Question

The earth takes 1 year to revolve around the sun at 1 A.U. distance (an astronomical unit = 93,000,000 miles). If a planet were 4 A.U. from the sun, how many years would it take to make 1 orbit?

Answer 1

8 years

Step-by-step explanation:

We can solve the problem by using Kepler's third law, which states that the cube of the radius of the orbit of a planet is proportional to the square of its orbital period. We can rewrite this law as follows:

`(r_1^3)/(T_1^2)=(r_2^3)/(T_2^2)`

where

`r_1 = 1 AU` is the distance of the Earth from the Sun

`T_1=1 y` is the Earth's orbital period

`r_2 =4 AU` is the distance of the planet from the Sun

`T_2` is its orbital period

By re-arranging the equation and substituting the numbers, we can find T2:

`T_2 = \sqrt{(r_2^3 T_1^2)/(r_1^3)}=\sqrt{((4AU)^3(1y)^2)/((1 AU)^3)}=√(4^3)=√(64)=8 y`