Magnitude of eclipse
Encyclopedia
The magnitude of eclipse or geometric magnitude is the fraction of the diameter of the eclipsed body which is in eclipse. This applies to both solar eclipse
s and lunar eclipse
s. During a partial or annular eclipse the magnitude of the eclipse is always between 0.0 and 1.0, while during a total eclipse the magnitude is always at least 1.0. If the magnitude is less than 0.0 there is no eclipse.
Technically, the magnitude is computed as such: draw a straight line between the centers of the eclipsed body and the eclipsing body (or shadow). Find out how large a fraction of this line within the eclipsed body is in eclipse; this is the geometric magnitude of the eclipse. If the eclipse is total, one can extend this line in one direction to the nearest limb of the eclipsing body (or shadow) and obtain a geometric magnitude larger than 1.0. If there is no eclipse but a near miss, one can also extend the line towards the nearest limb of the eclipsing body (or shadow), counting this distance as negative, and obtain a negative geometric magnitude.
This measure should not be confused with the astronomical magnitude
logarithm
ic scale of brightness. It should neither be confused with the obscuration of the eclipse, which is the fractional area which is eclipsed.
, the magnitude of the eclipse is the ratio between the apparent angular diameter
s of the Moon
and that of the Sun
during the eclipse, yielding a ratio less than 1.0.
In a total solar eclipse which also is a central eclipse, the magnitude is also the ratio between the apparent diameters of the Moon and of the Sun, but this time the ratio is 1.0 or bigger. If the total solar eclipse is non-central, the magnitude is a number between 1.0 and this ratio of apparent diameters.
In a partial solar eclipse, the magnitude of the eclipse is the fraction of the Sun's diameter occulted by the Moon at the time of maximum eclipse.
The Moon's and Sun's apparent sizes are approximately the same, but both vary because the distance between Earth
and Moon varies. (The distance between Earth and Sun also varies, but the effect is slight in comparison.)
When the magnitude of the eclipse is larger than one, the Moon's disk will completely cover the Sun's disk in the sky, and so the eclipse will be total. The path of totality (i.e. of the travelling shadow of the Moon cutting off all sunlight from reaching the Earth's surface) is a relatively narrow strip, at most a few hundreds of kilometers across.
When the magnitude of the eclipse is less than one, the disk of the Moon cannot completely cover the Sun. When the centers of the two disks are sufficiently aligned, a ring of sunlight remains visible around the Moon. This is called an annular eclipse, from Latin
annulus, meaning "ring".
The eclipse magnitude varies not only between eclipses, but also during a given eclipse. It may happen that an eclipse starts out as annular, and then becomes total. The reverse is also possible. In very rare cases, the eclipse may proceed from annular, via total, back to annular. These mixed-type eclipses are called hybrid.
Also, as seen from one location, the momentary eclipse magnitude varies, being exactly 0.0 at the start of the eclipse, rising to some maximum value, and then decreasing to 0.0 at the end of the eclipse. When one says "the magnitude of the eclipse" without further specification, one usually means the maximum value of the magnitude of the eclipse.
and the much brighter penumbra. A lunar eclipse will have two geometric magnitudes: the umbral magnitude and the penumbral magnitude. If the maximum value of the umbral magnitude is negative, the Moon doesn't reach into the Earth's umbra - it may still pass through the Earth's penumbra though, and such an eclipse is called a penumbral eclipse.
Solar eclipse
As seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
s and lunar eclipse
Lunar eclipse
A lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
s. During a partial or annular eclipse the magnitude of the eclipse is always between 0.0 and 1.0, while during a total eclipse the magnitude is always at least 1.0. If the magnitude is less than 0.0 there is no eclipse.
Technically, the magnitude is computed as such: draw a straight line between the centers of the eclipsed body and the eclipsing body (or shadow). Find out how large a fraction of this line within the eclipsed body is in eclipse; this is the geometric magnitude of the eclipse. If the eclipse is total, one can extend this line in one direction to the nearest limb of the eclipsing body (or shadow) and obtain a geometric magnitude larger than 1.0. If there is no eclipse but a near miss, one can also extend the line towards the nearest limb of the eclipsing body (or shadow), counting this distance as negative, and obtain a negative geometric magnitude.
This measure should not be confused with the astronomical magnitude
Apparent magnitude
The apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...
logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
ic scale of brightness. It should neither be confused with the obscuration of the eclipse, which is the fractional area which is eclipsed.
Effect of the magnitude on a solar eclipse
In an annular solar eclipseSolar eclipse
As seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
, the magnitude of the eclipse is the ratio between the apparent angular diameter
Angular diameter
The angular diameter or apparent size of an object as seen from a given position is the “visual diameter” of the object measured as an angle. In the vision sciences it is called the visual angle. The visual diameter is the diameter of the perspective projection of the object on a plane through its...
s of the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
and that of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
during the eclipse, yielding a ratio less than 1.0.
In a total solar eclipse which also is a central eclipse, the magnitude is also the ratio between the apparent diameters of the Moon and of the Sun, but this time the ratio is 1.0 or bigger. If the total solar eclipse is non-central, the magnitude is a number between 1.0 and this ratio of apparent diameters.
In a partial solar eclipse, the magnitude of the eclipse is the fraction of the Sun's diameter occulted by the Moon at the time of maximum eclipse.
The Moon's and Sun's apparent sizes are approximately the same, but both vary because the distance between Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
and Moon varies. (The distance between Earth and Sun also varies, but the effect is slight in comparison.)
When the magnitude of the eclipse is larger than one, the Moon's disk will completely cover the Sun's disk in the sky, and so the eclipse will be total. The path of totality (i.e. of the travelling shadow of the Moon cutting off all sunlight from reaching the Earth's surface) is a relatively narrow strip, at most a few hundreds of kilometers across.
When the magnitude of the eclipse is less than one, the disk of the Moon cannot completely cover the Sun. When the centers of the two disks are sufficiently aligned, a ring of sunlight remains visible around the Moon. This is called an annular eclipse, from Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
annulus, meaning "ring".
The eclipse magnitude varies not only between eclipses, but also during a given eclipse. It may happen that an eclipse starts out as annular, and then becomes total. The reverse is also possible. In very rare cases, the eclipse may proceed from annular, via total, back to annular. These mixed-type eclipses are called hybrid.
Also, as seen from one location, the momentary eclipse magnitude varies, being exactly 0.0 at the start of the eclipse, rising to some maximum value, and then decreasing to 0.0 at the end of the eclipse. When one says "the magnitude of the eclipse" without further specification, one usually means the maximum value of the magnitude of the eclipse.
Effect of the magnitude on a lunar eclipse
The effect on a lunar eclipse is quite similar, with a few differences. First, the eclipsed body is the Moon and the eclipsing 'body' is the Earth's shadow during a lunar eclipse. Second, since the Earth's shadow at the Moon's distance always is considerably larger than the Moon, a lunar eclipse can never be annular but is always partial or total. Third, the Earth's shadow has two components: the dark umbraUmbra
The umbra, penumbra and antumbra are the names given to three distinct parts of a shadow, created by any light source. For a point source only the umbra is cast.These names are most often used to refer to the shadows cast by celestial bodies....
and the much brighter penumbra. A lunar eclipse will have two geometric magnitudes: the umbral magnitude and the penumbral magnitude. If the maximum value of the umbral magnitude is negative, the Moon doesn't reach into the Earth's umbra - it may still pass through the Earth's penumbra though, and such an eclipse is called a penumbral eclipse.