Equation of the center

Imagine you are running around a circular race track with your friend. You are both running at the same speed, but your friend is running on the inside lane, while you are running on the outer lane. You will notice that your friend appears to be making tighter turns than you, and seems to be ahead of you at each turn.

Now, let's imagine that instead of a race track, you and your friend are both in circular orbits around the Sun. Just like on the race track, your friend, who is on the inside orbit, will travel a shorter distance in the same amount of time than you, who are on the outer orbit.

Now, let's consider the angle between your friend's position and the Sun, and your position and the Sun. Since your friend is closer to the Sun (and therefore traveling faster), their angle will increase more quickly than yours. This means that over time, your friend will appear to be "ahead" of where they would be if they were both traveling around the Sun at the same speed.

This difference in angle between your friend's position and where they would be if they were traveling at the same speed as you is called the "equation of the center." It's a bit like an adjustment that needs to be made to take into account the different speeds and distances of two planets orbiting the same star.

In summary, the equation of the center is a way to calculate the difference in angle between the position of two objects orbiting around a central body, when they are traveling at different speeds and distances.