Question

The distance between Pluto and the Sun is 39.1 times more than the distance between the Sun and Earth. Calculate the time taken by Pluto to orbit the Sun in Earth days.

Answer 1

Step-by-step explanation:

Given

Distance between Pluto and sun is 39.1 times more than the distance between earth and sun

According to Kepler's Law

`T^2=kR^3`

where k=constant

T=time period

R=Radius of orbit

Suppose
`R_1` is the radius of orbit of earth and sun

so Distance between Pluto and sun is
`R_2=39.1\cdot R_1`

`T_1` and
`T_2` is the time period corresponding to
`R_1` and R_2[/tex]

`(T_1)^2=k(R_1)^3---1`

`(T_2)^2=k(R_2)^3---2`

divide 1 and 2

`((365)/(T_2))^2=((R_1)/(39.1))^3`

`T_2^2=365^2* 39.1^3`

`T_2=89239.67\ Earth\ days`