A $$geo-stationary$$ satellite is orbiting the earth at a height at a above the surface of the earth, R being the radius of the earth. The time period of another satellite at a height of $$2.5R$$ from the surface of earth is

Question

Infinity Learn · Accepted Answer

The time period of a satellite orbiting at a distance r from the centre of the earth is given $$byT2=4$$$$π$$$$2r3GM2For$$ two satellites at distances $$r1$$ and $$r2$$, we $$haveT1T2=r1r23/2or$$ $$T2=T1r2/r13/2For$$ geostationary satellite,$$T1$$ $$=1day$$ $$=24hoursand$$ $$r1=6R+R=7RFor$$ other satellite $$r2=2$$⋅$$5R+R=3$$⋅$$5R$$∴ $$T2=24$$×$$(3$$⋅$$5R/7R)3/2=24$$×$$(1/2)3/2$$                                              $$=62$$ hours

A geo-stationary satellite is orbiting the earth at a height at a above the surface of the earth, R being the radius of the earth. The time period of another satellite at a height of 2.5R from the surface of earth is

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