Question

You are given a following data
G=9.81m/s^2.
R=6.67×10^6m
distance of the moon= 3.84×10^8m
Time period of moon revolution=27.3days Obtain mass of the earth in two different ways

Answer 1

The mass of earth is 5.97×10^24 kg and 6.02×10^24 kg respectively.

Explanation:

Given data:

G=9.81 m/s^2

R=6.67×10^6 m

Distance of moon (r) = 3.84×10^8m

Time period "T" = 27.3 days =27.3×24×60×60 s

1st method:

Me = gRe^2/G

      = 9.81×(6.37×106)^2 / 6.67×10−11

       =5.97×10^24 kg

2nd method:

mr(2π/T^2) = GMem/r^2

OR

Me=4π^2r^3 / GT^2

= 4×(22/7)^2 × (3.84×10^8)^3 / 6.67×10^−11 × (27.3×24×60×60)^2

= 6.02×10^24 kg

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