Question

The minimum and maximum distance of a satellite from the earth are 2r and 4r respectively.where r is the radius of the earth and m is the mass the earth. its maximum speed is

Answer 1

(a) Applying conservation of angular momentum

mυ1(2R)=mυ2(4R)

υ1=2υ2 ..(i)

From conservation of energy

12mυ21−GMm2R=12mυ22−GMm4R ..(ii)

Solving Eqs. (i) and (ii), we get

υ2=GM6R−−−−√,υ1=2Gm3R−−−−−√

(b) If r is the radius of curvature at point A

mυ21r=GMm(2R)2

r=4υ21R2GM=8R3 (putting value of υ1)