Question

Neptune is 30 AU away from the Sun on average. Use this distance along with Earth’s (1 AU from the sun and orbits every year) to calculate how many earth years it takes Neptune to orbit the Sun.

Answer 1

given the distance of earth from sun and its orbital period, we can find mass of sun ,

Using Kepler's third law

T² = ( 4² / GM ) r³

(365 * 24 * 60 * 60)² = ( 4² / 6.67e-11 * M ) 1.5e11³

2.9467e-19 = 4² / 6.67e-11 * M

M = 2e30 Kg ( mass of Sun)

sun is central body for Neptune also,

so using same formula.

T² = ( 4² / 6.67e-11 * 2e30 ) ( 30 * 1.5e11)³

T² = 2.685e19

T = 5.181e9 seconds

or

T = 164.32 years

Therefore,

Neptune takes around 164 earth years to complete one orbit.