Newton’s Law of Universal Gravitation

Law of Gravitation

	F	gravitational force	N
	G	universal gravitation constant = 6.67 × 10-11 N·m2/kg2
	m1, m2	masses of objects	kg
	r	distance between objects	m

Acceleration Due to Gravity

	g	acceleration due to gravity	m/s2
	G	universal gravitation constant = 6.67 × 10-11 N·m2/kg2
	mp	mass of planet	kg
	r	radius of planet	m

Tips to Remember

• Always remember that r is the center to center distance between the two objects. For instance, if an astronaut is 2000 km above the earth—which has radius 6400 km—then the center of the astronaut is 2000 km + 6400 km from the center of the earth. That means that r is 8400 km, or 8.4 × 10⁶ m.
• In the formula for the acceleration due to gravity on a planet, r actually is the radius of the planet. That’s because the center to center distance, which is what r measures, is from the center of the planet to the surface, i.e., the planet’s radius.
• When you calculate the force between two objects on earth, expect the answer to be small. Gravity is reallly a very wimpy force; you notice it only because you’re standing on something the size of a planet. You shouldn’t expect to notice the gravitational force between yourself and an object next to you.