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What Was the Importance of Kepler's Third Law?

In the 1600s, astronomer Johannes Kepler formulated three basic laws that accurately described the motions of the planets. The third law, called the Law of Periods, relates the duration of a planet's orbital period to its distance from the sun. Although it may seem abstract at first, the law has implications for the nature of gravity in general and can be used to calculate the masses of the sun and planets.

Law of Periods
- Kepler's Law of Periods states that for the eight known planets that revolve around the sun, the square of the orbital period divided by the cube of the distance equals a constant number called "C." If you apply the law to the orbits of Mercury, Mars and Neptune, for example, C always works out to the same number. The constant contains important information relating to the body about which the planets revolve -- in this case the sun. You can apply the same law to the many moons orbiting Jupiter, for example; here, C is the same for each of Jupiter's moons but different from that obtained for the planets.
Gravitational Constant
- When Isaac Newton formulated his laws of gravity, he studied Kepler's third law and realized the constant, C, contained a universal gravitational constant, G, multiplied by a mass, called "M," which is the mass of the object at the center of the planetary system.
Law of Gravitation
- Newton's Law of Gravity relates the force between two objects by their masses, the distance between them and a universal gravitational constant, "G." The gravitational force increases as the masses increase and decreases as the distance between them gets bigger. Although this law and Kepler's third law have similarities, Newton's is more general; because the sun's mass is so large relative to that of the planets, the simpler forms of Kepler's law ignore planetary masses.
Mass of the Sun
- Using Kepler's and Newton's equations, astronomers were able to "weigh" the sun by first measuring the distance to the sun from the Earth, Mars and other planets, then observing the orbital period of each. By dividing the cube of the average distance between a planet and the sun by the square of the planet's period, dividing by 12.566, then multiplying by the gravitational constant, the resulting number is the sun's mass.
Mass of Planets
- In addition to finding the sun's mass, astronomers applied the same laws to planets that have moons, such as Mars, Saturn and the Earth. By carefully observing and measuring the orbital periods of the moons of these planets, then plugging these numbers into the equation for Kepler's third law, scientists obtained the masses of the planets.

Astronomy