A spacecraft of mass m describes a circular orbit of radius us r₁around the earth.

(a) Show that the additional energy ΔE which must be imparted to the spacecraft to transfer it to a circular orbit of larger radius r₂ is where M is the mass of the earth.

(b) Further show that if the transfer from one circular orbit to the other circular orbit is executed by placing the spacecraft on a transitional semi elliptic path AB, the amounts of energy ΔEA and ΔEB which must be imparted at A and B are, respectively, proportional to r₁ and r₂ :

Transcribed Image Text:

ΔΕ = ΔΕ 12 * + r –ΔΕ το GMm(r = 1) 2012 ΔΕΒ = B -ΔΕ * + r