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Coordinate SystemsHorizonCoordinates, Refract

3.1 The EquatorCoordinates Function

Equator coordinates are useful in conjunction with star charts.

Calculating an object's position in equator coordinates.

EquatorCoordinates is typically applied to solar system objects such as Mars, Moon, and Io; stars such as Sirius and Alpha.Centaurus; constellations such as Leo and UrsaMajor; special objects such as SouthCelestialPole and Zenith; and so on.

Here you see that Mars is 21.6 degrees below the celestial equator, with a right ascension of 16.2 hours.

In[3]:=EquatorCoordinates[Mars, {1993,11,17,3,20,0}]

Out[3]=

In the EquatorCoordinates output, the first rule is used to represent the right ascension of the object, which is the angle (in hours) around the celestial equator. The second rule is used to represent the declination, which is the angle above the celestial equator. An AU is the standard astronomical unit, which equals about 149,597,900km and is the mean distance between the Earth and the Sun. Hour is used to denote the unit of right ascension, and equals exactly 15 degrees of angle.

Distance is typically given in astronomical units, as this is a sensible unit for measurement within the solar system. However, units of kilometers are used when a distance is less than 0.01 AU, and light years are used when a distance is greater than 1,000 AU. One light year equals about 63,240 AU.

The Sun is 0.988773 AU distant from the Earth on the given date.

In[4]:=EquatorCoordinates[Sun, {1993,11,17,3,20,0}]

Out[4]=

The distance to the Moon is 373,502 kilometers (or 0.00253 AU) on the given date.

In[5]:=EquatorCoordinates[Moon, {1993,11,17,3,20,0}]

Out[5]=

The ascension, declination, and distance of the Moon is now slightly different than in the previous call.

In[6]:=EquatorCoordinates[Moon, {1993,11,17,3,20,0},
ViewPoint -> TopoCentric]

Out[6]=

You can use the option setting ViewPoint -> object to specify any viewpoint. The default is the center of the Earth (i.e., Earth), but you can specify any other object. For instance, TopoCentric is used to specify the point on the surface of the Earth where you previously set your location.

With a TopoCentric viewpoint, the position of the Moon will appear slightly displaced relative to the position obtained using the default Earth viewpoint. For most objects, which are much further away than the Moon, it does not matter if you use TopoCentric or Earth as the viewpoint.

You can also find the equator coordinates of a star. The syntax for specifying a star name is the dot notation star.constellation, although the brightest 25 stars have been given aliases, so, for example, you can use Sirius, Canopus, and Polaris as star names.

Stars have fixed equator coordinates-that is, they do not change with time. (Actually they do change a little due to the precession of the Earth's axis, but the effect is very small. Use the option Epoch to see the effect.)

Here are the fixed equator coordinates of the star Alpha (alpha) Centauri.

In[7]:=EquatorCoordinates[Alpha.Centaurus, {1993,11,17,3,20,0}]

Out[7]=

This gives the equator coordinates of the point currently 30 degrees above the horizon and 60 degrees east of north on the given date.

In[8]:=EquatorCoordinates[{Azimuth -> 60*Degree,
Altitude -> 30*Degree},
{1993,11,17,3,20,0}]

Out[8]=

Allowing for Precession

The option Epoch is available in many functions, including EquatorCoordinates. The default setting is Epoch -> Automatic, which specifies the current epoch for the plane of the Earth's equator. However, you can use, say, Epoch -> 2000.0 to have ascension and declination returned relative to the equator at epoch year 2000.

Allowing for the effect of precession.

Precession causes the plane of the equator to rotate about 50 arc-seconds per year, and this precession makes an epoch specification necessary.

Use Epoch to find the epoch 2000.0 coordinates of the star Alpha (alpha) Centauri.

In[9]:=EquatorCoordinates[Alpha.Centaurus, Epoch->2000.0]

Out[9]=

The numbers are very slightly different for the epoch 1950.0 coordinates.

In[10]:=EquatorCoordinates[Alpha.Centaurus, Epoch->1950.0]

Out[10]=

The EclipticCoordinates Function

Equator coordinates measure the position of an object relative to the plane passing through the Earth's equator. Ecliptic coordinates, in contrast, measure the position relative to the plane of the Earth's orbit. The two planes are tilted by just 23.5 degrees, and so the coordinate systems are closely related.

Calculating an objects position in ecliptic coordinates.

In the EclipticCoordinates output, the first rule is used to represent the value of the ecliptic longitude of an object. The value will be very close to the right ascension of the object. Similarly, the second rule is used to represent the value of the ecliptic latitude. The value will be close (within 23.5 degrees) to the declination of the object.

By definition the ecliptic latitude of the Sun is zero.

In[11]:=EclipticCoordinates[Sun, {1993,11,17,3,20,0}]

Out[11]=

On the same date, Mars is just 0.44 degrees below the ecliptic line. It has an ecliptic longitude of 245 degrees.

In[12]:=EclipticCoordinates[Mars, {1993,11,17,3,20,0}]

Out[12]=

Coordinate SystemsHorizonCoordinates, Refract



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