**Unformatted text preview: **distance is , 2 r GM v e = and so the difference between escape speed and p v is, after some algebra, [ ] ⋅ +-=-) ( 1 / 1 1 2 p p p e a E r r r Gm v v Using the given values for the radii gives s. m 10 41 . 2 3 p e × =-v v The similar calculation at apogee give s, m 10 26 . 3 3 a e × =-v v so it is more efficient to fire the rockets at perigee. Note that in the above, the escape speed e v is different at the two points, s. m 10 77 . 8 and s m 10 09 . 1 3 ae 4 pe × = × = v v...

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