Hobbies And Interests
Instructions
Measure the diameter of the aperture of your telescope. This is the lens (in a refracting telescope) or mirror (in a reflecting telescope) that captures the light and focuses it through your eye. The aperture of your own eye is your pupil. It has a diameter of approximately 6 to 7 mm.
Calculate the relative light grasp of two different scopes by comparing the relative areas of the lens or mirror. The area will be proportional to the square of the diameter of the aperture. Using 6 mm as an estimate for a human pupil, a lens with a 12 mm aperture will capture four times as much light. A 24 mm aperture will capture four times as much light as this, or 16 times as much as your eye.
Understand the magnitude scale that astronomers use. The brighter an object is, the lower its magnitude. Each order of magnitude on this scale represents approximately 2.5 times the amount of brightness, so a star of magnitude 1 is 2.5 times brighter than a star of magnitude 2.
Compare the magnitude of stars detectable with two different telescopes, or a telescope and your eye, by using the formula M= 5 * log (d1/d2) where d1 and d2 are the diameters of the apertures you are comparing. Suppose you want to compare a 12 mm lens telescope to your naked eye. Use 12 for d1 and 6, the diameter of your pupil, for d2. The log of 2 is .301. Multiply by five to get 1.5. This is the magnitude gain of the lens. Note that this would be a very weak telescope, but is useful as an example, if not for actual star-gazing.
Add the magnitude gain of the lens to the highest magnitude objects viewable without it. Suppose you could see a 5 magnitude object with your naked eye. With a 12 mm lens, you could see a 6.5 magnitude object. Suppose now you have a telescope with a 100 mm lens, and you want to compare it to your 12 mm lens telescope. Plug this into the same formula you used before. 5 * log (100/12) = a magnitude gain of 4.6. If a 6.5 magnitude object was visible with the 12 mm lens, you should be able to see objects as dim as 11.1 with a 100 mm lens.
Remember that a 6.5 magnitude object is much brighter than an 11.1 magnitude object. The difference in magnitude is 4.6, so the 6.5 magnitude object is 2.5^4.6 which is about 68 times brighter than the 11.1 magnitude object. Remember also that if one star has a lower magnitude than another, that means it is brighter from our perspective here on Earth. The higher magnitude star might actually be much brighter than the lower magnitude one, but much further away.