A new planet MPSM, Mystery Planet of Spartan Men, is discovered following the orbital path of the Mystery Planet of Amazon Women. The gravitational field of the MPSM is measured during a satellite fly-by as 1.33 m/s2 at a distance of 5 planetary radii from the center of MPSM. What is the expected strength of the planet's gravity on its surface?

Explanation:

The strength of the gravitational field at a certain distance from the centre of a planet is given by:

where:

G is the gravitational constant

M is the mass of the planet

The equation can be rewritten as follows:

The term on the right is a constant term, so we can write:

where

is the gravitational field strength at distance

is the gravitational field strength at distance

Here we have:

When (the distance is 5 planetary radii), the gravitational field strength is

where R is the radius of the planet.

Instead at the surface

And so the strength of the gravitational field at the surface is:

be subject to a force andchange its motion