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:

If the gravitational force between two masses was 10 newtons at a certain distance, what would the gravitational force become if that distance was doubled?

Q2:

Determine the gravitational force between two identical balls each of mass 3.01 kg, given that the distance between their centers is 15.05 cm, and the universal gravitational constant is N⋅m²/kg².

Q3:

Given that the gravitational force between two bodies of masses 4.6 kg and 2.9 kg was N, find the distance between their centers. Take the universal gravitational constant .