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EclipseBegin, EclipseEndConjunction, ConjunctionEvents

6.4 The EclipseQ Function

EclipseQ is useful for deciding when an object is eclipsed by a second object from the light of a third object. The diameters of the first and second objects are taken into account, but the third object is treated as a point source.

Testing for eclipses.

The EclipseQ function returns either True or False to questions you input concerning eclipse events. EclipseQ will sometimes tell you something you already know. You can, for example, confirm that the Moon is really eclipsed by the Earth from the Sun during a lunar eclipse. Similarly, you can confirm that the Earth is really eclipsed by the Moon from the Sun during a solar eclipse.

By definition, the Moon is eclipsed during a lunar eclipse.

In[35]:=EclipseQ[Moon, LunarEclipse[]]

Out[35]=

Part of the Earth is eclipsed by the Moon from the Sun during a solar eclipse.

In[36]:=EclipseQ[Earth, Moon, Sun, SolarEclipse[]]

Out[36]=

Other uses of EclipseQ are possible. For instance, a transit of Venus occurred in the year 1769; to determine its precise time you can experiment with different date arguments.

The transit of Venus has not started at this time.

In[37]:=EclipseQ[Sun, Venus, Earth, {1769,6,4,6,0,0}]

Out[37]=

Now Venus is in transit.

In[38]:=EclipseQ[Sun, Venus, Earth, {1769,6,4,9,0,0}]

Out[38]=

Now it has finished its transit.

In[39]:=EclipseQ[Sun, Venus, Earth, {1769,6,4,13,0,0}]

Out[39]=

Of course, the precise beginning and ending of the transit can more easily be determined with EclipseBegin and EclipseEnd.

The transit begins at 06:16 Melbourne time on 1769 June 4.

In[40]:=EclipseBegin[Sun, Venus, Earth, {1762,1,1}]

Out[40]=

It ends 6 hours later at 12:34.

In[41]:=EclipseEnd[Sun, Venus, Earth, {1762,1,1}]

Out[41]=

Additionally, EclipseQ will test for conjunctions or lunar occultations. You can also determine when the Galilean moons Io, Europa, Ganymede, and Callisto undergo, say, a transit or occultation from the Earth, or an eclipse or shadow from the Sun.

This confirms the rare Mars-Venus conjunction in the year 1590.

In[42]:=EclipseQ[Mars, Venus, Earth, {1590,10,13,15,58,0}]

Out[42]=

This verifies the lunar occultation of the star Spica in 1995. The Moon passed directly between the Earth and Spica on 1995 January 23 at 22:00.

In[43]:=EclipseQ[Earth, Moon, Spica, {1995,1,23,22,0,0}]

Out[43]=

On the given date, Io is not in transit across the Jovian disk.

In[44]:=EclipseQ[Jupiter, Io, Earth, {1993,11,17,3,20,0}]

Out[44]=

EclipseBegin, EclipseEndConjunction, ConjunctionEvents



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