How We Weigh Planets
You can't put Jupiter on a scale. But you can measure its mass with remarkable precision using Kepler's Third Law and Newton's gravitation.
The Method
If an object of known orbital period (T) and semi-major axis (a) orbits a planet or star, you can rearrange the Newtonian form of the Third Law to solve for the central mass:
M = (4π² · a³) / (G · T²)
For example, to find the mass of Jupiter, observe one of its moons. Io orbits Jupiter with T = 1.77 days and a = 421,700 km. Plug in those values and G, and you get Jupiter's mass: approximately 1.90 × 1027 kg.
Applications
- The Sun's mass: Use Earth's orbital data (T = 1 year, a = 1 AU).
- Planet masses: Use the orbits of their moons. See the solar system data table for relevant values.
- Exoplanet host stars: The Kepler telescope measured transit periods; combined with stellar models, this gives the star's mass.
- Binary star masses: See Binary Stars.
- Black holes: Observing stars orbiting the center of the Milky Way allowed astronomers to calculate the mass of the supermassive black hole Sagittarius A*.
Try It
Use the worksheet to practice Third Law calculations, or explore moon data to compute planetary masses yourself.