A space vehicle moving in a circular orbit of radius r1 transfers to a larger circular o...

A space vehicle moving in a circular orbit of radius r₁ transfers to a larger circular orbit of radius r₂ by means of an elliptical path between A and B. (This transfer path is known as the Hohmann transfer ellipse.) The transfer is accomplished by a burst of speed Δv_A at A and a second burst of speed at B. Write expressions for Δv_A and Δv_B in terms of the radii shown and the value of g of the acceleration due to gravity at the earth’s surface. If each is Δv positive, how can the velocity for path 2 be less than the velocity for path 1? Compute each Δv if r₁ = (6371 + 500) km and r₂ = (6371 + 35 800) km. Note that r₂ has been chosen as the radius of a geosynchronous orbit.