Define period of revolution and derive an expression of period of revolution or time peiod of satellite for 1
Answers
Derive an expression of period of revolution or time period of satellite. prasanna 2016-12-24 13:23:00 UTC #2. Period of revolution of a satellite is the time taken by the satellite to complete one revolution round the earth. It is denoted byT. circumference of circular orbit.
Answer:
Time Period of Satellite:
⇒ For a satellite time taken to complete one round around the earth is known as time period of the satellite.
Derivation:
\begin{gathered}\implies \sf T = \dfrac{Circumference\;of\;orbit}{Velocity}\\ \\ \\ \implies \sf T = \dfrac{2\pi r}{v_{o}}\\ \\ \\ \implies \sf T = \dfrac{2\pi r r^{1/2}}{\sqrt{GM}}\\ \\ \\ \implies \sf T = \dfrac{2\pi r^{3/2}}{\sqrt{GM}}\\ \\ \\ \implies \sf T=2\pi\sqrt{\dfrac{r^{3}}{GM}}\\ \\ \\ \sf As\;we\;know,\;r=Re+h\\ \\ \\ \implies {\boxed{\sf T= 2\pi \sqrt{\dfrac{(Re+h)^{3}}{GM}}}}\;\;\;\;.......(1)\end{gathered}
⟹T=
Velocity
Circumferenceoforbit
⟹T=
v
o
2πr
⟹T=
GM
2πrr
1/2
⟹T=
GM
2πr
3/2
⟹T=2π
GM
r
3
Asweknow,r=Re+h
⟹
T=2π
GM
(Re+h)
3
.......(1)