A space vehicle si in circular orbit about the earth. The mass vehicle is 300 kg and the radious of the orbit is 2R_(e ). It is desired to transfer the vehicle to a circular orbit of radius 4R_(e ). (a) What is the minimum energy required for the transfer (b) If the transfer is accomplished through an elliptical orbit as shown in the figure. What initial and final velocity changes are required take g = 10 m//s^(2) earth's surface and R_(e ) = 6400km (radius of earth)

A space vehicle si in circular orbit about the earth. The mass vehicle

1.	A space vehicle si in circular orbit about the earth. The mass vehicle is 300 kg and the radious of the orbit is 2R_(e ). It is desired to transfer the vehicle to a circular orbit of radius 4R_(e ). (a) What is the minimum energy required for the transfer (b) If the transfer is accomplished through an elliptical orbit as shown in the figure. What initial and final velocity changes are required take g = 10 m//s^(2) earth's surface and R_(e ) = 6400km (radius of earth)
Answer» Solution :(a) `[(-GMm)/(2(4Re))]-[(-GMm)/(2(2Re))]` (b) `v_(1) = sqrt((GM)/(2Re)), (1)/(2) mv_(2)^(2) = [(-GMm)/(2((2Re+4Re)/(2)))]-[(-GMm)/(2Re)]` `DELTA v_(12)=v_(2)-v_(1)` `(1)/(2)mv_(3)^(2)=[(-GMm)/(2((2Re+4Re)/(2)))]-[(-GMm)/(4Re)]` `v_(4) = sqrt((GM)/(4Re))` `Delta v_(34)=v_(3)-v_(4)`