Celestial coordinate system
Astronomical coordinate systems are used to specify the position of celestial bodies. It is spherical coordinates, in the narrow sense to spherical coordinates because for finding the body in the sky whose distance does not matter.
The origin of the astronomical systems is the earth ( its center or a place on their surface, geocentric world view ), the sun ( heliocentric world view ), or another celestial body (such as a planet, relatively specify the location of its moons to himself). It is located in a to be chosen reference plane, within which one of the two astronomical angular coordinates is determined. The second angle is measured perpendicular to the reference plane to the heavenly bodies to be indicated.
The horizon system is the coordinate system that each observer is most familiar. It is located at the origin, the horizon is the reference plane. The angle above the horizon to the celestial body is its height h, the deviation of the point on the horizon directly below the body of the south direction is the azimuth of a
Relative Coordinate Systems
Relative coordinate systems are bound to an observer. They have their reference point at the location of the observer, ie on the surface of the earth, and also local coordinate systems or topocentric coordinate systems are called. Stationed on other celestial bodies observers with the exception of some astronauts who briefly resided on the moon, nor fictitious.
Apart from the horizon above system, there is the local equatorial system. His reference plane is the celestial equator, in the hour angle τ of the upper intersection of the local meridian with the celestial equator is measured from. The origin of the system is theoretically the center of the earth. Because of the small size of the earth relative to the distances of the heavenly bodies, it is mostly irrelevant to move this point to the observer on the Earth's surface. An exception observations from low Earth objects such as the transit of Venus.
Absolute coordinate systems
Have absolute coordinate systems originate in a place relative to the observer neutral point: at the center of the earth, sun or another celestial body or the galactic center. Your reference plane is also not bound to the observer, ie rotates relative to Him.
From the above-mentioned fixed equatorial coordinate system equatorial coordinate system, the rotating emerges ( see figure). It has its origin in the center of the earth also, but seemingly revolves around the Earth. In reality it is dormant, the reference point for the angle measurement in the equatorial plane of the sky is the fixed point in the sky spring. The value specified in the equatorial plane angle is the right ascension α. The declination angle δ is identical to the declination angle in the stationary equatorial system.
With the known as the ecliptic orbital plane in which the Earth orbits the sun once a year, as the reference plane two astronomical coordinate systems are defined. The first of the two ecliptic coordinate systems is the origin in the center of the earth ( geocentric), the second in the center of the Sun ( heliocentric ). In both cases, the angle coordinates are ecliptic longitude λ or ecliptic latitude ( reference point of the vernal equinox is ) called β.
Except topocentric (always relative ) systems, geocentric and heliocentric also barycentric and the galactic coordinate system are used.
The galactic coordinate system has its origin in the galactic center, its reference plane is the disk of the Galaxy.
A baryzentrisches coordinate system for example has its origin in the barycentre (common center of mass) of the Earth and Moon.
Angle data in hours instead of degrees
At the hour angle ( stationary equatorial coordinate system ) and the right ascension (rotating equatorial coordinate system ), the information in hours, minutes and seconds ( Stundenmaß or tempo ) were favored in degrees. The reason the hour angle, is that the change of hour angle of the sun determines the change in time of day. 15 ° change are an hour, that is their original definition.
Cause of this custom in the right ascension is the influence of the Earth's rotation, from which it is in principle independent, on the measurement. Two stars with 15 ° difference in right ascension through the meridian circle an observatory with an hour difference in sidereal time. A sidereal hour is about 10 seconds shorter than an hour. The monitoring plan in an observatory is based on the sidereal time, which is known for each star and can be read on a corresponding clock. This reads 0 clock sidereal time when the vernal equinox (a fictional star ) passes the meridian circle. The time of day running of the sidereal time by one day in the year, just as the sun (apparently) travels once a year backwards through the heavens.
Summary Table
Conversions
The conversions are carried out on the representations in Cartesian coordinates of both systems. Between the Cartesian of the systems is the transformation - a rotation about the y-axis - rather than ( y-coordinates are in both systems ) rotation through the angle 90 ° - φ ( φ = latitude ) in the first to the angle ε ( obliquity of the ecliptic ) in the second case.
In the following tables, the Cartesian coordinates x, y and z of the unit sphere in the target system are given as intermediate results in addition to the final results of conversions. It should be noted that the first two systems (horizontal and resting equatorial ) as a left - systems, the other two ( rotating geocentric equatorial and - ekliptikales ) are defined as legal systems.
Quiescent equatorial ( τ ) ↔ rotating equatorial coordinate ( α )
θ = sidereal time at the place of observation
- α = θ - τ
- τ = θ - α
Horizontal (a, h) → Cartesian coordinates → dormant equatorial coordinates ( τ δ, )
φ = latitude
Cartesian coordinates in the target system ( τ, δ )
- X = cos δ cos τ = cos φ sin φ · sin h cos h cos a
- Y = cos δ · sin τ = cos h · sin a
- Z = sin δ = sin φ · sin h - cos φ cos h cos a
Angular coordinates in the target system
- δ = arcsin (sin φ · sin h - cos φ cos h cos a)
- τ = arctan (sin a / (sin φ cos a cos φ tan · h) )
Quiescent equatorial ( τ, δ ) → Cartesian coordinates → horizontal coordinates (a, h)
φ = latitude
Cartesian coordinates in the target system (a, h)
- X = cos h cos a = - cos φ · sin δ sin φ cos δ cos τ
- Y = cos h · sin a = cos δ · sin τ
- Z = sin h = sin φ · sin δ cos φ cos δ cos τ
Angular coordinates in the target system
- H = arcsin (sin φ · sin δ cos φ cos δ cos τ )
- A = arctan (sin τ / (sin φ cos τ - cos φ · tan ) )
Rotating equatorial ( α, δ ) → Cartesian coordinates → horizontal coordinates (a, h)
φ = latitude, θ = sidereal time at the place of observation
Cartesian coordinates in the target system (a, h)
- X = cos h cos a = - cos φ · sin δ sin φ cos δ cos ( θ - α )
- Y = cos h · sin a = cos δ · sin ( θ - α )
- Z = sin h = sin φ · sin δ cos φ cos δ · cos ( θ - α )
Angular coordinates in the target system
- A = arctan (sin ( θ - α ) / (sin φ cos ( θ - α ) - cos φ · tan ) )
- H = arcsin (sin φ · sin δ cos φ cos δ · cos ( θ - α ) )
Rotating equatorial ( α, δ ) → ecliptic coordinates ( λ, β, geocentric )
ε = 23.44 ° = obliquity of the ecliptic
Cartesian coordinates in the target system ( λ, β )
- X = sin ε · sin δ cos ε · cos δ · sin α
- Y = cos δ cos α
- Z = cos ε · sin δ - sin ε cos δ · sin α
Angular coordinates in the target system
- β = arcsin ( z)
- λ = arccos (y / cos β ) = arccos (y / sqrt ( 1-z ²) )
- λ = arcsin ( x / cos β ) = arcsin (x / sqrt ( 1-z ²) )
Ecliptic ( λ, β, geocentric ) → rotating equatorial ( α, δ ) coordinates
ε = 23.44 ° = obliquity of the ecliptic
Cartesian coordinates in the target system ( α, δ )
- X = sin α cos δ = -sin ε · sin β cos ε · cos β · sin λ
- Y = cos α cos δ = cos β · cos λ
- Z = sin δ = cos ε · sin β sin ε cos β · sin λ
Angular coordinates in the target system
- δ = arcsin (cos ε · sin β sin ε cos β · sin λ )
- α = arctan ( (cos ε · sin λ - sin ε · tan β ) / cos λ )