Kepler’s Laws describe the motion of the planets around the Sun.
The planets orbiting the Sun have an elliptical orbit and so it is important to understand ellipses.
Ellipses
The below diagram shows an ellipse. They look like a squashed circle and have two focal points, indicated below by F1 and F2.
The Major Axis – this is the longest diameter of an ellipse, each end point is called a vertex. The axis passes from one vertex, through the centre and to the opposite vertex. The major axis is the widest part of an ellipse.
The Minor Axis – this is the shortest diameter of an ellipse, each end point is called a co-vertex. The axis passes from one co-vertex, through the centre and to the opposite co-vertex. The minor axis is the narrowest part of an ellipse.
The Semi-major Axis (a) – half of the major axis. It passes from one vertex to the centre.
The Semi-minor Axis (b) – half of the minor axis. It passes from one co-vertex to the centre.
Eccentricity (e) – the distance between the two focal points, F1 and F2, divided by the length of the major axis.
ae – the distance between one of the focal points and the centre of the ellipse (the length of the semi-major axis multiplied by the eccentricity).
If you have any questions about this, please leave them in the comments below. Soon I hope to have another post dedicated to ellipses and will share the link here once it is up.
Kepler’s Laws of Planetary Motion
Let’s move on to the reason you came here, Kepler’s Laws. There are three Laws that apply to all of the planets in our solar system:
First Law – the planets orbit the Sun in an ellipse with the Sun at one focus.
The diagram below exaggerates the eccentricity.
FUN FACT: The orbit of Earth around the Sun is almost circular. It’s eccentricity varies from almost 0 to around 0.07, it is currently around 0.017!
Second Law – the line connecting the planet to the sun sweeps out equal areas in equal times.
This law arises from the conservation of angular momentum.
In the below diagram if the planet travels from a to b in the same time it takes for it to travel from c to d, Area 1 and Area 2 must be equal, as per this law.
As you can see though, the distance a-b is much greater than the distance of c-d, therefore the planet must travel faster closer to the Sun.
Third Law – the square of the period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
We have the following equation:
Where T is the orbital period, G is the Gravitational Constant, M is the mass of the Sun and a is the semi-major axis.
This can be expressed simply as:
From this law we can see that the closer a planet is to the Sun the shorter its orbit.
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