Kepler's third law from planetary data

The idea

For every body orbiting the same central mass, the cube of the orbital radius divided by the square of the period is the same constant, fixed by the central mass.

What you need

• NASA planetary fact sheet values for distance from the Sun and orbital period (Mercury to Neptune)
• Spreadsheet or graph paper

How to do it

1. Tabulate each planet's mean distance r (in metres) and period T (in seconds) from the NASA fact sheet.
2. Compute r^3 / T^2 for every planet and compare the values.
3. Plot log T against log r and read the gradient.
4. Compute G M_sun / (4 pi^2) from the fact sheet's GM and compare with the mean r^3 / T^2.
5. Predict the period of a body at 2.0 astronomical units and check by the same rule.

What you should see

Using the fact sheet's rounded distances and periods, r^3 / T^2 lies between 3.358e18 m^3/s^2 (Mercury) and 3.448e18 m^3/s^2 (Neptune) for all eight planets (Earth 3.363e18, Jupiter 3.370e18), and GM_sun / (4 pi^2) = 3.362e18 m^3/s^2 with GM_sun = 1.32712e20 m^3/s^2. The least-squares gradient of log T against log r is 1.498. A body at 2.0 astronomical units has a period of 2.83 years (1033 days). Earth's period computed from GM_sun and its semimajor axis 1.49598e11 m is 365.26 days.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

• Planets farther out move faster to cover their bigger orbits; they move slower and take longer.
• Kepler's constant is the same for every system; it depends on the central mass.

Safety card

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

• Physics Stage 6 Syllabus (2017), current: Year 11 until the end of 2026, Year 12 until Term 3 2027PH12-12PH11/12-4PH11/12-5
• Physics 11-12 Syllabus (2025), not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027, first HSC examination 2028PY-12-01PY-12WS-05
• Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

1. www.nsw.gov.au/sites/default/files/noindex/2025-03/physics-stage-6-syllabus-2017.docx
2. education.nsw.gov.au/content/dam/main-education/en/home/schooling/curriculum/science/science-s6-physics-module-5-advanced-mechanics.docx
3. nssdc.gsfc.nasa.gov/planetary/factsheet
4. nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
5. nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
6. curriculum.nsw.edu.au/learning-areas/science/physics-11-12-2025/outcomes