Question

Determine the distance between a newly discovered planet and its single moon if the orbital period of the moon is 1.2 Earth days and the mass of the planet it orbits is 9.38E24 kg.You may assume the orbit to be circular.

Answer 1

The distance is
`r = 55430496 \ m`

Step-by-step explanation:

From the question we are told that

The period of the moon
`T = 1.2 days = 1.2 * 24 * 3600 = 103680 \ s`

The mass of the planet is
`m_p = 9.38*10^(24) kg`

Generally the period of the moon is mathematically represented as

`T = 2 * \pi * \sqrt{ (r^3 )/( G * m_p ) }`

Here G is the gravitational constant with value

`G = 6.67 *10^(-11) \ N \cdot m^2/kg^2`

=>
`T = 2 * \pi * \sqrt{ (r^3 )/( G * m_p ) }`

=>
`103680 = 2 * 3.142 * \sqrt{ (r^3 )/( 6.67*10^(-11) * 9.38*10^(24) ) }`

=>
`272218492.31 = (r^3)/( 6.67 *10^(-11) * 9.38*10^(24))`

=>
`r = \sqrt[3]{ 1.7031241*10^(23)}`j

=>
`r = 55430496 \ m`