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Astronomical Telescopes II:

Magnitude Scale and Light Gathering Power. Astronomical Telescopes II:. Light Gathering Power. LGP ~ D 2 This comes from: LGP = Area = 4 π R 2 R=D/2 R 2 = D 2 /4 LGP = 4 π D 2 /4 = π D 2 To compare the LGP of two telescopes: LGP 1 /LGP 2 = (D 1 /D 2 ) 2. Compared to human eye :

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Astronomical Telescopes II:

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  1. Magnitude Scale and Light Gathering Power Astronomical Telescopes II:

  2. Light Gathering Power LGP ~ D2 This comes from: LGP = Area = 4πR2 R=D/2 R2 = D2/4 LGP = 4πD2/4 = πD2 To compare the LGP of two telescopes: LGP1/LGP2 = (D1/D2)2 Compared to human eye: LGP of 8” telescope: 64,000 times better LGP of 10 m telescope: 156,000,000 times better

  3. Light Gathering Power II Relationship between the faintest observable object and the aperture of the telescope is not linear! The faintness of an object relates directely to its brightness. Brigtness is measured in Magnitude. Faintest observable magnitude goes as diameter of the telescope squared

  4. Magnitude Scale • When we look at the night sky we need a way to catalog what we see • We can see up to ~5000 stars on a dark night! • What is the best characteristic to use to describe objects in relation to each other? • Color? • Size? • Brightness? YES!! • The Magnitude Scale describes all objects in the sky based on their relative brightness

  5. Invention • The Ancient Greek Hipparchus first developed the magnitude scale in 134 B.C. • The brightest star in the sky was of 1st magnitude • The faintest star he could see was of 6th magnitude • Cataloged ~800 stars • Catalog first published by Ptolemy about 100 years later, with the addition of ~ 170 stars • With the aid of a telescope, Sir William Herschel discovered that a 1st magnitude star radiates 100x more light than a 6th magnitude star...

  6. Development • In 1856 the scale was official established by Norman Pogson • 5 steps of magnitude (from 1st to 6th) = 100 steps in brightness • Therefore 1 step in magnitude = 5√100 = 2.512 steps in brightness • Logarithmic scale! Why did it work out so well? --Our eyes are logarithmic!! • Magnitude INCREASES as Brightness DECREASES -1mag is brighter than +2mag

  7. Each step up in magnitude is 2.5x fainter than the last For two stars differing in m magnitudes: Brightness ratio= 2.5m Example: star 1 has mag=5, star 2 has mag = -2 brightness ratio = 2.55-(-2) = 2.57 = 610 star 2 is 610 times brighter than star 1 Look for Venus in the West just after sunset!

  8. Light Pollution The human eye can see down to ~6th magnitude on a dark night The stars of the Milky Way are ~6th magnitude Have you seen the Milky Way?

  9. Today's Lab • Each person should make their own measurements • Look through the telescope with the aperture completely open. Make sure you see 6 stars • Be sure the telescope is focused to your eye • Slowly close the aperture, watching the faintest star. Record the aperture diameter when this star disappears from view • Continue closing the aperture until each star disappears succesively, recording the aperture diameter each time, until no stars are visible

  10. Hints for the Questions • Question 3 asks you to calculate the brightness ratio between Mars and 1st magnitude star. • Remember mag difference = m, brightness ratio = 2.5m • For question 4, first convert to common units, then use LGP1/LGP2 = (D1/D2)2 .For a 10cm vs 100cm aperture: (100/10)2 = 102 = 100 • In question 5, use your eye as a comparison: Deye= 8 mm, and remember, your eye can see 6th magnitude stars • LGP1/LGP2 ~ brightness ratio = X, 1 inch = 25.4 mm • You will have an equation X = 2.5m to solve for m, use your calculator to take the log of both sides: logX = m*log2.5 so m = logX/log2.5, then add 6 since your eye sees to 6th magnitude. m = mag difference from 0, m + 6 = total faintness

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