Orbit and Phases of the Moon and Planets

The orbit of the Moon is very nearly circular (eccentricity ~ 0.05) with a mean separation from the Earth of about 384,000 km, which is about 60 Earth radii. The plane of the orbit is tilted about 5 degrees with respect to the ecliptic plane.

Revolution in Orbit

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, and reflects the corresponding orbital period of 27.3 days 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).  There are effects that cause small fluctuations around this value that we will not discuss. Since the Moon must move Eastward among the constellations enough to go completely around the sky (360 degrees) in 27.3 days, it must move Eastward by 13.2 degrees each day (in contrast, remember that the Sun only appears to move Eastward by about 1 degree per day). Thus, with respect to the background constellations the Moon will be about 13.2 degrees further East each day. Since the celestial sphere appears to turn 1 degree about every 4 minutes, the Moon crosses our celestial meridian about 13.2 x 4 = 52.8 minutes later each day.

Lunar Phases

The Moon appears to go through a complete set of phases as viewed from the Earth because of its motion around the Earth, as illustrated in the following figure. 

Phases of the Moon

In this figure, the various positions of the Moon on its orbit are shown (the motion of the Moon on its orbit is assumed to be counter-clockwise). The outer set of figures shows the corresponding phase as viewed from Earth, and the common names for the phases.

Perigee and Apogee

The largest separation between the Earth and Moon on its orbit is called apogee and the smallest separation is called perigee. Here is an online Lunar Perigee and Apogee Calculator that will allow you to determine the date, time, and distance of lunar perigees and apogees for a given year (Credit: John Walker). 

Rotational Period and Tidal Locking

The Moon has a rotational period of 27.3 days that (except for small fluctuations) exactly coincides with its (sidereal) period for revolution about the Earth. This is no coincidence; it is a consequence of tidal coupling between the Earth and Moon. Because of this tidal locking of the periods for revolution and rotation, the Moon always keeps essentially the same face turned toward the Earth (small fluctuation mean that over a period of time we can actually see about 55% of the Lunar surface from the Earth). 

The Planets

The planets, as viewed in the sky, exhibit characteristic aspects and phases. "Aspects" refers to the location of the planet with respect to our overhead sky reference (objects on the celestial sphere); "phases" refers to the fact that the planets, through a telescope, exhibit phases (differing amounts of lighted hemispheres as viewed from the earth). The terminology associated with these aspects and phases is different, depending on whether we refer to an inferior planet or a superior planet.

Aspects and Phases of the Inferior Planets

The inferior planets exhibit the aspects and phases illustrated in the following diagram.

Gibbous phases are phases between quarter and full phases. Greatest Elongation refers to the largest separation of the planet from the Sun in our sky, either to the East, or to the West. Thus, we see that the inferior planets exhibit a complete set of phases (just like the Moon) as viewed from the earth, and can never be further from the Sun than the angles defined by greatest elongation. 

Aspects and Phases of the Superior Planets

The aspects and phases of the superior planets differ from those of the inferior planets because of geometry: their orbits are outside that of the Earth. These aspects and phases are indicated in the following diagram. 

When a superior planet is at quadrature, it is on our celestial meridian at sunrise or sunset.  Comparing with the preceding diagram for the inferior planets, we notice two basic differences: (1) The superior planets do not exhibit a full range of phases; they are always gibbous or full. (2) The superior planets can be located at any distance East or West of the Sun in our sky, unlike the inferior planets where there is a limiting angle away from the Sun (greatest elongation).

10/01/2017