Suppose the angular separation of two stars is smaller than the angular resolution of your eyes. How will the?

Question

Suppose the angular separation of two stars is smaller than the angular resolution of your eyes. How will the stars appear to your eyes?

Answer 1

The two stars will appear as a single point of light.

Answer 2

Angular resolution is not well described by a single number. What you are really referring to is the MTF (modulation transfer function) of your eye. MTF is essentially an angular power spectrum of the impulse response of your eye.

The common definition of "angular resolution" (1.22 diameter over wavelength) actually defines the limit to integrate about 4/5 of the area under the MTF (more precisely a volume since the MTF is a 2-D function; it should be radially symmetrical for human eyes, howevefr).


Depending on how close together the stars are, they may appear as a point source, or an elongated point (or, if you have astigmatism some other odd shape) or two separate objects.

At a separation of the standard definition for resolution given above the point sources will appear as a single elongated source.

Answer 3

If this is a below college-level question or a college astronomy for jocks class (lol, I was a college jock), the answer is "b." They will appear as a single star. But Tina and Lowly Physic grad are right. If you are just below the angular resolution, and you have two stars similar in brightness, you will get a smeary photo where the stars are merged, but it looks a little like an elipsoid. So "c" can also be right. At less resolution, the two stars will be completely merged. But you will see light from both stars. So "e" is technically incorrect.

Answer 4

There are many double star systems in our galaxy. This time of year a good one to look at is Alberio, which is the eye of Cygnus the Swan. It appears to the unaided eye as a single star , but through even a pair of binoculars it can be resolved into a double. Through even a small scope (4 inch) it is possible to see that this double system consists of two stars, one which is very blue and the other gold. Very pretty. Look at Mizar the middle star in the handle of the big dipper with a pair of binoculars and it will show itself to be a double. The second star is Alcor. Perhaps the most famous multiple star system is the double-double in Lyria. Very close to the bright star Vega (part of the summer triangle) is a system which at first examination appears to be a double star system. upon closer scrutiny each one of thase two stars is seen to be a double!. So there are 4 stars where at first glance there appears to be one. It is often used as a test of how good one's eyesight is-to see if they can resolve the double-double.