Question

A comet orbits the Sun in 4,063 years. What is its average orbital distance from the Sun? Express your answer in AU (enter "AU" for units) and round it to the nearest integer.
An asteroid orbits the Sun at an average orbital distance of 1.15 AU. What is its average orbital period? Express your answer in years (enter "years" for units) and round it to two decimals.

A moon orbits a planet in 3.5 days. What is the mass of the planet if its average orbital radius is 371,163 kilometers? Express your answer in terms of M_Earth (M_Earth= 5.97 × 10²⁴kg; round your answer to two decimals, no unit required).

Answer 1

(a)

From kepler's third law,

T^2 = r^3

Here, T = Period

r = orbital distance

(4063)^2 = r^3

r^3 = 16507969

r = 255 AU

(b)

Given that,

r = 1.15 AU

Average orbital period,

T^2 = r^3

T = sqrt (1.15³)

T = 1.23 Years