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SpaceDifficulty 1-3

Solar System

The Sun and everything gravitationally bound to it: eight planets, their moons, dwarf planets such as Pluto, and countless smaller bodies including asteroids and comets. The Sun's gravity holds the whole system together and keeps the planets in elliptical orbits described by Kepler's laws of planetary motion.

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Deriving Kepler's Third Law from Newton's Law of Gravitation

For a planet of mass m in a circular orbit of radius r around the Sun (mass M), Newton's law of gravitation supplies exactly the centripetal force needed to keep it in that orbit.

GMmr2=m(2πT)2rG\dfrac{Mm}{r^2} = m\left(\dfrac{2\pi}{T}\right)^2 r

Gravitational force equals the centripetal force required for circular motion with period T.

Rearranging gives Kepler's third law directly, with the proportionality constant made explicit.

T2=4π2GMr3T^2 = \dfrac{4\pi^2}{GM} r^3

Orbital period squared, derived from Newton's law of gravitation for a circular orbit.

Info: This derivation assumes a circular orbit for simplicity; the full result for a genuine elliptical orbit replaces r with the semi-major axis a and requires more advanced orbital mechanics to derive, but yields exactly the same T² ∝ a³ relationship.

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Sources and methodology

  • The Sun contains more than 99% of the Solar System's total mass and gravitationally dominates the orbits of the eight planets.
  • The Solar System's eight planets, in order of increasing distance from the Sun, are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.
  • Planetary orbits around the Sun are ellipses rather than perfect circles, with the Sun at one focus — Kepler's first law of planetary motion.
  • A planet's orbital period squared is proportional to its average orbital distance from the Sun cubed (Kepler's third law), consistent with the measured orbital periods and distances of the Solar System's planets.

Content status: published, last reviewed 30 September 2026.