spacemotion.jl

pvstar(pv::Vector{Vector{Float64}})

Convert star position & velocity vector to catalog coordinates.

Input (Note 1)

• pv – pv-vector (AU, AU/day)

Output (Note 2)

• ra – right ascension (radians)
• dec – declination (radians)
• pmr – RA proper motion (radians/year)
• pmd – Dec proper motion (radians/year)
• px – parallax (arcsec)
• rv – radial velocity (km/s, positive = receding)

Note

1. The specified pv-vector is the coordinate direction (and its rate of change) for the date at which the light leaving the star reached the solar-system barycenter.

2. The star data returned by this function are "observables" for an imaginary observer at the solar-system barycenter. Proper motion and radial velocity are, strictly, in terms of barycentric coordinate time, TCB. For most practical applications, it is permissible to neglect the distinction between TCB and ordinary "proper" time on Earth (TT/TAI). The result will, as a rule, be limited by the intrinsic accuracy of the proper-motion and radial-velocity data; moreover, the supplied pv-vector is likely to be merely an intermediate result (for example generated by the function eraStarpv), so that a change of time unit will cancel out overall.

   In accordance with normal star-catalog conventions, the object's right ascension and declination are freed from the effects of secular aberration. The frame, which is aligned to the catalog equator and equinox, is Lorentzian and centered on the SSB.

   Summarizing, the specified pv-vector is for most stars almost identical to the result of applying the standard geometrical "space motion" transformation to the catalog data. The differences, which are the subject of the Stumpff paper cited below, are:

   (i) In stars with significant radial velocity and proper motion, the constantly changing light-time distorts the apparent proper motion. Note that this is a classical, not a relativistic, effect.

   (ii) The transformation complies with special relativity.

3. Care is needed with units. The star coordinates are in radians and the proper motions in radians per Julian year, but the parallax is in arcseconds; the radial velocity is in km/s, but the pv-vector result is in au and au/day.

4. The proper motions are the rate of change of the right ascension and declination at the catalog epoch and are in radians per Julian year. The RA proper motion is in terms of coordinate angle, not true angle, and will thus be numerically larger at high declinations.

5. Straight-line motion at constant speed in the inertial frame is assumed. If the speed is greater than or equal to the speed of light, the function aborts with an error status.

6. The inverse transformation is performed by the function starpv.

References

Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.

starpv(ras::Float64, dec::Float64, pmras::Float64, pmdec::Float64,
       plx::Float64, rvel::Float64)

Convert star catalog coordinates to position+velocity vector.

Input (Note 1)

• ra – right ascension (radians)
• dec – declination (radians)
• pmr – RA proper motion (radians/year)
• pmd – Dec proper motion (radians/year)
• px – parallax (arcseconds)
• rv – radial velocity (km/s, positive = receding)

Output (Note 2)

• pv – pv-vector (au, au/day)

Note

1. The star data accepted by this function are "observables" for an imaginary observer at the solar-system barycenter. Proper motion and radial velocity are, strictly, in terms of barycentric coordinate time, TCB. For most practical applications, it is permissible to neglect the distinction between TCB and ordinary "proper" time on Earth (TT/TAI). The result will, as a rule, be limited by the intrinsic accuracy of the proper-motion and radial-velocity data; moreover, the pv-vector is likely to be merely an intermediate result, so that a change of time unit would cancel out overall.

   In accordance with normal star-catalog conventions, the object's right ascension and declination are freed from the effects of secular aberration. The frame, which is aligned to the catalog equator and equinox, is Lorentzian and centered on the SSB.

2. The resulting position and velocity pv-vector is with respect to the same frame and, like the catalog coordinates, is freed from the effects of secular aberration. Should the "coordinate direction", where the object was located at the catalog epoch, be required, it may be obtained by calculating the magnitude of the position vector pv[1][1:3] dividing by the speed of light in au/day to give the light-time, and then multiplying the space velocity pv[2][1:3] by this light-time and adding the result to pv[1][1:3].

   Summarizing, the pv-vector returned is for most stars almost identical to the result of applying the standard geometrical "space motion" transformation. The differences, which are the subject of the Stumpff paper referenced below, are:

   (i) In stars with significant radial velocity and proper motion, the constantly changing light-time distorts the apparent proper motion. Note that this is a classical, not a relativistic, effect.

   (ii) The transformation complies with special relativity.

3. Care is needed with units. The star coordinates are in radians and the proper motions in radians per Julian year, but the parallax is in arcseconds; the radial velocity is in km/s, but the pv-vector result is in au and au/day.

4. The RA proper motion is in terms of coordinate angle, not true angle. If the catalog uses arcseconds for both RA and Dec proper motions, the RA proper motion will need to be divided by cos(Dec) before use.

5. Straight-line motion at constant speed, in the inertial frame, is assumed.

6. An extremely small (or zero or negative) parallax is interpreted to mean that the object is on the "celestial sphere", the radius of which is an arbitrary (large) value (see the constant PXMIN). When the distance is overridden in this way, the status, initially zero, has 1 added to it.

7. If the space velocity is a significant fraction of c (see the constant VMAX), it is arbitrarily set to zero. When this action occurs, 2 is added to the status.

8. The relativistic adjustment involves an iterative calculation. If the process fails to converge within a set number (IMAX) of iterations, 4 is added to the status.

9. The inverse transformation is performed by the function pvstar.

References

Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.