Question

An artificial satellite in a circular orbit around the Sun has a period of 8 years. Determine the ratio of the satellite's orbital radius to that of the earth's orbital radius. Assume that the earth's orbit around the Sun is circular.

Answer 1

Answer:

The ratio is  $R_c:R_e = 4 : 1$

Explanation:

From the question we are told that

   The period of the satellite is  $T_c = 8 \ years$

Generally the period of earth around the sun is $T_e = 1 \ year$

Generally from Kepler's third law , which is mathematically represented as

      $\frac{T_c ^2}{T_e^2} = \frac{R_c^3}{R_e^3}$

Here  $R_c$ is the radius of the orbit which the satellite rotate around the sun

         $R_e$ is the radius of the orbit which the earth rotate around the sun

=>  $\frac{R_c^3}{R_e^3} = [\frac{8}{1} ]^2$

=>   $\frac{R_c}{R_e} = \sqrt[3]{[\frac{8}{1} ]^2}$      

=>   $\frac{R_c}{R_e} = \frac{4}{1 }$      

=>   $R_c:R_e = 4 : 1$