1. Find the magnitude of the gravitational force a 66.5 kg person would experience while standing on the surface of each of the following planets:
Gravit Force
Planet
Earth
Mars
Pluto
Mass
5.97 x 10^24 kg
6.42 x 10^23 kg
1.25 x 10^22 kg
Radius
6.38 x 10^6 m
3.40 x 10^6m
1.20 x 10^6m

Gravitational forces: Earth: , Mars: , Pluto:

Explanation:

The weight (), measured in newtons, experimented by the person on the surface of the planet is defined by Newton's Laws of Motion:

(1)

Where:

- Mass, measured in kilograms.

- Gravitational acceleration, measured in meters per square second.

From Newton's Law of Gravitation we derive this expression for gravitational acceleration:

(2)

Where:

- Gravitational constant, measured in cubic meters per kilogram-square second.

- Mass of the planet, measured in kilograms.

- Radius of the planet, measured in meters.

By (2) we calculate the gravitational acceleration for each planet:

Earth (, , )

Mars (, , )

Pluto (, , )

Lastly, we calculate the gravitational force for each case by (1):

Earth (, )

Mars (, )

Pluto (, )

the maxium height is 34m/s