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Grade 11Mechanics

If the orbital velocity of moon is 1020m/s,find the time taken by the moon to complete one revolution around the eath.explain why this period is different from the period that is obseved from the earth which is 29.5day.

Profile image of Deepesh kumar Lall
14 Years agoGrade 11
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1 Answer

Profile image of Devesh Lall
ApprovedApproved Tutor Answer14 Years ago

SOLUTION

Let the time taken by the moon to complete 1 revolution around the earth be T

'     '   orbital velocity of the moon be vo = 1020m/s = √[(r + h)/GM]

'     '   radius of the earth be r = 6.4 X 106 m

'     '   distance of moon from the earth be h = 3.4 X 108 m 

Since we know that the time period is given by :- T=2∏√[(r + h)3/GM] [Here G ---> Gravitational Constant and M --> Mass of earth]

Therefore now

 T = 2∏√[(6.4 X 106 + 3.4 X 108)/6.67 X 10-11 X 6 X 1034] sec

On simplifying this you will get your answer.