The Moon's Angular Size Is About 12ã¢ë†ëœ. What Is This In Arcminutes?

Astronomers use angular measure to describe the apparent size of an object in the night sky. An bending is the opening between two lines that meet at a point and angular measure out describes the size of an bending in degrees, designated by the symbol °. A full circle is divided into 360° and a right bending measures xc°. I degree tin exist divided into 60 arcminutes (abbreviated 60 arcmin or sixty'). An arcminute tin also be divided into 60 arcseconds (abbreviated sixty arcsec or lx").

The angle covered past the diameter of the total moon is virtually 31 arcmin or 1/2°, and then astronomers would say the Moon's angular diameter is 31 arcmin, or the Moon subtends an angle of 31 arcmin.

If y'all extend your hand to arm'southward length, you tin use your fingers to guess angular distances and sizes in the sky. Your index finger is about 1° and the distance across your palm is about 10°.

hand diagrams-600x200.jpg

The Small-Angle Formula

The angular sizes of objects show how much of the sky an object appears to cover. Angular size does non, however, say anything about the actual size of an object. If you extend your arm while looking at the full moon, yous tin can completely comprehend the moon with your thumb, but of course, the moon is much larger than your thumb, it only appears smaller because of its distance. How large an object appears depends non just on its size, but too on its distance. The apparent size, the bodily size of an object, and the distance to the object can be related past the small angle formula:

D = θ d / 206,265

D = linear size of an object
θ = angular size of the object, in arcsec
d = distance to the object

Example:

A certain telescope on Earth can see details equally small as two arcsec. What is the greatest distance you could encounter details as small the the meridian of a typical person (1.6 m)?

d = 206,265 D / θ = 206,265 × 1.6 grand / 2 = 165,012 chiliad = 165.012 km

This is much less than the distance to the Moon (approximately 384,000 km) and then this telescope would not be able to see an astronaut walking on the moon. (In fact, no World based telescope could.)

Exercise Questions

The boilerplate distance to the Moon is approximately 384,000 km. The Moon subtends and bending of 31 arcminutes, or about ane/2°. Use this information and the small-angle formula to find the diameter of the moon in kilometers.
At what distance would yous have to hold a quarter (which has a diameter of near 2.5 cm) for it to subtend and bending of 1°?

Answers: