Question

In the distant future, space explorers from earth discover a new planet. They can measure the radius of the planet to be 7350 km, but they want to know its mass. They observe what the planet has a moon in a circular orbit 32,800 km above the surface of the planet. The moons orbit speed is 3.9 1 km/s.

A) find the mass of the planet

B) how much would a 65 kg person weigh on the surface of this planet? Is this more or less than their weight on earth?

Answer 1

The radius of the orbit of the moon

Where R_p is the radius of the planet and d is the distance of the orbit from the surface of the planet.

We know the orbital velocity is 3.91 km/s, which is given by

Where g_o is acceleration due to gravity at the orbit. Which can be written as

PART A:

Now putting all the values in SI units

So, the mass of the planet is 9.197 x 10²⁴ kg

PART B:

On the surface of the planet, the weight (force) of a 65 kg person can be calculated using this equation

Using expression for Mp for more accuracy

The weight of the person on this planet is 738.55 N

The weight of the person on the earth is 65 x 9.8 = 637 N

So clearly, the person weighs more on the planet than on the earth.