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?

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