Astronomical Units of Time
Unit Associated Periodic Motion
Day Rotation of Earth on axis
Month Revolution of Moon on orbit
Year Revolution of Earth on orbit

Months and Years

The natural units of time set by the most obvious periodic motions in the sky are the day, the month, and the year. As summarized in the adjacent table, these are correlated with the time interval for rotation of the Earth on its axis, revolution of the Moon in its orbit, and revolution of the Earth in its orbit, respectively. Similar to the sidereal day and solar day, the time units of month and year can be defined in somewhat different ways depending on what reference point we choose to determine when a cycle is complete.
Sidereal and Synodic Months
The month is the period for the Moon to complete one revolution. If this is measured from the Earth with respect to the distant stars, we term this a sidereal month. A sidereal month corresponds to about 27.3 days. On the other hand, if we use the Sun as a reference (that is, we ask how long it takes the Moon to go through a complete set of phases as viewed from Earth), we get a longer period of about 29.5 days. We call this the synodic month.

The sidereal and synodic months differ because of the motion of the Earth on its orbit around the Sun over the period of a month (similar to the reason for the sideral and solar day differing in length). This animation illustrates the difference between sidereal and synodic months.

Sidereal and Tropical Years
The period of revolution of the Earth around the Sun as referenced to the distant stars is called the sidereal year. It has a length of 365.2564 mean solar days. On the other hand, it is also common to define a year as being the interval between two successive returns of the Sun to the vernal equinox. This is called the tropical year, and it has a length of 365.2422 mean solar days. The sidereal year is the "true" year, but our calendar is based on the tropical year because the seasons are correlated with the tropical year.

The sidereal year and the tropical year differ because of precession of the equinoxes (which is caused by the precession of the Earth's rotation axis). Because of precession, the vernal equinox "moves to meet" the Sun a small amount as it goes around the ecliptic, so the Sun returns to the vernal equinox slightly before it returns to the point in the sky where the vernal equinox was one year before. The effect is very small because the rate of precession is slow, but this causes the tropical year to be about 20 minutes shorter than the sidereal year. This animation illustrates the difference between sidereal and tropical years.