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EclipseTrackPlotEclipseBegin, EclipseEnd

6.2 The MoonShadow and SolarEclipse Functions

MoonShadow is useful for computing details of the Moon's shadow during either a total or annular solar eclipse. To determine the precise time of the solar eclipse, use SolarEclipse.

Determing circumstances of solar eclipses.

A total solar eclipse is visible from only a small spot on the Earth, where it can last up to 7.6 minutes. You can use the option Separation to adjust how close the Sun and Moon have to be for the event to be considered an eclipse. The default is Separation -> 1.16*Degree, which is large enough to catch both partial and total solar eclipses. Reduce the separation if you are only interested in total solar eclipses.

Note that the time returned by SolarEclipse is such that the separation of the Sun and the Moon is a local minimum; that is, Separation[Sun, Moon, SolarEclipse[]] is a local minimum.

This is the precise date and time of the middle of the annular solar eclipse in 1994.

In[6]:=SolarEclipse[{1994,1,1}]

Out[6]=

The location of the center of the shadow on the Earth's surface at this time corresponds to a spot in North America. The degree of totality is only 0.89 at this particular time, so only 89% of the Sun is covered by the Moon; hence this is an annular eclipse. The annular eclipse lasts 6.0 minutes.

In[7]:=MoonShadow @ SolarEclipse[{1994,1,1}]

Out[7]=

The precise date and time of the middle of the total solar eclipse in 1994 is shown here.

In[8]:=SolarEclipse[{1994,6,1}]

Out[8]=

In this example, the geographic location is off the coast of Argentina. The degree of totality is now 1.11, so 100% of the Sun is covered; hence this is a total eclipse. The total eclipse lasts 4.3 minutes.

In[9]:=MoonShadow @ SolarEclipse[{1994,6,1}]

Out[9]=

At the time of eclipse, and as viewed from the Moon's shadow on the surface of the Earth, the Sun and Moon are separated by an extremely small angle.

In[10]:=Separation[Sun, Moon, SolarEclipse[{1994,6,1}],
ViewPoint -> %]

Out[10]=

The third rule output from MoonShadow tells you how much of the area of the Sun is covered by the Moon as seen from Earth. The rule, therefore, represents the totality of the eclipse. If the totality is greater than 1, the eclipse is total; if less than 1, the eclipse is annular.

The fourth rule tells you how long the Moon is in front of the Sun as seen from the returned geographic location given by the first two rules. This duration rule is the time interval between when the trailing edge of the Moon enters the solar disk and the leading edge of the Moon leaves the solar disk. Total eclipses, therefore, have a positive duration, but annular eclipses, where the Sun is never fully covered, have a negative duration because the trailing edge of the Moon enters before the leading edge leaves.

The EarthShadow Function

A function related to MoonShadow is EarthShadow, which computes details of the Earth's shadow during a lunar eclipse. To determine the precise time of the lunar eclipse use LunarEclipse.

Determing circumstances of lunar eclipses.

A total lunar eclipse is visible from half the Earth (i.e., the side facing the Moon), where it can last up to 1 hour 44 minutes. A partial lunar eclipse can last 4 hours. Use the option Separation to adjust how close the Sun and Earth have to be, as seen from the Moon, for the event to be considered an eclipse. The default is Separation -> 0.70*Degree, which is large enough to catch both partial and total lunar eclipses. Reduce the separation if you are only interested in total lunar eclipses.

Note that the time returned by LunarEclipse is such that the separation of the Sun and the Moon is a local maximum near 180 degrees. That is, Separation[Sun, Moon, LunarEclipse[]] is a local maximum.

This is the precise time of the middle of a lunar eclipse in 1993.

In[11]:=LunarEclipse[{1993,11,17}]

Out[11]=

The Earth's shadow is only 0.36 degrees away from the Moon at the middle of the lunar eclipse of 1993 November 29. The Moon itself is only half a degree in diameter, so this event is a total lunar eclipse.

In[12]:=Separation[Moon, EarthShadow[%], %]

Out[12]=

The shadow of the Earth during this lunar eclipse is a cone pointing in a direction specified by 4.3 hours of right ascension and 21.5 degrees of declination. The total shadow, at the distance of the Moon, is 1.3 degrees in diameter.

In[13]:=EarthShadow @ LunarEclipse[{1993,11,17}]

Out[13]=

The output from EarthShadow contains information about the size of the umbra and penumbra shadows of the Earth projected at the distance of the Moon. The shadow of the Earth is a cone-shaped region centered on the Sun and passing by the edges of the Earth. The third rule output from EarthShadow gives the angular diameter of the umbra, or total shadow, of the Earth; the second rule gives the angular diameter of the penumbra, or partial shadow.

EclipseTrackPlotEclipseBegin, EclipseEnd



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