Astronomy Lab · Angular size

Why does something look smaller when it is farther away?

Apparent size describes how large an object appears in the sky. It depends on both its true diameter and its distance from you.

observer closer farther larger angle smaller angle
Same physical size, different apparent angular size
The idea

From physical size to angular size.

Imagine holding an apple at arm’s length. Move the same apple farther away and it appears smaller even though its physical diameter has not changed. Astronomy uses exactly the same idea when describing the apparent diameter of the Moon, planets and other Solar System objects.

We measure that apparent diameter as an angle. A full circle contains 360°. Because astronomical angles are often tiny, they are commonly expressed in arcminutes (1° = 60′) and arcseconds (1° = 3600″).

Angular diameter
\[ \delta = 2\,\arctan\left(\frac{d}{2D}\right) \]
δ apparent angular diameter d physical diameter D distance to the object

The Moon is about 3,474 km across and roughly 384,400 km from Earth on average, giving it an apparent diameter close to half a degree — one reason a total solar eclipse is possible when the Sun appears almost the same size.

Interactive calculator

How much can apparent size change?

Select an object to compare its apparent angular diameter at its approximate minimum and maximum distance from Earth.

Results update instantly when you choose an object.
Result

Moon

3,474 km diameter
Farthest 406,300 km
1,763.72″
29.395′ · 0.4899°
Closest 356,700 km
2,008.97″
33.483′ · 0.5580°
Apparent diameter change 13.9%