SLA_DMOON - Approx Moon Pos/Vel

ACTION:

Approximate geocentric position and velocity of the Moon (double precision).

CALL:

CALL sla_DMOON (DATE, PV)

GIVEN:

DATE

D

TDB (loosely ET) as a Modified Julian Date (JD$-$2400000.5)

RETURNED:

PV

D(6)

Moon $[ x,y,z,\dot{x},\dot{y},\dot{z} ]$, mean equator and equinox of date (AU, AU s$^{-1}$)

NOTES:

1. This routine is a full implementation of the algorithm published by Meeus (see reference).
2. Meeus quotes accuracies of $10\hspace{-0.05em}^{'\hspace{-0.1em}'}$ in longitude, $3\hspace{-0.05em}^{'\hspace{-0.1em}'}$ in latitude and $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ arcsec in HP (equivalent to about 20 km in distance). Comparison with JPL DE200 over the interval 1960-2025 gives RMS errors of $3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.7$ and 83 mas/hour in longitude, $2\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$ arcsec and 48 mas/hour in latitude, 11 km and 81 mm/s in distance. The maximum errors over the same interval are $18\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.50$ /hour in longitude, $11\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.24$ /hour in latitude, 40 km and 0.29 m/s in distance.
3. The original algorithm is expressed in terms of the obsolete time scale Ephemeris Time. Either TDB or TT can be used, but not UT without incurring significant errors ( $30\hspace{-0.05em}^{'\hspace{-0.1em}'}$ at the present time) due to the Moon's $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ /s movement.
4. The algorithm is based on pre IAU 1976 standards. However, the result has been moved onto the new (FK5) equinox, an adjustment which is in any case much smaller than the intrinsic accuracy of the procedure.
5. Velocity is obtained by a complete analytical differentiation of the Meeus model.

REFERENCE:

Meeus, l'Astronomie, June 1984, p348.