Lesson: Newton’s Law of Universal Gravitation Mathematics

In this lesson, we will learn how to apply Newton’s law of universal gravitation to find the gravitational force between two masses.

Lesson Plan

Students will be able to

recall that, for two bodies, the gravitational force between them, , is calculated using the formula , where is the gravitational constant, and are their respective masses, and is the distance between their centers of mass,
recall the definition of the universal gravitational constant,
calculate the gravitational force for two bodies given their masses and the distance between their centers of mass,
calculate the mass of Earth given its radius and vice versa (assuming that the gravitational force of Earth is equal to 9.8 N),
use the universal law of gravitation to determine the acceleration due to gravity on Earth,
use the relation to compare the accelerations due to gravity on the surfaces of two bodies,
solve problems for particles moving away from or toward Earth’s surface using the law of universal gravitation.

Lesson Presentation

Lesson Video

Lesson Explainer

Lesson Worksheet

Q1:

Find the mass of a planet, given that the acceleration due to gravity at its surface is 6.003 m/s², its radius is 2,400 km, and the universal gravitational constant is N⋅m²/kg².

Q2:

Two planets are separated by a distance of km. The mass of the first is metric tons, and that of the other is metric tons. Given that the universal gravitational constant is N⋅m²/kg², and that 1 metric ton equals 1,000 kilograms, find the force of gravity between them.

Q3:

A planet has a mass of kg and a radius of 5,723 km. Given that the mass of the Earth is kg, its radius is 6,340 km, and the acceleration due to gravity at its surface is 9.8 m/s², find the acceleration due to gravity at the surface of the other planet, approximating your answer to the nearest two decimal places.