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MoonShadow, SolarEclipse, EarthShadow, LunarEclipseEclipseQ

6.3 The EclipseBegin and EclipseEnd Functions

EclipseBegin and EclipseEnd are useful for determining the precise times when an object is eclipsed by a second object from the light from 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.

Beginning and ending times of an eclipse.

You can determine, for instance, when the Galilean moon Io is just beginning to be eclipsed from the Sun by Jupiter moving between the two objects. Similarly, you can determine when the Great Red Spot is next visible.

Io is eclipsed from the Sun at 16:46 on 1993 November 18.

In[14]:=EclipseBegin[Io, Jupiter, Sun, {1993,11,17,3,20,0}]

Out[14]=

A short time later, at 17:05, Io moves behind the Jovian disk, as seen from Earth.

In[15]:=EclipseBegin[Io, Jupiter, Earth, {1993,11,17,3,20,0}]

Out[15]=

Io reappears, in sunlight, on the other side of the Jovian disk about two hours later, at 19:17.

In[16]:=EclipseEnd[Io, Jupiter, Earth, {1993,11,17,3,20,0}]

Out[16]=

The Great Red Spot is next visible at 05:45 on 1993 November 17.

In[17]:=EclipseBegin[Jupiter, JupiterGreatRedSpot, Earth,
{1993,11,17,3,20,0}]

Out[17]=

It rotates out of view roughly 5 hours later at 10:43.

In[18]:=EclipseEnd[Jupiter, JupiterGreatRedSpot, Earth,
{1993,11,17,3,20,0}]

Out[18]=

Other Uses

Since three objects are normally supplied to EclipseBegin and EclipseEnd, you can search for many different types of events. Use them for solar and lunar eclipses; satellites disappearing into Earth's shadow; transits of Mercury or Venus across the solar disk; transits, shadows, occultations, and eclipses of the Galilean moons; and lunar occultations of stars by the Moon.

Beginning time of a solar or lunar eclipse.

Beginning time of a transit of Mercury or Venus.

Beginning time of various Jovian moon events.

Beginning time of Great Red Spot visibility.

Beginning time of a lunar occultation.

Beginning time of satellite disappearance.

Although the order of the objects might appear confusing, there is a consistency to it. Remember that the last object is the one treated as a point source, whereas the first two objects are treated as disks of the correct size.

Thus EclipseBegin[Earth, Moon, Sun] determines when any part of the Moon's disk begins to move in front of any part of the disk of the Earth, as viewed from the center of the Sun. This is the time when a partial solar eclipse becomes visible from somewhere on Earth.

Similarly, EclipseBegin[Sun, Moon, TopoCentric] determines when any part of the Moon's disk begins to move between any part of the disk of the Sun and the current location on Earth. This is the time when a solar eclipse becomes visible from the current topocentric location.

A near total solar eclipse occurred over the lower part of the Pacific in February, 1981.

In[19]:=eclipse1981 = SolarEclipse[{1981,2,5}]

Out[19]=

The eclipse nearly passed over Melbourne, Australia. Here the site location of Melbourne is set.

In[20]:=SetLocation[GeoLongitude -> 145.0*Degree,
GeoLatitude -> -37.8*Degree,
GeoAltitude -> 0.0*KiloMeter,
TimeZone -> 11];

The partial eclipse phase begins at 06:33 for observers located at Melbourne, Australia. (TopoCentric represents the location set earlier with SetLocation.)

In[21]:=EclipseBegin[Sun, Moon, TopoCentric, eclipse1981]

Out[21]=

The partial eclipse phase ends at 08:34 for observers located at Melbourne, Australia.

In[22]:=EclipseEnd[Sun, Moon, TopoCentric, eclipse1981]

Out[22]=

The average of the two times above is the approximate time of maximum eclipse for the location. By trial and error minimizing Separation[Sun, Moon, date, ViewPoint->TopoCentric] you find the actual time of maximum eclipse occurs about three minutes earlier.

In[23]:=besttime = {1981,2,5,7,30,59}

Out[23]=

The maximum eclipse happens only an hour after sunrise for observers located at Melbourne.

In[24]:=SunRise[eclipse1981]

Out[24]=

The eclipse appears 9 degrees above the eastern horizon.

In[25]:=HorizonCoordinates[Moon, besttime,
ViewPoint -> TopoCentric]

Out[25]=

This is how the eclipse appeared at its maximum.

In[26]:=PlanetPlot3D[Sun, besttime,
ViewPoint -> TopoCentric,
ViewVertical -> Zenith];

Jovian Moon Events

As mentioned earlier, EclipseBegin and EclipseEnd can be used to determine the precise time of various alignments involving the Earth, the Sun, Jupiter, and a Galilean moon. There are essentially four types of events that can take place.

A Jovian eclipse occurs when a moon of Jupiter is blocked from the light of the Sun; this is an alignment involving the Jovian moon, Jupiter, and the Sun. A Jovian occultation occurs when a moon of Jupiter is hidden behind the Jovian disk as seen from the Earth; this is an alignment involving the Jovian moon, Jupiter, and the Earth. A Jovian shadow occurs when the shadow of a moon of Jupiter passes across the Jovian disk; this is an alignment involving Jupiter, the Jovian moon, and the Sun. A Jovian transit occurs when a moon of Jupiter passes across the Jovian disk as seen from the Earth; this is an alignment involving Jupiter, the Jovian moon, and the Earth.

Here are two functions which compute the disappearance and reappearance times of a Jovian eclipse (i.e., a Jovian moon blocked from the light of the Sun).

In[27]:=EclipseDisappear[jovianMoon_, neardate___] :=
EclipseBegin[jovianMoon, Jupiter, Sun, neardate]

In[28]:=EclipseReappear[jovianMoon_, neardate___] :=
EclipseEnd[jovianMoon, Jupiter, Sun, neardate]

Here are two functions which compute the disappearance and reappearance times of a Jovian occultation (i.e., a Jovian moon hidden behind the Jovian disk).

In[29]:=OccludeDisappear[jovianMoon_, neardate___] :=
EclipseBegin[jovianMoon, Jupiter, Earth, neardate]

In[30]:=OccludeReappear[jovianMoon_, neardate___] :=
EclipseEnd[jovianMoon, Jupiter, Earth, neardate]

Here are two functions which compute the ingress and egress times of a Jovian moon's shadow across the Jovian disk.

In[31]:= ShadowIngress[jovianMoon_, neardate___] :=
EclipseBegin[Jupiter, jovianMoon, Sun, neardate]

In[32]:= ShadowEgress[jovianMoon_, neardate___] :=
EclipseEnd[Jupiter, jovianMoon, Sun, neardate]

Here are two functions which compute the ingress and egress times of a transit of a Jovian moon across the Jovian disk.

In[33]:=TransitIngress[jovianMoon_, neardate___] :=
EclipseBegin[Jupiter, jovianMoon, Earth, neardate]

In[34]:=TransitEgress[jovianMoon_, neardate___] :=
EclipseEnd[Jupiter, jovianMoon, Earth, neardate]

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