PH105 Kepler’s Laws of Planetary Motion

In this exercise you are to use Interactive Physics to explore Kepler’s laws of planetary motion and the universal law of gravitation.

Kepler’s 1st law State the 1st law in your own words.

Set up a miniature planetary system in Interactive Physics. Go to the World Menu and choose universal gravity. Place a ‘Sun’ on the screen with a mass of 10¹² kg and a ‘planet’ with a mass of 0.1 kg. By giving the planet an appropriate initial velocity, show how you can establish circular or elliptical orbits.

Choose the velocity so that the orbit is distinctly non-circular. Turn on tracking and run the simulation for one complete orbit. Display velocity, force, and acceleration vectors for the orbiting planet. State where in the orbit the following quantities are the greatest? The least? Explain why.

- speed

- force

- acceleration

- kinetic energy

- potential energy

- total energy

- angular momentum about the sun

The torque acting on the orbiting planet due to the gravitational force is zero. Explain why. What does this say about how the angular momentum of the planet changes?

Kepler’s 2nd law State the 2nd law in your own words.

From the distance between adjacent tracks and the distance between the sun and the planet, you can estimate the area (approximately a triangle) swept out by the radius vector in one time interval. Does it appear that the areas swept out at perihelion and aphelion are approximately the same? (You don’t have to make measurements.) Explain.

Kepler’s 3rd law State the 3^rd law in your own words.

Place a second planet in an orbit beyond the first planet. Give both planets initial velocities so that they each orbit without colliding. Which planet has the greater period? Is this consistent with the third law? Explain.

Measure the period, T, and the semi-major axis, a, for each planet. Is the ratio T²/a³ approximately the same for the two planets?