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The physical group size equivalent to m minutes of arc can be calculated as follows: group size = tan( m / 60 ) × distance. In the example previously given, for 1 minute of arc, and substituting 3,600 inches for 100 yards, 3,600 tan( 1 / 60 ) ≈ 1.047 inches. In metric units 1 MOA at 100 metres ≈ 2.908 centimetres.
(The Sun's diameter is 400 times as large and its distance also; the Sun is 200,000 to 500,000 times as bright as the full Moon (figures vary), corresponding to an angular diameter ratio of 450 to 700, so a celestial body with a diameter of 2.5–4″ and the same brightness per unit solid angle would have the same brightness as the full Moon.)
The distance between the Moon and Earth varies from around 356,400 km (221,500 mi) to 406,700 km (252,700 mi) (apogee), making the Moon's distance and apparent size fluctuate up to 14%. [202] [203] On average the Moon's angular diameter is about 0.52°, roughly the same apparent size as the Sun (see § Eclipses).
Charon has an angular diameter of 4 degrees of arc as seen from the surface of Pluto; the Sun appears much smaller, only 39 to 65 arcseconds. By comparison, the Moon as viewed from Earth has an angular diameter of only 31 minutes of arc, or just over half a degree of arc. Therefore, Charon would appear to have eight times the diameter, or 25 ...
Horrocks' model predicted the lunar position with errors no more than 10 arc-minutes; [33] for comparison, the diameter of the Moon is roughly 30 arc-minutes. Newton used his theorem of revolving orbits in two ways to account for the apsidal precession of the Moon. [ 34 ]
The largest possible apparent diameter of the Moon is the same 12% larger (as perigee versus apogee distances) than the smallest; the apparent area is 25% more and so is the amount of light it reflects toward Earth. The variance in the Moon's orbital distance corresponds with changes in its tangential and angular speeds, per Kepler's second law.
But this theory, applied to its logical conclusion, would make the distance (and apparent diameter) of the Moon appear to vary by a factor of about 2, which is clearly not seen in reality. [15] (The apparent angular diameter of the Moon does vary monthly, but only over a much narrower range of about 0.49°–0.55°. [16])
The method relies on the relatively quick movement of the moon across the background sky, completing a circuit of 360 degrees in 27.3 days (the sidereal month), or 13.2 degrees per day. In one hour it will move approximately half a degree, [1] roughly its own angular diameter, with respect to the background stars and the Sun.