Section 2 review
The law of universal gravitation specifies the mutual force of attraction between two objects. The law states that the force of gravity is proportional to the product of the two objects’ masses and inversely proportional to the square of the distance between them. Gravity is the force that keeps satellites and planets in their orbits, which can be circular or elongated (elliptical). If a planet orbits a star, its orbital speed and period depend on the star’s mass and the distance between the two bodies: The planet’s mass is irrelevant! A black hole is an object whose escape velocity exceeds light speed; it can be studied by the effects it has on other objects, such as the radiation emitted by any mass that falls into it.

For more information to research the historical development of the concept of the gravitational force, see
  • Gravity’s Arc: The Story of Gravity from Aristotle to Einstein and Beyond by D. Darling,
  • On The Shoulders Of Giants by Stephen J. Hawking (ed.), and
  • Gravity’s Engines: How Bubble-Blowing Black Holes Rule Galaxies, Stars, and Life in the Cosmos by C. Scharf.
Read the text aloud
law of universal gravitation, satellite, orbit, orbital period, escape velocity, black hole

F=G m 1 m 2 r 2
R= Gm v 2 v= Gm R

Review problems and questions

  1. Using the formula for the universal law of gravitation, calculate the strength of the gravitational force between two spheres. Each sphere has a mass of 100 kg, and the distance between the centers of the spheres is 2 m. Compare the force to the weight of either sphere. How easy do you think it would be to measure this gravitational force? Read the text aloud Show
  1. A 15.0 kg dog rests on Earth’s surface. Since Earth is nearly spherical, assume that you can pretend that Earth’s mass is all at the planet’s center. Earth’s radius is 6,370 km, and its mass is 5.98×1024 kg.
    1. What is the strength of the gravitational attraction between the dog and the Earth?
    2. Calculate the ratio of this force to the dog’s mass (in kilograms).
    3. What is the significance of the ratio you just computed? Read the text aloud Show
Planets Zorg, Kwazu, and Daewok
  1. Planet Zorg has two moons named Kwazu and Daewok. Kwazu and Daewok have the same mass, but Kwazu is three times as far from Zorg as Daewok is.
    1. Which moon feels a stronger gravitational pull from Planet Zorg?
    2. How many times stronger is the force on that moon when compared to the force on the other (that is, what is the ratio)?
    Read the text aloud Show

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