A spacecraft can gain in mechanical energy as they encounter a planet This may appear as a violation of the conservation of

Question

A spacecraft can gain in mechanical energy as they encounter a planet This may appear as a violation of the conservation of energy but it is not The gained energy is at the expense of the orbital energy of the plang The easiest way to see how this works in principle is to treat the problem as an one dimensional collision Let the spacecraft have mass m and just before the encounter a velocity v the planet of mass M and velocity V Both velocities are relative to the sun and they are in opposite directions Thus the angle between v V is 180 Assume that the space craft round the planet and depart in opposite direction Thus after the encounter the velocity of the space crafts is in the same direction as of V Assume M m 41 What is the speed of spacecraft after the encounter in terms of m M and speed of the spacecraft before the encounters and the speed of the planet before the encounter M m A B V 2v M m C 4M m M m V 2MV M m V 2VM M m Mm M m D None of these

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