<p>You will need to know the moon to earth distance in km and also the topocentric elongation in radians.</p>
<p><strong>topo_moon_radius</strong> = asin(1737.1 / moon_to_earth_distance_in_km) * (180 / π)</p>
<p>1737.1 is the moon radius in km.</p>
<p><strong>topo_cresent_width_in_degrees</strong> = topo_moon_radius * (1 - (cos(topo_elongation_in_radians)))</p>

CC BY-SA 4.0
2023-08-22T15:04:24.080Z
2023-08-22T15:04:24.080Z
orchid
<p>I have the Topocentric Moon Altitude, T. Moon Azimuth, T. Sun Altitude, T. Sun Azimuth, T. Elongation, T. Phase Angle.</p>
<p>How do I calculate the Topocentric Crescent Width and the Topocentric Moon Radius/Semi-Diameter?</p>
<p>Is there any other piece of information I need to do this?</p>

CC BY-SA 4.0
2023-06-28T00:43:18.043Z
You can say radius instead of semi-diameter
Snack Exchange
CC BY-SA 4.0
2023-06-28T12:04:40.843Z
You need to know the distance to the Moon to calculate the semi-diameter.
JohnHoltz
CC BY-SA 4.0
2023-06-28T13:46:06.577Z
Is that the topocentric distance? I have that also. What's the formula?
orchid
<the-moon>
How to calculate Topocentric Crescent Width and Moon Radius/Semi-Diameter?
orchid
# How to calculate Topocentric Crescent Width and Moon Radius/Semi-Diameter?

(Asked by: username_0 on 2023-06-28)

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?

**Tags:** the-moon

> **Comments:**
> **username_1**: You can say radius instead of semi-diameter  
> **username_2**: You need to know the distance to the Moon to calculate the semi-diameter.  
> **username_0**: Is that the topocentric distance? I have that also. What's the formula?  

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## 1 answers

### Answer by username_0 on 2023-08-22. Score: 2

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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