As described in Step 7, the true length of the shadow is best determined by using the angle between the cape's top and the shadow tip as measured along the angle between the sub-solar point and the cape's top from the Moon's center.

The radius of the Moon in kilometres can be looked up in any basic astronomy book or the Internet:

R = 1737.5 kilometres

In order for our next calculation to work properly, the shadow angle must be expressed in units of radians, which can be calculated using the following:

Dg_rad = [ p / 180^o ] Dg

Dg_rad = 0.0122735 radians

The true length of the shadow can now be determined using the following equation:

L_shadow = RDg_rad

L_shadow = 21.32543669 kilometres

Of course, the length of the shadow is not known to such a high accuracy. The decimal places are being kept for now to avoid any rounding errors that might be encountered along the way.