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equatorial.jl

Astrometry.SOFA.ae2hd — Function
ae2hd(azimuth::Float64, altitude::Float64, latitude::Float64)

Horizon to equatorial coordinates. Transform azimuth and altitude to hour angle and declination

Input

  • azimuth – azimuth
  • altitude – altitude (informally, elevation)
  • latitude – site latitude

Output

  • equatorial – hour angle and declination

Note

  1. All the arguments are angles in radians.

  2. The sign convention for azimuth is north zero, east +pi/2.

  3. HA is returned in the range +/-π. Declination is returned in the range +/-π/2.

  4. The latitude ϕ is π/2 minus the angle between the Earth's rotation axis and the adopted zenith. In many applications it will be sufficient to use the published geodetic latitude of the site. In very precise (sub-arcsecond) applications, ϕ can be corrected for polar motion.

  5. The azimuth az must be with respect to the rotational north pole, as opposed to the ITRS pole, and an azimuth with respect to north on a map of the Earth's surface will need to be adjusted for polar motion if sub-arcsecond accuracy is required.

  6. Should the user wish to work with respect to the astronomical zenith rather than the geodetic zenith, ϕ will need to be adjusted for deflection of the vertical (often tens of arcseconds), and the zero point of ha will also be affected.

  7. The transformation is the same as Ve = Ry(ϕ-π/2)Rz(π)Vh, where Ve and Vh are lefthanded unit vectors in the (ha,dec) and (az,el) systems respectively and Rz and Ry are rotations about first the z-axis and then the y-axis. (n.b. Rz(π) simply reverses the signs of the x and y components.) For efficiency, the algorithm is written out rather than calling other utility functions. For applications that require even greater efficiency, additional savings are possible if constant terms such as functions of latitude are computed once and for all.

  8. Again for efficiency, no range checking of arguments is carried out.

source
Astrometry.SOFA.hd2ae — Function
hd2ae(HA::Float64, Dec::Float64, ϕ::Float64)

Equatorial to horizon coordinates: transform hour angle and declination to azimuth and altitude.

Input

  • HA – hour angle (local)
  • Dec – declination
  • ϕ – site latitude

Output

  • azimuth – azimuth
  • altitude – altitude (informally, elevation)

Note

  1. All the arguments are angles in radians.

  2. Azimuth is returned in the range 0-2pi; north is zero, and east is +pi/2. Altitude is returned in the range +/- pi/2.

  3. The latitude ϕ is pi/2 minus the angle between the Earth's rotation axis and the adopted zenith. In many applications it will be sufficient to use the published geodetic latitude of the site. In very precise (sub-arcsecond) applications, ϕ can be corrected for polar motion.

  4. The returned azimuth az is with respect to the rotational north pole, as opposed to the ITRS pole, and for sub-arcsecond accuracy will need to be adjusted for polar motion if it is to be with respect to north on a map of the Earth's surface.

  5. Should the user wish to work with respect to the astronomical zenith rather than the geodetic zenith, ϕ will need to be adjusted for deflection of the vertical (often tens of arcseconds), and the zero point of the hour angle ha will also be affected.

  6. The transformation is the same as Vh = Rz(pi)Ry(pi/2-ϕ)Ve, where Vh and Ve are lefthanded unit vectors in the (az,el) and (ha,dec) systems respectively and Ry and Rz are rotations about first the y-axis and then the z-axis. (n.b. Rz(pi) simply reverses the signs of the x and y components.) For efficiency, the algorithm is written out rather than calling other utility functions. For applications that require even greater efficiency, additional savings are possible if constant terms such as functions of latitude are computed once and for all.

  7. Again for efficiency, no range checking of arguments is carried out.

source
Astrometry.SOFA.hd2pa — Function
hd2pa(HA::Float64, Dec::Float64, latitude::Float64)

Parallactic angle for a given hour angle and declination.

Input

  • HA – hour angle
  • Dec – declination
  • latitude – site latitude

Output

  • angle – parallactic angle

Note

  1. All the arguments are angles in radians.

  2. The parallactic angle at a point in the sky is the position angle of the vertical, i.e. the angle between the directions to the north celestial pole and to the zenith respectively.

  3. The result is returned in the range -pi to +pi.

  4. At the pole itself a zero result is returned.

  5. The latitude ϕ is pi/2 minus the angle between the Earth's rotation axis and the adopted zenith. In many applications it will be sufficient to use the published geodetic latitude of the site. In very precise (sub-arcsecond) applications, ϕ can be corrected for polar motion.

  6. Should the user wish to work with respect to the astronomical zenith rather than the geodetic zenith, ϕ will need to be adjusted for deflection of the vertical (often tens of arcseconds), and the zero point of the hour angle ha will also be affected.

References

Smart, W.M., "Spherical Astronomy", Cambridge University Press, 6th edition (Green, 1977), p49.

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