What is the orbital period of the Moon?
There are two periods involved with the orbit of the Moon around the Earth. This often leads to some confusion, but can be easily understood. Let's investigate!
Measuring the motion of the Moon around the Earth relative to the distant stars leads us to what is called the sidereal period. The sidereal period is the time required for a celestial body within our solar system to complete one revolution with respect to the fixed stars‹i.e., as observed from some fixed point outside the system. The sidereal period of the Moon is the time needed for it to return to the same position against the background of stars.
The Moon appears to move completely around the celestial sphere once in about 27.3 days as observed from the Earth. This is called a sidereal month. It represents the orbital period of the Moon around the Earth.
Measuring the motion of the Moon around the Earth relative to the Sun leads us to what is called the synodic (pronounced si-nod-ik) period. The synodic period is the time required for a body within the solar system, such as a planet, the Moon, or an artificial Earth satellite, to return to the same or approximately the same position relative to the Sun as seen by an observer on the Earth. The Moon's synodic period is the time between successive recurrences of the same phase; e.g., between full moon and full moon.
The Moon takes 29.5 days to return to the same point on the celestial sphere as referenced to the Sun because of the motion of the Earth around the Sun; this is called a synodic month (lunar phases as observed from the Earth are correlated with the synodic month).
Hint: Remember that the Earth moves in its own orbit around the Sun. The synodic period is related to the lunar phases; it depends on the relative locations of the Sun-Earth-Moon. If we start measuring at Full Moon, then one sidereal month later we will not yet be back to a Full Moon, since the Moon must travel further in its orbit around the Earth to reach the relative Sun-Earth-Moon alignment...all because during the 27.3 days of the sidereal month, the Earth moved along in its orbit and now the Moon must "catch up".
Let's do the math! In one sidereal month, the Earth travels about (.985 degrees per day) x (27.321 days) = 26.91 degrees along its orbit around the Sun. The Moon moves at a speed of about 13.17 degrees per day. So to get back to the same relative Sun-Earth-Moon position, the Moon has to travel an additional 26.91/13.17 = 2.043 days. This means that from one lunar phase to the next one a month later, the time interval is 27.321 + 2.043 = 29.365 days. This accounts for nearly all of the synodic month. The rest is taken up by slight differences due to the fact that both orbits (the Earth around the Sun and the Moon around the Earth) are elliptical, not circular.
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