Question

Uranus has an orbital period of 84.07 years. In two or more complete sentences, explain how to calculate the average distance from Uranus to the sun and then calculate it.

The formula is p^2=a^3

Answer 1

The Average Distance from Uranus to the Sun is 27.506. One way to solve this is by doing the oppsite of how you find the orbitial period. The way you find the orbitial period is by raising the distance to the 3rd. So what i did was take the square root of the orbitial period which is 9.16 and multiplied it by 3 to get 27.506.

Answer 2

Average distance from Uranus to the sun, a = 2.88 billion km

Step-by-step explanation:

It is given that,

Orbital period of Uranus, T = 84.07 years = 2.65 × 10⁹ s

We have to find the average distance from Uranus to the sun. It can be calculated using Kepler's third law as :

`T^2\propto a^3`

or
`T^2=(4\pi^2)/(GM)a^3`

Where

T is orbital period

a is the average distance from Uranus to the sun

G is universal gravitational constant

M is mass of sun,
`m=1.98* 10^(30)\ kg`

`a^3=(T^2GM)/(4\pi^2)`

`a^3=((2.65* 10^9)^2* 6.67* 10^(-11)* 1.98* 10^(30))/(4\pi^2)`

`a^3=2.34* 10^(37)\ m`

`a=2.86* 10^(12)\ m`

a = 2.88 billion km

Hence, this is the required solution.