## 3 oct. 2013

### Astronomical games III. The Sun and planetary skies

In two last entries, everything about solar system scales, sizes of the sun and the planets, distances from the planets to the sun and characteristics about their composition and their skies. However, how big is the sun in every planetary sky?

Well, maybe you can imagine that the sun size is biggest in Mercury sky and smallest in Pluto sky. But how big is it and how small?

The apparent size of any object depends of its real size and of the distance from it. We can see this apparent size as an angular one. In an easy exercise, you can put your index and middle fingers in the way of two scissors that can be opened or closed as we need. Put them close to your eyes and try to measure the size of the objects around you. How open your two fingers are is a measurement of the apparent size of each thing that you see.

The branch of mathematics known as trigonometry studies the angles and its properties. We can draw a diagram of the sun seen at two different distances and for that reason; it is easy to see two different angles that form two different triangles. These triangles are named rectangles because one of its angles is 90°. The half of the angle that we are looking for is denominated a. If we call D the distance between the sun and the planet (you can see that D is also the base of the triangle or adjacent cathetus to angle a) and R the size of the sun radius (opposite cathetus to angle a), then trigonometry relates the catheti and the angle a in the following way:

tan (a) = R/D

Where tan refers to the trigonometry tangent function. If you solve this equation for the angle a and put the real radius measurement in R and the distance D of the planet to the sun, you can obtain the angular size of the sun for every planetary sky.

If you see the sun size in an Earth landscape, you can imagine or draw the size of the sun for other skies in relation to the Earth’ sky. I made this and obtained this diagram that share to you and only needs your own extraterrestrial landscape.

Well, start drawing! Who knows what marvelous thing you can do?