Kepler’s Laws Orbit Worksheet
Goal: Use Kepler’s laws to connect an orbit’s size and shape to its period and to the planet’s changing speed.
What to do
- Press the “Earth-like” preset and record the readouts in the table.
- Press “Mars-like” and record the readouts.
- Set Semi-major axis to 4, Eccentricity to 0 and Star mass to 1. Record the readouts.
- Press “Stretched orbit”. Record the readouts with Orbit progress at 0% (closest to the star), then at 50% (farthest). Press Play simulation and watch the speed change.
- Set Semi-major axis to 1, Eccentricity to 0 and Star mass to 2. Record the readouts.
Record your results
| Setting | Orbital period | Current speed | Star distance |
|---|---|---|---|
| Earth-like | |||
| Mars-like | |||
| a = 4 AU, e = 0 | |||
| Stretched orbit, 0% progress | |||
| Stretched orbit, 50% progress | |||
| a = 1 AU, e = 0, star mass 2 |
Questions
Kepler’s third law says P² = a³ for a Sun-like star (P in years, a in AU). Predict the period for a = 4 AU before checking your table. Show your work.
How long is a year on Mars, in Earth years? Do planets farther from the Sun take more or less time per orbit?
In the stretched orbit, how fast is the planet moving at its closest point and at its farthest point? About how many times faster is it when close?
Kepler’s second law says the line from star to planet sweeps out equal areas in equal times. Use it to explain your answer to question 3.
The stretched orbit (a = 3 AU) takes about 5.2 years. Predict: if you set Eccentricity to 0 and keep a = 3 AU, will the period change? Test it.
What happened to the period when the star’s mass doubled? Why?
Free from The Astronomy Lab · theastronomylab.com · MS-ESS1-2: Model the role of gravity in the motions within galaxies and the solar system. HS-ESS1-4: Use mathematical or computational representations to predict the motion of orbiting objects.