# angular diameter of the sun

From: Lori Lambertson (loril@exploratorium.edu)
Date: Fri Nov 19 1999 - 12:43:09 PST

> I would like a more detailed explaination including a formula for computing
> the diameter of the sun. Also, for those of us who are not astronomy
> whizzes, what is "angular diameter"? How is it different from just plain
> "diameter"?
>
> Thank you.

Hello Snack Makers,
Those are great questions.
You can find the diameter of the sun with some simple materials and an
the LINEAR diameter of the sun. (I'll explain the angular diameter next.)
On a sunny day, take a piece of cardboard, a pushpin, a piece of white
cardboard (or white paper taped to cardboard), a pencil, and a meter stick
outside. Bring along a friend to help, too. Make a pinhole near the
center of the cardboard. Hold the cardboard perpendicular to the rays of
the sun (do not look at the sun, ever!) about 1 meter above the white
cardboard. The two pieces of cardboard should be parallel to each other.
Look for a small image of the sun (focused through the pinhole) on the
white cardboard. (If you are not convinced that the spot of light you see
is an image of the sun, try this with an irregularly shaped pinhole.)
Imagine two similar triangles, one on each side of the pinhole. The
vertical angles on opposite sides of the pinhole are equal! Therefore, the
distance from the pinhole to the image on the white board is proportional
to the distance from the pinhole to the sun, and the diameter of the image
on the white board is proportional to the actual diameter of the sun. You
can set this up as a proportion, with the diameter of the sun as your
"unknown". (You still need to know the distance to the sun to solve this.)
Here is the proportion:
diameter of image/distance from pinhole to image = diameter of sun/distance
to sun

To explain the difference between angular diameter and "normal" or linear
diameter, I usually like to have a few props. It is easier to model than
it is to explain. Imagine that you have a beach ball, whose diameter is 1
meter. Whether the ball is in your hands, across the room, or a mile away,
its diameter is still 1 meter. That's linear diameter, which doesn't
change with distance.

Now imagine that you are holding that ball in your hands. If I taped a
piece of string from the top of the ball, then to your eye, and then to the
bottom of the ball, I would have illustrated an angle. Your eye is at the
vertex of that angle. Let's say that angle is 90 degrees. Now imagine
that same ball placed across the room. If I took a longer piece of string,
and again taped it to the top of the ball, then to your eye, then back to
the bottom of the ball, I would illustrate another angle. Your eye is
still at the vertex of this new angle, but the angle has gotten much
smaller. The angular diameter of the beach ball changes with distance.
The same object farther away from you sweeps out a smaller angle in your
field of view than it did when it was closer to you.

The earth-sun distance is relatively constant, so the sun's angular
diameter is also relatively constant: 1/2 degree. Don't look at the sun to
measure this! My "Reflections of a Star" snack is a safe way to measure
this angle.