The Laws of Planetary Motion
Before Newton, Johannes Kepler, using the meticulous observational data of Tycho Brahe, derived three empirical laws that describe the motion of the planets around the Sun.
The Anatomy of an Ellipse
Kepler's first law requires understanding an ellipse.
An ellipse is a shape drawn around two points called foci (singular: focus). For any point on the ellipse, the sum of the distances to the two foci is a constant.
The semi-major axis (a) is half of the longest diameter of the ellipse. It represents the planet's average distance from the Sun.
Eccentricity (e) is a measure of how 'squashed' the ellipse is. An eccentricity of 0 is a perfect circle. An eccentricity close to 1 is a very elongated ellipse.
Kepler's Three Laws
1.Kepler's First Law (The Law of Ellipses): The orbit of every planet is an ellipse with the Sun at one of the two foci.
This overturned the long-held belief in perfect circular orbits.
This means a planet's distance from the Sun is not constant. The closest point is called perihelion, and the farthest point is aphelion.
2.Kepler's Second Law (The Law of Equal Areas): A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
The practical consequence of this law is that a planet moves fastest when it is at perihelion (closest to the Sun) and slowest when it is at aphelion (farthest from the Sun).
3.Kepler's Third Law (The Law of Harmonies): The square of a planet's orbital period (P) is directly proportional to the cube of the semi-major axis (a) of its orbit.
P² ∝ a³
This means that planets that are farther from the Sun have much longer orbital periods (years). This law allows us to calculate the distance of a planet if we know its period, or its period if we know its distance.
Newton later showed that Kepler's laws are a direct consequence of his own Law of Universal Gravitation.