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part 1 said:A rock of massmorbits Earth, massM, radiusRwith angular momentumLand energyE. Argue directly, considering the direction of motion at its nearest pointrto the Earth's centre, thatLcan written r*sqrt(2m(E + GMm/r))

Even at this early stage I'm bewildered and my searchings and own ponderings still leave me confused. If anyone can quite highlight how L can progress anywhere beyond the obvious r x v (where x is the cross product, and v is the tangental velocity of the rock at it's nearest point to Earth) I'd be forever in their debt

For fun, here is the rest which flows from this first section

part2 said:Solve forr, and by interpretting the two solutions, deduce the relation e = -GMm/(Ellipse Length)

part3 said:Suppose the rock is set off by being thrown from the North pole at such a (very fast) speed to have total Enegy E=0 in a direction of our choice.

part4 said:Conclude (without further calculation) that the escpae velocity is independent of throwing direction

I'm not asking people to do the question for me (although feel free ;) ), any general direction would be pretty damn useful

Thanks in Advance