Lesson Plan: Newton’s Law of Universal Gravitation Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to apply Newton’s law of universal gravitation to find the gravitational force between two masses.


Students will be able to

  • recall that, for two bodies, the gravitational force between them, 𝐹, is calculated using the formula 𝐹=πΊπ‘šπ‘šπ‘ŸοŠ§οŠ¨οŠ¨, where 𝐺 is the gravitational constant, π‘šοŠ§ and π‘šοŠ¨ are their respective masses, and π‘Ÿ 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 𝑔𝑔=π‘šπ‘šΓ—π‘Ÿπ‘ŸοŠ§οŠ¨οŠ§οŠ¨οŠ¨οŠ¨οŠ¨οŠ§ 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.


Students should already be familiar with

  • the kinematic equations,
  • uniform acceleration,
  • vertical motion due to gravity.


Students will not cover

  • problems where mass is variable.

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