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I have the Topocentric Moon Altitude, T. Moon Azimuth, T. Sun Altitude, T. Sun Azimuth, T. Elongation, T. Phase Angle.

How do I calculate the Topocentric Crescent Width and the Topocentric Moon Radius/Semi-Diameter?

Is there any other piece of information I need to do this?

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  • $\begingroup$ You can say radius instead of semi-diameter $\endgroup$ Jun 28, 2023 at 0:43
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    $\begingroup$ You need to know the distance to the Moon to calculate the semi-diameter. $\endgroup$
    – JohnHoltz
    Jun 28, 2023 at 12:04
  • $\begingroup$ Is that the topocentric distance? I have that also. What's the formula? $\endgroup$
    – orchid
    Jun 28, 2023 at 13:46

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You will need to know the moon to earth distance in km and also the topocentric elongation in radians.

topo_moon_radius = asin(1737.1 / moon_to_earth_distance_in_km) * (180 / π)

1737.1 is the moon radius in km.

topo_cresent_width_in_degrees = topo_moon_radius * (1 - (cos(topo_elongation_in_radians)))

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