Question

The period of moon around the earth is 27.3 days and radius of the orbit is 3.9 into 10 to the power 5 km equals to 6.67 into 10 to the power minus 11 newton per metre square per kg square find the mass of the earth

Answer 1

The mass of the earth is 7.39 x 10²⁴ kg.

Explanation:

Given ,

T = 27.3 days = 27.3 x 86400 sec

r = 3.9 x 10⁵ km = 3.9 x 10⁸ m

G = 6.67 x 10⁻11

We know that time period of a satellite,

T = 2π$\sqrt{r^3 /GM}$

=>M   = (4π² x 3.9³ x 10²⁴)/(27.3² x 86400² x 6.67 x 10⁻¹¹)

=> M = 7.39 x 10²⁴ kg.

Hence the mass of the earth is 7.39 x 10²⁴ kg.