Question

The Sun has an angular diameter of about 0.5 and an average distance of about 150 million. What is the Sun's approximate physical diameter?

Answer 1

Approximately `1.3` million kilometres

Explanation:

In radians, `0.5^@` is `0.5*pi/180=pi/360`

The physical diameter will be approximately:

`150000000 * sin (pi/360) ~~ 150000000 * pi/360~~1300000`km

that is `1.3` million kilometres.

This is about `100` times the diameter of the Earth, so the Sun has a volume approximately `100^3 = 1000000` times that of the Earth.

Footnote

The actual diameter is closer to `1.4` million kilometres, meaning that the angular diameter is closer to `0.54^@`. This makes the sun `109` times the diameter and about `1.3` million times the volume of the Earth. The mass of the sun is estimated to be about `333000` times the mass of the Earth, so its average density is about one quarter of the Earth's average density.