Equatorial coordinate system
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The equatorial coordinate system is a widely-used method of mapping celestial objects. It functions by projecting the Earth's geographic poles and equator onto the celestial sphere. The projection of the Earth's equator onto the celestial sphere is called the celestial equator. Similarly, the projections of the Earth's north and south geographic poles become the north and south celestial poles, respectively.
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[edit] Use in astronomy
The equatorial coordinate system allows all earthbound observers to describe the apparent location in the sky of sufficiently distant objects using the same pair of numbers: the right ascension and declination. For example, a given star has roughly constant equatorial coordinates. In contrast, in the horizontal coordinate system, a star's position in the sky is different based on the geographical latitude and longitude of the observer, and is constantly changing based on the time of day.
The equatorial coordinate system is commonly used by telescopes equipped with equatorial mounts by employing setting circles. Setting circles in conjunction with a star chart or ephemeris allow a telescope to be easily pointed at known objects on the celestial sphere.
Over long periods of time, precession and nutation effects alter the Earth's orbit and thus the apparent location of the stars. Likewise, proper motion of the stars themselves will affect their coordinates as seen from Earth. When considering observations separated by long intervals, it is necessary to specify an epoch (frequently J2000.0, for older data B1950.0) when specifying coordinates of planets, stars, galaxies, etc.
[edit] Declination
The latitudinal angle of the equatorial system is called declination (Dec for short). It measures the angle of an object above or below the celestial equator.[1][2] Objects in the northern celestial hemisphere have a positive declination, and those in the southern celestial hemisphere have a negative declination. For example, the north celestial pole has a declination of +90°.
[edit] Right ascension
The longitudinal angle is called the right ascension (RA for short). It measures the angle of an object east of the apparent location of the center of the Sun at the moment of the March equinox, a position known as the vernal equinox point or the first point of Aries.[1] The vernal equinox point is one of the two points where the ecliptic intersects with the celestial equator. Unlike geographic longitude, right ascension is usually measured in sidereal hours instead of degrees, because an apparent rotation of the equatorial coordinate system takes 24 hours of sidereal time to complete. There are (360 degrees / 24 hours) = 15 degrees in one hour of right ascension.
[edit] Hour angle
When calculating geography-dependent phenomena such as sunrise or moonrise, right ascension may be converted into hour angle as an intermediate step.[3] A celestial object's hour angle is measured relative to the observer's location on the Earth; a star on the observer's celestial meridian at a given moment in time is said to have a zero hour angle. One sidereal hour later (approximately 0.997269583 solar hours later), the Earth's rotation will make that star appear to the west of the meridian, and that star's hour angle will be +1 sidereal hour.
[edit] GEI Coordinates
There are a number of cartesian variants of equatorial coordinates. The most common of these is called the geocentric equatorial inertial (GEI) coordinate system.
- GEI coordinates have the z-axis pointing along the axis of rotation of the earth (north positive), the x-axis pointing in the direction of the Sun during the vernal equinox and the y-axis defined as the cross product of z and x (in that order) to create a right-handed coordinate system. Like the polar variants described above, the direction of the x-axis drifts due to orbital precession and thus an epoch must be specified.
- In this context, J2000.0 can also refer not just to the Julian 2000 Epoch, but also to the entire GEI coordinate frame at that epoch.
- GEI systems are also sometimes "True of Date". This means that the epoch at the exact moment at which the data is collected is used as the epoch of the coordinate system.
- The direction of the x-axis is also described as the first point of the constellation Aries.
- This system is often used for describing the state vectors of spacecraft as well as various phenomena in space physics.[4][5][6]
[edit] See also
[edit] References
- ^ a b Peter Duffett-Smith. Practical Astronomy with Your Calculator, third edition. Cambridge University Press. pp. 28–29. ISBN 0521356997.
- ^ Meir H. Degani (1976). Astronomy Made Simple. Doubleday & Company, Inc. p. 216. ISBN 0-385-08854-X.
- ^ Peter Duffett-Smith. Practical Astronomy with Your Calculator, third edition. Cambridge University Press. pp. 34–36. ISBN 0521356997.
- ^ Geocentric coordinate systems, http://sspg1.bnsc.rl.ac.uk/Share/Coordinates/geo_sys.htm
- ^ Space physics coordinate systems, http://www.iki.rssi.ru/vprokhor/coords.htm
- ^ Christopher T. Russell, Geophysical Coordinate Transformations, http://dawn.ucla.edu/personnel/russell/papers/gct1.html/
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