Editing Solid angle (section)

=== Celestial objects ===
By using the definition of [[angular diameter]], the formula for the solid angle of a celestial object can be defined in terms of the radius of the object, <math display="inline">R</math>, and the distance from the observer to the object, <math>d</math>:

<math display=block>\Omega = 2 \pi \left (1 - \frac{\sqrt{d^2 - R^2}}{d} \right ) : d \geq R.</math>  

By inputting the appropriate average values for the [[Sun]] and the [[Moon]] (in relation to Earth), the average solid angle of the Sun is {{val|6.794|e=-5}} steradians and the average solid angle of the [[Moon]] is {{val|6.418|e=-5}} steradians. In terms of the total celestial sphere, the [[Sun]] and the [[Moon]] subtend average ''fractional areas'' of {{val|0.0005406}}% ({{val|5.406|u=[[part per million|ppm]]}}) and {{val|0.0005107}}% ({{val|5.107|u=ppm}}), respectively. As these solid angles are about the same size, the Moon can cause both total and annular solar [[Solar eclipse|eclipses]] depending on the distance between the Earth and the Moon during the eclipse.