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Antoine,

You asked: "Are these NAL formulas "complete" in the sense that they contain only the 2 terms published"?

The formula in the NA is a series approximation to the exact result. The factor 0.0032 degrees = ( a / R ) * ( e^2 / 2 ) * ( pi / 180 )

where a is the Earth's equatorial radius
R is the geocentric distance of the Moon for the standard H.P. of 57.7' used in the NA i.e. ( a / R ) = sin( 57.7' )
e^2 = 0.00669454 and e is the eccentricity of the figure of the Earth

In the recent past I also became interested in the lunar parallax formula in the Nautical Almanac and set out to derive it. I attach a scan of my notes on this. I'm not really sure my scrawls will be intelligible to anyone else.

Deriving the exact result requires some 3D vector geometry and makes use of the following key points.

1) At the position of the observer, the direction of the Moon is known but not its distance.
2) The distance of the Moon from the centre of the Earth is known but not its direction
3) The position of the observer relative to the centre of the Earth is known.

These facts allow the distance and direction of the Moon to be computed at both the centre of the Earth and the observer's location.

The distance of the Moon from the observer yields its apparent semi-diameter and the change in the vertical component of the Moon's direction between the observer's location and centre of the Earth gives the parallax correction.

I confess to using Mathematica to do the algebraic manipulations for the final series expansion from the exact result.

Regards,
Robin Stuart

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