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To determine lunar distance rate, my program begins with the space
velocity vectors of the bodies and resolves them into components
(radians per day) that are perpendicular to the line of sight and in the
plane of the observer and both bodies. I could show a worked example but
the math would be tedious and probably not helpful.

To practical accuracy you can use the obvious algorithm: get coordinates
of the Moon and Venus one minute apart, then calculate the separation
angle rates.

For example, here are topocentric apparent right ascension and
declination (degrees, with respect to the true equator and equinox) for
42.97 N 70.95 W from the JPL Horizons online calculator:

Moon
2020-Jan-29 22:10:00  6.47496  -3.38550
2020-Jan-29 22:11:00  6.47991  -3.38218

Venus
2020-Jan-29 22:10:00  350.68358  -5.08514
2020-Jan-29 22:11:00  350.68433  -5.08478

At 22:10 the angular separation is 15.83885°. One minute later it's
15.84337. Difference is .00452°, or .271′ (increasing with time).

In one minute the Moon moves .00595° and Venus .00083. Total angular
velocity is therefore .00678° per minute. But the bodies are not moving
directly toward or away from each other, so their separation changes
just .00452° per minute, or 67% of the total angular velocity.

Any coordinate system will work for the angular separation rate
calculation. However, to calculate percentage utilization of the total
angular velocity you can't use a coordinate system which rotates with
the Earth, such as az/alt. On my first attempt I made that mistake.
That's why I have a program to do this stuff.

   

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