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**A space probe initially moving in a 1 AU circular orbit around the sun (i.e. moving with the earth). The aim is to put this space probe in an orbit that will encounter Mars, using the least possible expenditure of rocket fuel (energy). This orbit, it turns out, is one in which perihelion (closest approach to the sun) is at the earth's orbit (r=1AU), and aphelion (furthest approach from the sun) is at Mars' orbit**.

Suppose that the rockets had fired so that the change in velocity was in the radial direction (outwards). Calculate a (semi major axis) Will this orbit ever reach Mars?

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