Question

The period of the earth around the sun is 1 year and its distance is 150 million km from the sun. An asteroid in a circular orbit around the sun is at a distance 440 million km from the sun. What is the period of the asteroid’s orbit? Answer in units of year.

Answer 1

5.024 years

Step-by-step explanation:

T1 = 1 year

r1 = 150 million km

r2 = 440 million km

let the period of asteroid orbit is T2.

Use Kepler's third law

T² ∝ r³

So,

`\left ( (T_(2))/(T_(1)) \right )^2=\left ( (r_(2))/(r_(1)) \right )^3`

`\left ( (T_(2))/(1) \right )^2=\left ( (440)/(150) \right )^3`

T2 = 5.024 years

Thus, the period of the asteroid's orbit is 5.024 years.