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

What is the period of the asteroid's orbit? Answer in units of year.

The period of the earth around the sun is 1 year and its distance id 150 million km from the sun. An asteriod in a circular orbit around the sun is at a distance 239 million km from the sun.

astrosonu | Student

It is 2.011221777 year of Earth is the asteroid's period.

astrosonuthird | Student

I am right.

neela | Student

We assume that the period of earth and its distance from the sun is T1 and R1.

We assume that the perod of the arteroid is T2 with a distance R2 from the sun.By Newton Kepler's Law,

(T2/T1)^2 = ( R2/R1)^3.

Therefore,

T2 = T1* sqrt[(R2/R1)^3].................(1)

R1 = 150 million km = 150*10^6*10^3= 1.5*10^11 meter. T1 = 1 year. R2 =239million km = 239*10^6*10^3 m = 2.39*10^11 meter. Substituting the values in (1) we get:

T = 1 * sqrt[(239/150)^3]

=2.011221777 year of earth is the asteroid,s period.