Gamma (denoted as γ) of an eclipse describes how centrally the shadow of the Moon or Earth strikes the other body. This distance, measured at the moment when the axis of the shadow cone passes closest to the center of the Earth or Moon, is stated as a fraction of the equatorial radius of the Earth or Moon.
The sign of gamma defines, for a solar eclipse, if the axis of the shadow passes north or south of the center of the Earth; a positive value means north. The Earth is defined as that half which is exposed to the Sun (this changes with the seasons and is not related directly to the Earth's poles or equator; thus, the Earth's center is wherever the Sun is directly overhead).
For a lunar eclipse, it defines whether the axis of the Earth's shadow passes north or south of the Moon; a positive value means south.
Gamma changes monotonically throughout any single saros series. The change in gamma is larger when Earth is near its aphelion (June to July) than when it is near perihelion (December to January). Gamma decreases for ascending nodes and increases for descending nodes. This simple rule describes the current behavior of gamma, but this has not always been the case. The eccentricity of Earth's orbit is presently 0.0167, and is slowly decreasing. It was 0.0181 in the year -2000 and will be 0.0163 in +3000. In the past, when the eccentricity was larger, there were Saros series in which the trend in gamma reversed for one or more Saros cycles before resuming its original direction. These instances occur near perihelion when the Sun's apparent motion is highest and may, in fact, overtake the eastward shift of the node. The resulting effect is a relative shift west of the node after one Saros cycle instead of the usual eastward shift. Consequently, gamma reverses direction.
The absolute value of gamma (denoted as |γ|) distinguishes between different types of solar eclipses that are seen on Earth. [1]
If the Earth were a perfect sphere, the maximum value of |γ| that a central eclipse [α] could have would be 1.0. However, due to the oblateness of the Earth (which causes the length of the Earth's polar radius to be about 20 km shorter than the equatorial radius), the maximum value of |γ| that a central eclipse could have is 0.9972. [2]
|γ| | Type of eclipse | Notes |
---|---|---|
0 | Central [α] | The axis of the shadow cone is exactly between the northern and southern halves of the sunlit side of the Earth |
between 0 and 0.9677826 | Central [α] | |
between 0.9677826 and 0.9972 | Central [α] (one limit) | One edge of the shadow cone misses the Earth |
between 0.9972 and 1.0266174 | non-central | The axis of the shadow cone misses Earth, but, portions of the umbra or antumbra do intersect the Earth (generally in the polar regions) given the shadow cone's nonzero width. |
between 1.0266174 and approximately 1.55 [β] | Partial | |
Greater than approximately 1.55 [β] | No eclipse |
The Solar eclipse of April 29, 2014, with a gamma of -0.99996, is an example of the special case of a non-central annular eclipse. The axis of the shadow cone barely missed Earth's south pole. Thus, no central line could be specified for the zone of annular visibility. [3]
The next non-central eclipse in 21st century is total solar eclipse of April 9, 2043.
There are three types of lunar eclipses:
The gamma is the limit of:
|γ| | Type of eclipse | Notes |
---|---|---|
0 | Central lunar eclipse | The Moon's center passes exactly through the axis of the Earth's umbral shadow |
between 0 and 0.2725 | Central lunar eclipse | At least part of the Moon's disk passes through the axis of the Earth's umbral shadow |
between 0.2725 and 0.48 | Total lunar eclipse | The entire Moon's disk passes through the Earth's umbral shadow |
between 0.44 and 1.0266174 | Partial lunar eclipse | Part of the Moon's disk passes through the Earth's umbral shadow |
between 0.987 and 1.0266174 | Total penumbral lunar eclipse | The entire Moon's disk passes through the Earth's penumbral shadow without entering the Earth's umbral shadow |
between 1.0266174 and approximately 1.55 | Penumbral lunar eclipse | Part of the Moon's disk passes through the Earth's penumbral shadow without entering the Earth's umbral shadow |
Greater than approximately 1.55 | No eclipse |