.

Explanation / Answer

In orbital mechanics, the Hohmann transfer orbit /ho.mn/ is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane.

The orbital maneuver to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the transfer orbit and a second to move off it. This maneuver was named after Walter Hohmann, the German scientist who published a description of it in his 1925 book Die Erreichbarkeit der Himmelskörper ("The Accessibility of Celestial Bodies

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