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Dear Aditya
initial radiusof the orbit of satellite is nR
here the gravitation pull of the earth provides the necessary centripital force
hence GMm/r2 =mv2/r where r is the radius of the orbit of satellite at any time and v is the velocity.
hence v=√GM/r
it is given that resistance to motion of satellite issgiven by F=av2
so F=mdv/dt
hence av2=mdv/dt
mdv/v2=adt
integrating with limits of t varying from o to T and that of v varying from √GM/nR to √GM/R
∫mdv/v2=∫adt
m(√nR/GM -√R/GM)=aT
T=m/a*√R/GM*(√n-1)
Good Luck AskIITIANS Expert Abhinav Batra
Good Luck
AskIITIANS Expert
Abhinav Batra
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