3.Assume the orbital of a lunched satellite around the earth iscircular. (a)Show

Question

3.Assume the orbital of a lunched satellite around the earth iscircular.

(a)Showthatthereisonlyonespeedthatasatellitecanhaveifthesatelliteistoremaininanorbitwitha fixed radius and it does not depend on the mass of thesatellite.

(b) What is the speed and height H above the earth’ssurface at which all synchronous satellite (regardless of mass)must be placed in orbit, assuming the earth is spherical?

(c) If a synchronous satellite has a mass m. How muchadditional kinetic energy is needed for it to escape from theearth?

Explanation / Answer

A: Fnet= (mv2)/R Fnet = Fgrav (mv2)/R = (GMm)/(R2) Simplify: v2 =GM/R v=(GM/R)^(1/2) B:?? C: KEsyn= 1/2m(Vsync)2= GMm/2r Vsyn= sqrt(GM/R) Vesc= sqrt(2GM/R) KEesc=1/2m(Vesc)2= GMm/r = 2(KEsync)

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