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3. Coordinate Functions
A system of coordinates is needed to represent the position of any object in space. This chapter discusses the systems that are built into Scientific Astronomer.
Coordinate Systems
The Earth's equatorial plane, when extended out into the sky, forms a great circle known as the celestial equator. The Sun moves along another great circle known as the ecliptic, which, due to the tilt of the Earth's axis, is inclined to the celestial equator by an angle of about 23.5 degrees. These two great circles intersect at two points known as equinoxes. One is called the vernal equinox and is the position of the Sun at about March 21 of each year. The other is the autumnal equinox.
You can use the celestial equator and the vernal equinox to define a coordinate system known as celestial coordinates, or equator coordinates. The equator coordinates system specifies the position of an object by its right ascension and declination. Right ascension measures the angle, in hours of time, from the vernal equinox along the celestial equator; declination measures the angle north of the celestial equator. Stars have fixed equator coordinates, unlike the planets, which continually wander through the celestial sphere, although always staying near the ecliptic. Sirius, the brightest star, has a fixed right ascension of 6h45m and a declination of -16°43'. The EquatorCoordinates function finds the equator coordinates of an object (such as a planet, the Moon, the Sun, or a star) on a given date.
Equator coordinates are useful in conjunction with star charts. There is, however, another more natural coordinate system that is useful out in the field and is based on the horizon. It is known as alt-azi coordinates, or more commonly as horizon coordinates.
Horizon coordinates specifies the position of an object by its azimuth and altitude. Azimuth measures the compass angle around the local horizon with 0 degrees being north and 90 degrees being east, and altitude measures the angle above the local horizon with +90 degrees being overhead and -90 degrees being an unviewable point directly below the observer. Apart from geo-stationary satellites, no object normally has fixed horizon coordinates because the local horizon constantly changes throughout the night. The HorizonCoordinates function finds the horizon coordinates of an object on a given date.
Yet another coordinate system is known as ecliptic coordinates. This system specifies the position of an object by its ecliptic longitude and latitude. Ecliptic longitude measures the angle around the plane of the Earth's orbit, with 0 degrees being the so-called first point in Aries. Ecliptic latitude measures the angle above the plane of the ecliptic. The EclipticCoordinates function finds the ecliptic coordinates of an object on a given date.
Complications
The Earth's axis gyrates around the pole of the ecliptic in a period of about 25,800 years. This effect, known as precession, can shift the celestial coordinates of objects by a few minutes of arc over several years. Stars, therefore, are not completely fixed on the celestial sphere, and the published celestial coordinates assigned to each star are valid only for a specified epoch, usually taken as 1950 January 1 or 2000 January 1. Most functions in Scientific Astronomer accept the option Epoch to let you choose something other than the current epoch.
Setting Your Site Location
As normal, before you use Scientific Astronomer, you must load the package and set your time zone and location on Earth.
Load the package.
In[1]:=<<Astronomer`HomeSite`
This sets your location to Melbourne, Australia.
In[2]:=SetLocation[GeoLongitude -> 145.0*Degree,
GeoLatitude -> -37.8*Degree,
GeoAltitude -> 0.0*KiloMeter,
TimeZone -> 11];
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