Kepler's Second Law

Kepler Second Law 

see Kepler's First Law

Figure %: A planet sweeps out equal areas in equal times.

1. If we draw a line from the sun to the planet in question (a radius), then as the planet moves around in its orbit it will sweep out some area $A_1$ in time $t$. If we consider the planet elsewhere on its orbit, then over the same time interval $t$ its radius will sweep out another area, $A_2$. Kepler's Second Law states that $A_1 = A_2$. This law is often referred to as the "law of equal areas."
2. Alternatively, any two radial lines between the sun and the elliptical orbit of a planet form some area (for convenience let us again call this $A_1$). The points where these radii intersect the orbit are labeled $p_1$ and $q_1$. We then choose two more radial lines that form another area $A_2$ that is equal in size to $A_1$ and label the points where these radii intersect $p_2$ and $q_2$. Then Kepler's Second Law tells us that the time taken for the planet to pass between points $p_1$ and $q_1$ is equal to the time taken to pass between points $p_2$ and $q_2$.

Keplers Second Law means that the closer a planet is to the sun, the faster it must be moving on its orbit. When the planet is far away from the sun, it only has to move a relatively small distance in order to sweep out a large area. However, when the planet is close to the sun it must move a lot further in order to sweep out an equal area. This can be seen most clearly in .