Kepler’s Laws

Kepler’s Laws

  1. The law of orbits: All planets move in elliptical orbits, with the sun at one focus.
  2. The law of areas : A line that connects a planet to the sun sweeps out equal areas in equal times.
  3. The law of periods : The square of the period of any planet is proportional of the cube of the semi major axis of its orbit.

1st law

a = semi major axis of ellipse
e = eccentricity of the ellipse

Orbit Eccentricity
The eccentricity of an ellipse can be defined as the ratio of the distance between the center of the ellipse and one focus to the semi major axis of the ellipse.
The eccentricity is zero for a circle. Of the planetary orbits, only Pluto has a large eccentricity

Because of this different eccentricities, planets have their own orbits.

2nd law

A planet orbiting the sun sweeps out equal areas in equal times.

In this image, the planet takes the same time to move from A to B as it takes to move from X to Y . The green and blue shaded areas are equal. The planet speeds up when it is closer to the sun.

3rd law

The square of the period of any planet is proportional of the cube of the semi major axis of its orbit.

After applying Newton’s law of motion and Newton’s law of gravity, we find in modern notation, it becomes,

References:
Kepler’s Third Law of Motion

~Gawesha Gunasinghe

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