Question

The radius of a planet is 2400 km, and the acceleration due to gravity at its surface is 3.6 m/s2.

What is the mass of the planet?

Answer 1

`3.1\cdot10^(23)\:\mathrm{kg}`

Step-by-step explanation:

We can use Newton's Universal Law of Gravitation to solve this problem:

`g_P=G(m)/(r^2)`., where
`g_P` is acceleration due to gravity at the planet's surface,
`G` is gravitational constant
`6.67\cdot 10^(-11)`,
`m` is the mass of the planet, and
`r` is the radius of the planet.

Since acceleration due to gravity is given as
`m/s^2`, our radius should be meters. Therefore, convert
`2400` kilometers to meters:

`2400\:\mathrm{km}=2,400,000\:\mathrm{m}`.

Now plugging in our values, we get:

`3.6=6.67\cdot10^(-11)(m)/((2,400,000)^2)`,

Solving for
`m`:

`m=(2,400,000^2\cdot3.6)/(6.67\cdot 10^(-11)),\\m=\fbox{$3.1\cdot10^(23)\:\mathrm{kg}$}`.