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    Re: Moon Venus Lunar - Interpretation of results
    From: Paul Hirose
    Date: 2020 Feb 3, 11:00 -0800

    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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