stylistic:tone, information:filtering, structural:scholar_edition, structural:summarization
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, R {\textstyle R}, and the distance from the observer to the object, d {\displaystyle d}:

Ω = 2 π (1 − d 2 − R 2 d): d ≥ R. {\displaystyle \Omega =2\pi \left(1-{\frac {\sqrt {d^{2}-R^{2}}}{d}}\right):d\geq R.}

By inputting the appropriate average values for the Sun and the Moon (in relation to Earth), the average solid angle of the Sun is 6.794 × 10 steradians and the average solid angle of the Moon is 6.418 × 10 steradians. In terms of the total celestial sphere, the Sun and the Moon subtend average fractional areas of 0.000 5406 % (5.406 ppm) and 0.000 5107 % (5.107 ppm), respectively. As these solid angles are about the same size, the Moon can cause both total and annular solar eclipses depending on the distance between the Earth and the Moon during the eclipse.