Q.
The relative uncertainty in the period of a satellite orbiting around the earth is 10−2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :
Time period of revolutions of a satellite revolving around Earth of mass M in orbit of radius r is given by T=2πGMr3 ⇒T2=GM4π2r3
Taking log of both sides, we get logT2=logGM4π2r3=logG4π2r3−log(M) ⇒2logT=logk−logM ⇒2TΔT=MΔM ⇒MΔM=2×10−2
(∵ Given relative uncertainty in period, TΔT=10−2 )