Kepler's Laws Home

Using data on the positions of the planets in the sky compiled largely by Tycho Brahe, Johannes Kepler deduced three laws that account for these motions and published the first two in 1609 and the third in 1619.  They are not only important in their own right, but also because in 1687 Isaac Newton showed that his theory of universal gravitation could account for Kepler's laws of planetary motion.

1. The First Law.

The orbit of a planet is an ellipse with the Sun at one focus.

An ellipse is one of a family of mathematical curves known as conic sections as illustrated on the right.  It is a symetrical oval shape having two principal axes and two points, each a focus.  The Sun is at one of these.
The two principal axes are the major axis, AB, and the minor axis, CD.  Half these are known as the semi-axis major, designated a, and the semi-axis minor, designated b.  The position of the focus, say F1, is such that OF1/OA = e, the eccentricity, itself defined as e = √(1 - b²/a²).  e is a number between 0 (a circle) and 1 (another curve called a parabola).

2. The Second Law

A line segment joining a planet and the Sun sweeps out equal areas in equal intervals of time.

This law sounds very complicated but is only so because it is quantitative.  It is illuntrated on the right.  If the areas of the sectors I have coloured red and green are the same, then the planet takes the same time to go from Q to R as it does to go from S to T.  What this means qualitatively is that the planet moves more quickly when close to the Sun than when further from the Sun.
In the diagram the point P, the closest point to the Sun, is called the perihellion, and the furthest point, A, is the aphelion (pronounced ap-helion).

3. The Third Law

The square of a planet's orbital period is proportional to the cube of the length of the semi-axis major of its orbit.

What this means in simple terms is that the orbital period, P, of a planet is related to its distance from the Sun, R, by the equation P² ∝ R³. If the orbital period is measured in years, and the distance in Astronomical Units (AU), then the equation becomes P² = R³. Bode's Law yields the distance from the Sun in AU and this relationship gives the period in years. To a close approximation anyway.

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