The Atmosphere Rules

Gary Smith

Tired of listening to those big aperture folks tell about all the things they can see? Sometimes it's the little things that count. Let me explain.

Let's say you want to take a detailed image of the face of a star. You face two problems:

1. the limits of telescope size (you can't be proud here)

2. turbulence of Earth's atmosphere (aaah)

A question that must be asked is what is the apparent size of a star? In other words, what is the size of the disk it forms as viewed in the sky?

Let's look at Venus first. At its closest approach to the Earth, Venus subtends about one arcminute, or 1/60 of a degree. Those of us with very good eyes are just capable of resolving a disk that is one arcminute across; that is, seeing it as a disk and not as a point. A telescope with a 150 millimeter (about 6 inch) mirror or lens can do 60 times better than your eye, because its aperture is about that much larger than your pupil. In such a scope, a star appears as a fuzzy disk about one arcsecond in diameter, regardless of the star's size, because the telescope cannot form a smaller image. The fuzziness is caused by the diffraction of light passing through the aperture; the smaller the aperture, the larger the image produced. (Here is some cause for joy among the small aperture crowd.)

Now, one arcsecond is about the size of a gnat in the center field bleachers as seen from home plate (probably the Sox, not Cubs), or about the size of the largest moon of Jupiter as seen from (where else?) Earth. Betelgeuse, a red giant star in the constellation Orion, forms the largest disk in the sky for a star (aside from the Sun). It is only 1/15 the size of that gnat in the bleachers or about 0.06 arcsecond (60 milliarcseconds) in diameter. The greatest majority of the stars you can see with your unaided eye are only a few millarcseconds or less across in the sky. The first measurements of stars of this size were done by Albert A. Michelson and Francis G. Pease in the 1920's. Just think, if your eye had that kind of resolving power, you would be able to see the individual atoms in your hand at (what else?) arms length.

Now we are getting to why those of us who have small aperture telescopes can be proud. The resolving power of a telescope - its ability to discriminate small images - improves in proportion to the telescope aperture, so obviously we should use a larger telescope. If a 150 millimeter (6 inch) telescope can resolve a one-arcsecond disk, then a 2.5-meter telescope might resolve Betelgeuse, and one of the 10-meter Keck scopes on Mauna Kea, Hawaii, might show us details on its surface and resolve many other bright stars.

Unfortunately, in practice, increasing the size of the telescope beyond 150 millimeters does no good until we cope with the effects of the turbulent atmosphere. There you have it, you small aperture observers, it's time to rejoice and tell those who have big telescopes, "Mine is good enough because of the atmosphere!"

Anything bigger and it's like trying to read a letter that's laying at the bottom of a swimming pool on a windy day. The ripples on the water surface distort the light waves coming from the bottom of the pool. Observing the light from stars through Earth's atmosphere is a similar exercise. But alas, let's not get too happy, since our bigger aperture brethren can still gather more light and therefore see fainter images, although those images get fuzzier and fuzzier the bigger their apertures get. There is a saying among amateur astronomers that "Aperture Rules!" I beg to's the atmosphere that rules!


Ref: "A Sharper View of the Stars" by Arsen R. Hijian and J. Thomas Armstrong, Scientific American, March 2001

Published in the July 2001 issue of the NightTimes