# Estimating Magnitudes Using Interpolation

Any optical instrument's resolving power is greatest at its center of field, in other words, when the star is centered within the ocular. As a result, when the comparison star and the variable are widely separated, they should not be viewed simultaneously. They should be brought successively into the center of the field of view. You will do this by making slight adjustments, moving the optical tube assembly (OTA) of your telescope so that each star is centered. Some times you'll need to repeat this adjustment until you're confident with your estimate. Take your time doing this. It's important.

If the variable star and the comparison star are close together they can be placed at equal distance from the center. To do this, first mentally draw an imaginary line between the two stars. This imaginary line should be parallel to your viewing frame of reference to prevent what is known as position angle error. Turn your head or your erecting prism to improve this alignment. In the worst case, the position angle effect can produce inaccuracies of up to 0n.'5 so it's important to eliminate this potential error.

I will mention the following several times because it is critical: all observing must be done near the center of your eyepiece's field of view. Usually, there is greater distortion of the image the further it is positioned away from the center of the field of view. Keeping the star centered, or nearly so, helps keep it within the distortion-free region of your eyepiece.

Use at least two comparison stars, and if possible, more. If the brightness interval between your comparison stars is very large, say 0T5 or greater, take extreme care in estimating how the interval between the brighter comparison star and the variable compares with that between the variable and the fainter comparison star. Again, this is important.

Record exactly what you see, regardless of perceived discrepancies in your observations. You should go into vJ0 Methods ^

each observing session with no expectations regarding the brightness of the variable star; do not let your estimates be prejudiced by your previous estimates or by what you think the star should be doing. This becomes more difficult as you tire during a long evening of observing. It's best to stop observing when you're very tired. Or at least, switch to casual observing and go look at the "pretty things."

If the variable is not seen because of extreme faintness, haze, or moonlight, then note the faintest comparison star visible in the region. If the faintest star visible should be 12T0, then record your observation as < 12.0. The left pointing bracket is a symbol for "fainter than." This means that the variable is invisible and must have been fainter than magnitude 12T0.

When observing variables that have an unmistakably red color, make your estimate using the so-called quick glance method rather than by prolonged stares. You remember that due to the Perkinje effect, red stars tend to excite the retina of the eye when observed for an extended period or time. So, red stars will appear to become excessively bright in comparison to blue stars if viewed too long. This can be a source of errors when estimating relative brightness.

Another technique for making magnitude estimates of red stars is called the out-of-focus method. Place the red star at the center of the field of view, then draw the eyepiece out of focus until it become visible as a colorless disk. The comparison star will also be out of focus and be visible as a colorless disk. Using this method, the systematic error due to the Perkinje effect can be avoided. If the color of the variable is visible even when the stars are out of focus, you may need to use a smaller telescope or an aperture mask. You may even need to consider using binoculars on bright stars. Another good reason to keep binoculars handy.

An aperture mask is simply a cover, with a hole cut into it, placed over the front of your telescope. The hole, smaller than the aperture of your telescope, should be cut off-center for Newtonian and Schmidt-Cassegrain telescopes to avoid the central mirror supports. For example, if you have an 8 inch aperture, you may find need for a 4 inch mask that reduces the amount of light entering your telescope. This mask can be made of sturdy cardboard or something similar. Simply tape it to the front of your telescope, taking care not to touch any lens or corrector plate. Don't place tape on your lens or corrector plate!

Using an aperture mask will change the focal ratio of your telescope. This isn't anything with which to really be concerned if you're visually observing. However, if you're using a camera it will be important to remember that your focal ratio has changed. Let's examine this idea for a moment.

Assume that your 8 inch telescope with a 2000 mm focal length has an //10 focal ratio. This relationship can be shown by simply converting 8 inches to millimeters (approximately 200 mm); then divide the focal length of your telescope, in this case 2000 mm, by the aperture (2000/200 = 10). The answer is your focal ratio, in this case 10.

When you place your aperture mask on the front of the telescope, the aperture is changed from 8 inches to 4 inches. Now do the math. Your "new" aperture, 4 inches, equals approximately 100 mm, and your 2000 mm focal length remains the same but is now divided by 100. This gives you a focal ratio of//20. Again, this is nothing to be concerned with when visually observing. However, when using a camera, it will become important.

For faint stars, you may wish to try making your estimate by using averted vision. To do this, keep the variable and the comparison stars near the center of the field of view while concentrating your gaze to one side. When doing this, you're using your peripheral vision. Move your eye around. If you are viewing at the extreme limit of your equipment, faint stars seem to "pop" into view. This is tough work. Sometimes, lightly tapping the side of your telescope will cause the star to come into view for a moment. Eye drops will help too. You can also place a large piece of black cloth over your head and eyepiece to block all ambient light. You'll notice that on some nights you can see fainter stars than on other nights. Be careful that you don't "wish" the star into view. A good rule of thumb is to see the star at least three times before recording it. Sometimes, it helps to leave a very faint star and come back to it in a few minutes.

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