The mean distance of an asteroid from the Sun is 3.90 times that of Earth from the Sun. From Kepler's law of periods, calculate the number of years required for the asteroid to make one revolution about the Sun.

Number of years for the asteroid to make one revolution about the sun is 2.83 years

Explanation:

The square of the period , T of any planet in a circular orbit with radius, r is given by:

T^2= (4pi^2/Gm) × r^3 ...eq1

For earth,T^2earth= (4pi^2/Gm) × r^3 ...

eq2

Where m is mass of the sun

Divide eq1 by eq2 , you get:

T^2/T^2earth = (r/rearth)^3

Substituting r=2reath , we get:

T^2/T^2earth =( 2rearth/rearth)^3

T/Tearth = Sqrt(8)

T/Tearth= 2.83

The period the earth revolves around the sun is 1 year

T/1 = 2.83

T= (1 × 2.83)years

T = 2.83 years