Kepler’s Third Law: T² versus a³

Time the orbital period at several semi-major axes. Fit T² versus a³ and recover the hidden GM of the model Sun from slope = 4π²/GM.

Kids· 22 min·Related simulator: Gravity & OrbitsKepler's Laws

Goal

Verify T² ∝ a³ and determine GM from T² = (4π²/GM) a³, so GM = 4π² / slope.

Equipment

Orbit sandbox (model Sun)
Semi-major axis control
Stopwatch

Experiment

Ellipse about a focus. No live period on the bench — the stopwatch fires only when you record.

Lengths are model units (u). The central mass parameter is hidden. Eccentricity is fixed and small: the period depends only on the semi-major axis a.

Semi-major axis aa = 140 u

Stopwatch: no reading

Record at least 6 values of a across 80–200 model units, then fit the data.

Measurements

№	a u	T s	T² s²	a³ u³
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Kepler’s Third Law: T² versus a³

Generated: 24 Aug 2026, 22:29

Goal

Verify T² ∝ a³ and determine GM from T² = (4π²/GM) a³, so GM = 4π² / slope.

Measurement table

#	a (u)	T (s)	T² (s²)	a³ (u³)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted GM agrees with the hidden central mass parameter. Main uncertainties: stopwatch noise and treating the orbit as Keplerian about a fixed Sun.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

Kepler III for a two-body orbit about a fixed central mass is T² / a³ = 4π²/GM. The bench hides the period readout and the ready-made T²/a³ ratio. You time the orbit. Lengths are the simulator’s model units.

Procedure

Eccentricity is fixed and small enough that the period still depends only on a. GM is hidden. You only change the semi-major axis a.
Record. A stopwatch logs the period T of one revolution with small timing noise. There is no live T or T²/a³.
The notebook computes T² and a³. Repeat for at least 6 values of a from about 80 to 200 model units.
Fit T² versus a³; GM = 4π² / slope. Compare with the reference.

Conclusion

The fitted GM agrees with the hidden central mass parameter. Main uncertainties: stopwatch noise and treating the orbit as Keplerian about a fixed Sun.