Lesson: Newton’s Law of Universal Gravitation Mathematics

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.