Gamma (eclipse)

Gamma of a central total eclipse. This illustrates solar eclipse gamma: The red line shows the least distance from the center of the Earth, in this case approximately 75% of radius of the Earth. Because the umbra passes north of the Earth's center, gamma in this example is +0.75.

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.

Sign

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.

Limiting cases for solar eclipses on the earth

The absolute value of gamma (denoted as |γ|) allows us to distinguish different kinds of solar eclipses from the earth:[1]

If the Earth were a sphere, the limit for a central eclipse would be 1.0, but because of the oblateness of the Earth (which causes the distance between the Earth's north and south poles to be slightly shorter than if the Earth were perfectly spherical), it is 0.9972.[2]

  • If |γ| is 0, the axis of the shadow cone is exactly between the northern and southern halves of the sunlit side of the Earth when it passes over the center.
  • If |γ| is lower than 0.9972, the eclipse is central. The axis of the shadow cone strikes the Earth and there are locations on Earth, where the Moon can be seen central in front of the Sun. Central eclipses can be total or annular (if the tip of the umbra only barely reaches the surface of the Earth, the type can change during the eclipse from annular to total and/or vice versa; this is called a hybrid eclipse).
  • If |γ| is between 0.9972 and 1.0260, the axis of the shadow cone misses Earth, but, because the umbra or antumbra has a nonzero width, part of the umbra or antumbra may touch down in the polar regions of the Earth. This is called a non-central total or annular eclipse.
  • If |γ| is between 0.9972 and 1.0260 and the special circumstances mentioned above do not occur, or if |γ| is greater than 1.0260 but less than approximately 1.55, the eclipse is partial; the Earth traverses only the penumbra.[3]
  • If |γ| exceeds approximately 1.55, the shadow cone misses the Earth completely, and no eclipse occurs.

The Solar eclipse of April 29, 2014, with a gamma of 1.0001, 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.[4]

References

  1. ↑ J. Meeus: Astronomical Algorithms. 2nd ed., Willmann-Bell, Richmond 2000, ISBN 0-943396-61-1, Chapter 54
  2. ↑ J. Meeus: Mathematical Astronomy Morsels III. Willmann-Bell, Richmond 2004, ISBN 0-943396-81-6, Chapter 6
  3. ↑ The radius of penumbra of the Moon in the fundamental pane is about 0.53 to 0.57 of the Earth's radius.
    J. Meeus: Mathematical Astronomy, Morsels, Willmann-Bell, 2000, ISBN 0-943396-51-4, Fig. 10.c. und
    J. Meeus: Mathematical Astronomy, Morsels III, Willmann-Bell, 2004, ISBN 0-943396-81-6, Page 46
  4. ↑ Fred Espenak: Path of the Annular Solar Eclipse of 2014 Apr 29
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