Question

A moon is in orbit around a planet. The​ moon's orbit has a semimajor axis of 4.3 times 10 Superscript 8 Baseline m and has an orbital period of 1.516 days. Use these data to estimate the mass of the planet.

Answer 1

The mass of the planet is
`2.7*10^(27)\ kg`.

Step-by-step explanation:

Given that,

Semi major axis
`a= 4.3*10^(8)`

Orbital period T=1.516 days

Using Kepler's third law

`T^2=(4\pi^2)/(GM)a^3`

`M=(4\pi^2)/(GT^2)a^3`

Where, T = days

G = gravitational constant

a = semi major axis

Put the value into the formula

`M=(4*(3.14)^2)/(6.67*10^(-11)(1.516*24*60*60)^2)(4.3*10^(8))^3`

`M=2.7*10^(27)\ kg`

Hence, The mass of the planet is
`2.7*10^(27)\ kg`.