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Maharashtra Class 10 Answered

How much time would a satellite in an orbit at a height of 35780 km above the earths surface take to complete one revolution around the earth, if the mass of the earth were four times it's original mass?   
Asked by Annonymous4210 | 09 Feb, 2020, 11:39: AM
answered-by-expert Expert Answer
When a Satellite is orbiting around earth with orbital radius R, centripetal force is same as gravitational attraction force
 
Hence we have,    mv2/R  = GMm/R2 ..................(1)
 
where m is mass of satellite, v is speed of satellite, G is gravitational constant and M is mass of earth
 
Let T is period of revolution . By using the substitution v = 2πR/T  in eqn.(1) and after simplification we get, 
 
T begin mathsize 14px style proportional to end style 1/√M 
 
[ Orbital radius R is kept constant ]
 
Hence if mass of earth has increased 4 times , time period will decrease to half of initial value
 
Answered by Thiyagarajan K | 09 Feb, 2020, 02:00: PM

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How much time would a satellite in an orbit at a height of 35780 km above the earths surface take to complete one revolution around the earth, if the mass of the earth were four times it's original mass?   
Asked by Annonymous4210 | 09 Feb, 2020, 11:39: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
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