Circular Orbits & Orbital Speed
1 · Predict
If you place the satellite in a larger circular orbit, how will the orbital speed it needs to stay on that circle change?
- A wider orbit needs a faster speed
- The speed is the same at every radius
- A wider orbit needs a slower speed
2 · Set Up
- Open the circular-orbit simulation and press Reset.
- Enable the radius (r) probe and the eccentricity (e) readout, and turn on the speed probe.
- For each radius below, launch the satellite tangentially, press Play, and — once e settles near 0 (a true circle) — record its orbital speed.
3 · Collect Data
| Satellite mass m (kg) | Orbit radius r (m) | Orbital speed v (m/s) | Centripetal force F = m·v² / r (N) |
|---|---|---|---|
| 1 | 2 | ||
| 1 | 3 | ||
| 1 | 4 |
Plot orbital speed v (y-axis) against orbit radius r (x-axis). Then plot v against 1/√r and describe which one is a straight line.
4 · Analyze
- Show your work computing v = √(GM/r) with GM = 40 m³/s² for one trial, and compare it to the speed you read from the simulation.
- As the radius increases, does the orbital speed rise or fall? Use numbers from your table to argue whether v ∝ r, v ∝ 1/r, or v ∝ 1/√r.
5 · Extend
- Your data used a 1 kg satellite. Would a 2 kg satellite need a different orbital speed at the same radius? Explain using v = √(GM/r) — does the satellite's own mass appear in it?
- The centripetal force in the last column is supplied entirely by gravity. Explain what would happen to the orbit if the satellite were launched at the same radius but faster than √(GM/r).
The Physics Behind This Experiment
Circular Orbital Speed
For a stable circular orbit, gravity supplies exactly the centripetal force, which fixes the speed at v = √(GM/r). It depends only on the central mass (through GM) and the radius — never on the satellite's own mass.
Centripetal Force
Any body moving in a circle of radius r at speed v is pulled inward with force F = m·v²/r. Here that inward force is provided by the central mass's gravitational attraction.