Angular Diameter - Use in Astronomy

Use in Astronomy

In astronomy the sizes of objects in the sky are often given in terms of their angular diameter as seen from Earth, rather than their actual sizes. Since these angular diameters are typically small, it is common to present them in arcseconds. An arcsecond is 1/3600th of one degree, and a radian is 180/ degrees, so one radian equals 3600*180/ arcseconds, which is about 206265 arcseconds. Therefore, the angular diameter of an object with visual diameter d at a distance D, expressed in arcseconds, is given by:

= 206265 d / D arcseconds.

The angular diameter of Earth's orbit around the Sun, from a distance of one parsec, is 2″ (two arcseconds).

The angular diameter of the Sun, from a distance of one light-year, is 0.03″, and that of the Earth 0.0003″. The angular diameter 0.03″ of the Sun given above is approximately the same as that of a person at a distance of the diameter of the Earth.

This table shows the angular sizes of noteworthy celestial bodies as seen from the Earth:

Celestial body Angular diameter Relative size (10 pixels per arcsecond)
Sun 31.6′ – 32.7′ 28.7 – 29.7 times the maximum value for Venus (orange bar below) / 1896″ – 1962″
Moon 29.3′ – 34.1′ 26.6 – 31.0 times the maximum value for Venus (orange bar below) / 1758″ – 2046″
Venus 9.565″ – 66.012″

Read more about this topic:  Angular Diameter

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