Question

10. A certain planet orbits the Sun with a period of 84 years. What is its distance from the Sunin Astronomical Units? (1 AUthe average distance between the Earth and the Sun)

Answer 1

From Kepler's third law, there relationship between the period and average distance between the earth and the sun is expressed as

P^2 = a^3

where

P = sidereal period in years

a = average distance between the earth and the sun

From the information given,

P = 84

By subsituting the value into the formula, we have

84^2 = a^3

7056 = a^3

Taking the cuberoot of both sides,

`\begin{gathered} a\text{ = }\sqrt[3]{7056} \\ a\text{ = }19.2 \end{gathered}`

The distance is 19.2 AU