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Weighing the Sun and planets
Intermediate
Orbital data give masses of central bodies.
M = 4π²a³/GT²From a planet's orbital radius and period, M = 4π²a³/GT². With Earth's a = 1.496×10¹¹ m and T = 1 yr, M☉ ≈ 2×10³⁰ kg.
Jupiter's moons give Jupiter's mass.
You can find a body's mass from the motion of satellites.
In more detail
Measuring the orbits of planets, moons and satellites gives their masses through Kepler's third law and gravitational dynamics. Spacecraft tracking provides precise values.
Real-world uses
- Mission tracking data reveals the mass of the Moon and planets.
- Astronomers weigh the Sun from the orbits of the planets.
- Astronomers estimate the mass of the Sun or a distant star from the orbits of planets or companion stars.
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Frequently asked questions
How was the Sun weighed?
From the orbits of the planets, using Kepler's third law with Newton's gravity.
Why do we use orbital data?
Because gravity is the only measurable force on large bodies at a distance.
Can I weigh a planet using its moon?
Yes. The moon's orbital period and radius give the planet's mass using Kepler's third law.
Related topics in Gravitation & Orbits
Two-body problem · Effective potential · Binary stars · Gravitational lensing · Gravitational waves · Black holes