# Lunar Sidereal

### Lunar Sidereal and Synodic Periods

The Moon’s sidereal orbital period (the sidereal month) is ~27.3 days; this is the time interval that the Moon takes to orbit 360° around the Earth relative to the “fixed” stars.

The period of the lunar phases (the synodic month), e.g. the full moon to full moon period, is longer at ~29.5 days.

At New Moon, the Moon is aligned with the Sun. During the lunar month the Earth orbits (revolves) ~30° around the Sun and the Moon orbits (revolves) ~390° to align with the Sun again.

If **P _{SID}** is the Moon’s sidereal orbital period (in days), then the Moon revolves around the Earth at a rate of 360 /

**P**° per day. So in a time interval

_{SID}**t**days, the Moon revolves around the Earth

**t**× 360 /

**P**°.

_{SID}If **P _{YEAR}** is the Earth’s sidereal orbital period (in days), then the Earth revolves around the Sun at a rate of 360 /

**P**° per day and so in

_{YEAR}**t**days the Earth revolves around the Sun

**t**× 360 /

**P**°.We wish to determine the time interval when the angle that the Moon has revolved around the Earth

_{YEAR}**minus 360°**is equal to the angle the Earth has revolved around the Sun.

Hence **t** × 360 / **P _{SID}** − 360 =

**t**× 360 /

**P**

_{YEAR}Divide by **t** × 360, so

1 / **P _{SID}** − 1 /

**t**= 1 /

**P**

_{YEAR}By definition **t** = **P _{SYN}** .

Now **P _{SID}** = 27.32158 days,

**P**= 365.25636 days,

_{YEAR}hence

**P**= 29.53049 days.

_{SYN}