Sidereal Days and Solar Days

The sidereal day is defined to be the length of time for the vernal equinox to return to your celestial meridian. The solar day is defined to be the length of time for the Sun to return to your celestial meridian. The two are not the same, as illustrated in the following animation.

Because the Earth is in motion on its orbit around the Sun in the course of a day, the Earth must turn about four minutes longer each day (3 minutes and 56 seconds, to be exact) to bring the Sun back to the celestial meridian than to bring the vernal equinox back to the celestial meridian. Thus, the solar day is 3 minutes and 56 seconds longer than the sidereal day. (In this animation the angle corresponding to four minutes of rotation has been exaggerated for clarity.) The difference between the length of the solar and sidereal days for Earth is not very large because the period for the Earth to rotate on its axis is small compared with the period for one revolution around the Sun. For some other planets the difference is much larger, as described in the box below. For example, the length of the solar day on Mercury is two sidereal (Mercury) years.

Technically Speaking: Sidereal and Solar Days for Planets The general formula for the relationship between the true or sidereal rotation period and the length of the solar day for a planet can be expressed as 1/d = 1/R - 1/P where d is the length of the solar day, R is the true (sidereal) rotation period for the planet, and P is the sidereal period of revolution for the planet (with all quantities expressed in the same time units). In using this expression, the quantities d and R are positive numbers if the rotation is prograde (in the same sense as the Earth), and negative numbers if the rotation is retrograde (in the opposite sense of the Earth). For example, Venus has a sidereal rotational period of R = -243 days (negative because it is retrograde) and a sidereal orbital period of P = 224.7 days. Solving the above formula for the length of the solar day d and inserting the numbers for Venus gives d = RP / (P - R) = (-243 d x 224.7 d) / (224.7 d - (- 243 d)) = - 116.7 d with the negative numbers indicating that the rotation of Venus is retrograde. Thus, it takes 116.7 mean solar days for the Sun to return to the celestial meridian on Venus, and the apparent motion of the Sun would be in the opposite sense of the Sun's apparent motion as observed from Earth (west to east on Venus).