Mechanics
Kepler's third law
After one full orbit, compare measured T²/r³ to 4π²/GM.
Kepler's third law — interactive Mechanics simulation. After one full orbit, compare measured T²/r³ to 4π²/GM. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Kepler's third law
For a circular orbit, the square of the period is proportional to the cube of the radius: T² ∝ r³.
Combining centripetal force with gravity gives the orbital period. Comparing T and r for different orbits reveals the same T²/r³ ratio for a given central mass.
- T²/r³ = 4π²/GM
- v = 2πr/T
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
A satellite circles a central mass in a stable circular orbit. When you move it to a larger orbit radius, how does the time for one full revolution change?
Predictions to weigh
- A larger orbit takes longer per revolution.
- The period stays the same at any radius.
- A larger orbit takes less time per revolution.
Variable roles
What you set:
- Orbit radius r (m)
What you measure:
- Circular speed v (m/s)
- Measured period T (s)
How the investigation runs
- Open the grav-kepler-law preset. A satellite orbits the central mass; the orbit timer and period probe are already attached.
- Set the satellite's orbit radius r, then launch it sideways at the circular-orbit speed shown on the v = √(GM/r) formula card so the orbit stays circular.
- Let the satellite complete at least one full loop and read the orbital period T from the timer once the orbit is steady.
Governing equation
Kepler's Third Law — T² / r³ = 4π² / GM
For any orbit around a given central mass, the period squared is proportional to the mean radius cubed: T²/r³ = 4π²/GM. The ratio is the same for every orbit, so timing one orbit at a known radius reveals GM.
Circular Orbital Speed — v = √(GM / r)
A body in a circular orbit of radius r must travel at v = √(GM/r): the speed that makes gravity supply exactly the centripetal force needed. Launching at this speed keeps the orbit circular rather than elliptical.
What the printable worksheet asks students to work out
- For each row compute T²/r³. Are the three values roughly equal? Compare their average to 4π²/GM using GM = 40 (so 4π²/GM ≈ 0.99 s²/m³).
- Your T²-vs-r³ line should pass through the origin. Explain why that straight-line, through-origin shape is exactly what T² = (4π²/GM)·r³ predicts, and what the slope represents.
Where this shows up beyond the lab
- Real planets obey the same law: Mercury (small orbit) races around the Sun in 88 days while Neptune (large orbit) takes 165 years. Use T²/r³ = constant to explain this huge difference.
- Kepler's constant here is 4π²/GM, so it depends on the central mass, not on the satellite. Predict what happens to every orbit's period if GM of the central body were doubled.
- 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
- Welcome to Grav Kepler Law
- Select the satellite
- Press Play
- Period and radius
- Open the data
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
Kepler's Laws of Planetary Motion