The synodic periodof the Sun is the apparent period of the Sun as seen from Earth;it is not the true period of the Sun. This is because Earth also moves as we observe a sunspot moving across the surface of Sun. This situation is similar to you trying to measure the speed of a train while sitting in a moving car; your result might be useful in some ways but won't be the true speed of the train.

Since Earth orbits the Sun from west to east as the Sun rotates, the true rotational period of the Sun, known as the sidereal period of rotation, is the time it takes for a point on the Sun to rotate once with respect the distant stars. In the time that it takes a point on the Sun to turn 360 degrees with respect to the stars, the Earth will have moved ahead in its orbit. The Sun will have to rotate a little further to catch up with Earth. Therefore the Synodic period is a bit longer than the sidereal period. Fortunately, we can correct for this added time, since we know how fast the Earth goes around the Sun (about one revolution every 365.25 days). Once you have measured the synodic period, you can determine the sidereal period of the Sun using the formula below:

Sidereal period of the Sun (in days) = (Synodic period x 365.25) / (Synodic period + 365.25)

What is the sidereal period of the Sun? Express your answer in the format of (? x 365.25) / (? + 365.25) = ? days

Caution: when using a calculator, do NOT omit the parenthesis in the formula. For example, the result of (1 x 365.25) / (1 + 365.25) is very different from 1 x 365.25 / 1 + 356.25! Try it with your calculator to find out! Click to view