Question

the period of moon around earth is 27.3 days and the radius of its orbit is 3.9*10*10*10*10*10 km.find the mass of the earth

Answer 1

Given:

Time period = 27.3 days

Radius = 3.9 * 10^5 km

To find:

The mass of the earth

Solution:

By formula,

Time period = 2 π √ ( Radius )^3 / Gravity * mass

Here,

π = 3.14

Gravity = 6.67 * 10^-11

Substituting,

We get,

27.3 = 2 * 3.14 ( 3.9 * 10^5 )^3 / 6.67 * 10^-11 * Mass

Solving for mass,

Mass = 2 * ( 3.14 )^2 * ( 3.9 )^3 * 10^15 / 3.335 * 10^11 * ( 27.3 )^2

Hence,

Mass ≅ 6.05 * 10^24 kg

Answer 2

Time take will be = 2 * pi * root (r^3 / GM)

27.3 = 2 * 3.14 * root [(3.84 * 10^5)^3 / 6.67 * 10^-11 * M]

On solving the equation further,

M = 2 * (3.14)^2 * (3.84)^3 * 10^15 / 3.335 * 10^-11 *27.3^2 = 6.02 * 10^24

Hence, earth’s mass = 6.02 * 10^24