Definition
The semidiameter of a celestial body is the angle under which its radius is seen from the Earth. In other words, it is half the apparent diameter, measured in minutes and seconds of arc. The Sun and the Moon both have a semidiameter of about 16′, which is why they look the same size in the sky, while the planets range from about 1″ for Neptune to 31″ for Venus at its closest.
Because an object's apparent size is inversely proportional to its distance, the semidiameter can be written as a constant divided by the distance:
S = S₀ / ΔS₀ semidiameter at a distance of 1 AUΔ distance from the Earth, in AUMoon: S = 358473400 / Δ(km) (arcseconds)For planets with a noticeable oblateness, Meeus gives separate equatorial and polar values. The Moon is so close that its formula uses its distance in kilometres directly.
Values at unit distance
| Body | S₀ at 1 AU | Typical apparent diameter |
|---|---|---|
| Sun | 959.63″ | 31′ 28″ to 32′ 32″ |
| Mercury | 3.36″ | 4.5″ to 13″ |
| Venus | 8.41″ | 10″ to 63″ |
| Mars | 4.68″ | 3.5″ to 25″ |
| Jupiter | 98.44″ (equator), 92.06″ (pole) | 30″ to 50″ |
| Saturn (globe) | 82.73″ (equator), 73.82″ (pole) | 15″ to 20″ |
| Uranus | 35.02″ | 3.3″ to 4.1″ |
| Neptune | 33.50″ | 2.2″ to 2.4″ |
Venus shows the largest range: about 10″ across when it is on the far side of the Sun, and 62″ (a full arcminute) near inferior conjunction, when it is a thin crescent only 0.27 AU away. Mars grows from 4″ near conjunction to 25″ at a close perihelic opposition, like the one of August 2003.
The Moon from perigee to apogee
The Moon's distance varies between about 356,500 km and 406,700 km. Its semidiameter changes accordingly, from 16′ 46″ at perigee to 14′ 41″ at apogee, a difference of 14%. A full Moon near perigee is the "supermoon" of the media. It is about 14% wider and 30% brighter than a full Moon near apogee, but the difference is hard to notice without a side-by-side comparison.
There is also a small topocentric effect. When the Moon is overhead, the observer is about one Earth radius closer to it than when it rises, and it appears about 1.5% larger, roughly 15″ in semidiameter. Meeus calls this the augmentation of the semidiameter.
| Moon distance | Semidiameter | Apparent diameter |
|---|---|---|
| 356,500 km (perigee) | 16′ 46″ | 33′ 31″ |
| 384,400 km (mean) | 15′ 33″ | 31′ 05″ |
| 406,700 km (apogee) | 14′ 41″ | 29′ 23″ |
Semidiameter and eclipses
The type of a central solar eclipse depends on the two semidiameters. The Sun's ranges from 15′ 44″ in July to 16′ 16″ in January, and the Moon's from 14′ 41″ to 16′ 46″. When the Moon's disk is larger, it can cover the Sun completely and the eclipse is total. When the Moon is near apogee, it is too small, and a bright ring of sunlight remains around it: the eclipse is annular.
Semidiameters also appear in rise and set calculations. Sunrise and sunset are defined by the upper edge of the Sun, 16′ above its centre, which is why the standard altitude of the Sun's centre at sunrise is −50′: 34′ of refraction plus 16′ of semidiameter.
Current values
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| Body | Distance from the Earth | Semidiameter | Apparent diameter |
|---|
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Frequently asked questions
Why do the Sun and the Moon look the same size?
By coincidence. The Sun is about 400 times wider than the Moon, but also about 400 times farther away, so both have a semidiameter close to 16′. This coincidence makes total solar eclipses possible.
How big does a planet look in a telescope?
Divide its S₀ by its distance in AU. Jupiter at opposition, about 4.2 AU away, has a semidiameter of 98.44″ / 4.2 ≈ 23″, or 47″ across. At 50× magnification it looks slightly larger than the full Moon does to the naked eye.
Is the Moon larger on the horizon?
No. It is actually about 1.5% smaller on the horizon than high in the sky, because you are farther from it. The large rising Moon is an optical illusion.