An elliptical satellite orbit has perigee R and apogee 7R. A circular orbit around the same planet has radius 2R. If T_e/T_c=2√n, find n.
Physics · Gravitation · sattelite and keplers law
JEE Advanced Irodov Level

Question

An elliptical satellite orbit has perigee R and apogee 7R. A circular orbit around the same planet has radius 2R. If T_e/T_c=2√n, find n.

G1 Physics · Accepted Answer

Ellipse semi-major axis a=(R+7R)/2=4R. Thus T_e/T_c=(4R/2R)^(3/2)=2√2, giving n=2.