Gravitation and Kepler’s Laws - Iowa State University

[Pages:7]Gravitation and Kepler's Laws

Useful Equations

Kepler's Laws

1. A planet's orbit around the sun is the shape of an ellipse with the sun at one focal point

2. The area swept out between two points in a planet's orbit is always constant with respect to time

3. The square of the orbital period is proportional to the cube of the semi-major axis length

Warmup Problem

You are an astronaut on another planet and want to experimentally determine the gravitational acceleration of the planet. If you determine the period of a simple pendulum with a length of 0.75 m to be 3 s, what is the surface gravity of the planet?

Example Problem

When an object passes the event horizon of a black hole, nothing can escape from its gravitational pull, including light (v = 3*10^8 m/s). If the black hole has a mass of 4 million solar masses (8.15*10^36 kg), what is the event horizon radius?

Example Problem

Given that on average, Saturn is 9 times further away from the sun than earth, what is Saturn's orbital period in Earth years?

Final Questions

State Kepler's laws in your own words How can Kepler's third law be used to measure the mass of other planets? Besides kinematics, what are some ways gravitational acceleration can be measured?

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