On Sat, 05 Jun 2004 04:33:47 GMT, Mark Lepkowski wrote:

How bright does a star have to be to be visible with a small telescope in
broad daylight?

Well, let's assume 80mm is what you mean by small.

Stars will be roughly 130 times brighter through such a telescope than to
the naked eye.

Let's say 100 times brighter for simplicity, because that's an even five
magnitude difference.

The day sky varies in brightness, but a rough figure of mag -3 will do.
That means a star needs to be brighter than mag -3 to be visible.

Assuming a pupillary aperture of about 3mm (it's daytime, after all), the
minimum useful magnification of that 80mm telescope is 80/3 = ~26x. At
that magnification, the sky will look just about as bright in the
telescope as to the naked eye, because the additional light collected by
the telescope is spread over a larger area. Stars, however, are point
sources, so the extra light collected is all sent to basically the same
point in the image plane.

So, the sky remains unchanged, but stars brighten by our
chosen-for-simplicity factor of 100, or by five magnitudes.

So, to become brighter than the sky (at about mag -3), a star would have
to be brighter than mag 2.

If you increase the magnification, the sky will become darker, because the
light collected is spread over an even larger area, and the exit pupil
becomes smaller than the eye's pupil. The change in brightness of the
stars, however, remains the same (mostly). So, as magnification goes up,
the magnitude ceiling for stars to be visible goes up. Eventually, of
course, the diffraction pattern becomes more like an extended image than a
point image, after which additional magnification will not reveal more
stars (quite the opposite).

Basically, you can create a night sky through magnification. The larger
the aperture, the more magnification you can use before the size of
diffraction images becomes an issue.

Of course, the higher the magnification, the smaller the field of view,
and the more difficult it is to locate any stars at all (even at night).


--
- Mike

Remove 'spambegone.net' and reverse to send e-mail.