Two satellites of the Earth move in a common plane along circular orbits, the radii being `r` and `r-Deltar(Deltar lt lt r)`. What is the time interval between their periodic approches to each other over the minimum distance Take to `M_(c )` to be the mass of the Earth.
`(M_(c )=6xx10^(24)kg`, `r=7000km`, `Deltar=70km`).

Explanation

`T=2pisqrt((r^(3))/(GM))=1.62 hrs` , `dT=(2pi)/(sqrt(GM))xx(3)/(2)r^(1//2)dr`
`(dT)/(T)=(3)/(2)(dr)/(r )`
`df=(3)/(2)xx(70)/(7000)xxT=0.015T`.
Let first satelliete catch up with the second after `n` revolution, then
`nT=(n+1)(T-dT)`
`(n)/(n+1)=0.985rArrn=65.67`
`:. `Periodic time of approach `-nT=106.38 hrs`.