Mechanics

Circular orbit

Watch a near-circular orbit: radius stays steady and eccentricity e ≈ 0.

Circular orbit — interactive Mechanics simulation. Watch a near-circular orbit: radius stays steady and eccentricity e ≈ 0. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.

Circular orbit

A satellite in a circular orbit has just enough tangential speed so centripetal acceleration matches gravitational acceleration.

For a stable circle, v²/r = GM/r², giving v = √(GM/r). The speed is fixed by radius for a given central mass.

• v = √(GM/r)
• T² ∝ r³

Investigation brief

Plan the question before you open the lab

The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.

Driving question

If you place the satellite in a larger circular orbit, how will the orbital speed it needs to stay on that circle change?

Predictions to weigh

• A wider orbit needs a faster speed
• The speed is the same at every radius
• A wider orbit needs a slower speed

Variable roles

What you set:

• Satellite mass m (kg)
• Orbit radius r (m)

What you measure:

• Orbital speed v (m/s)
• Centripetal force F = m·v² / r (N)

How the investigation runs

1. Open the circular-orbit simulation and press Reset.
2. Enable the radius (r) probe and the eccentricity (e) readout, and turn on the speed probe.
3. For each radius below, launch the satellite tangentially, press Play, and — once e settles near 0 (a true circle) — record its orbital speed.

Governing equation

Circular Orbital Speed — v = √(GM / r)

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 — F = m·v² / r

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.

What the printable worksheet asks students to work out

• 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.

Where this shows up beyond the lab

• 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).

• AP Physics 1 — Unit 6: Energy and Momentum of Rotating Systems
• AP Physics C: Mechanics — Unit 6: Energy and Momentum of Rotating Systems
• IB Physics — A.4 Rigid body mechanics
• IB Physics — D.1 Gravitational fields
• General High School Physics — Rotation, gravitation & orbits
• NGSS High School Physics — Gravitational and electrostatic forces

1. Welcome to Grav Circular Orbit
2. Select the satellite
3. Press Play
4. Steady orbit
5. Open the data
6. You did it!

Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.

Open Interactive Lab →

Download lab sheet →

Newton's Law of Universal Gravitation