Question

35.A satellite is launched into a circular orbit of radius R around the earth.A second satellite is launched into an orbit of radius 1.01R.The time peiriod of the second satellite is larger than that of the first one by approximately--------

Answer 1

Kepler's third law (law of periods):

T2αr3T2=kr3Here,kisaproportionalityconstant

Apply logarithm on both sides:

logT2=logk+logr32logT=logk+3logrlogT=logk2+32logr


Differentiate on both sides with respect to r on both sides:

1TdTdr=0+32(1r)dTT=32(drr)=32(1.01R−RR)=0.015=1.5%