Mechanics · Quick Reference

Gravitation Cheat Sheet

Mechanics · Lesson 17/19

In one line: gravity is the force that pulls every mass in the universe toward every other mass — from apples falling to the ground to entire galaxies staying bound together.

Key Ideas

1Newton's Law of Universal Gravitation. Every two masses attract each other with a force F = G*m1*m2/r^2, where G is the gravitational constant, and r is the distance between their centers.

2The Gravitational Constant (G). G ≈ 6.674 x 10^-11 N*m^2/kg^2, an extremely small number reflecting how weak gravity is compared to other fundamental forces at everyday scales.

3Gravitational Field Strength (g). The force per unit mass at a location; near Earth's surface, g ≈ 9.8 m/s^2, which is also the acceleration experienced by any freely falling object there.

4Weight vs. Mass. Mass measures the amount of matter in an object (constant everywhere); weight = m*g measures the force of gravity on that mass (which changes depending on location, like the Moon vs. Earth).

5Orbital Motion. A satellite in orbit is really in continuous free-fall, with gravity providing exactly the centripetal force needed to keep it moving in a circular (or elliptical) path.

Worked Examples

Find the weight of a 70 kg person on Earth (g=9.8 m/s^2).

686 N

The Moon's gravity is about 1/6th of Earth's. Find the weight of the same 70 kg person on the Moon.

Approximately 114.3 N (much less than on Earth, though mass stays 70 kg)

If the distance between two masses doubles, how does the gravitational force between them change?

The force becomes 1/4 as strong

Formulas

F = G*m1*m2/r^2

Weight = m*g

Practice Yourself

Find the weight of a 50 kg person on Earth (g=9.8).

490 N

If distance between two masses triples, how does force change?

Becomes 1/9 as strong (divided by 3^2)

What is the difference between mass and weight?

Mass is the amount of matter (constant); weight is the force of gravity on that mass (varies by location)