Unassigned%20Problems%202

# Unassigned%20Problems%202 - Chapter 5 Problems 2. max =...

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Chapter 5 Problems 2. 6 max .29cm 1m 10 μ m 5.5K 100cm λ ⎛⎞ × ⎜⎟ ⎝⎠ , so max 527 μ m = , which is longer than the 3 to 200 μ m operating range. 3. The amount of light collected by a telescope depends on the area of the mirror, and the area depends on the square of the diameter. A 6-m telescope is 3 times bigger in diameter than a 2-m telescope, so it has 3 2 = 9 times the light-gathering power. The larger telescope will gather light 9 times faster than the smaller telescope, so what the 2-m telescope can accomplish in 1 hour, the 6-m can accomplish in 1/9 hour or 6.7 minutes. A 12-m telescope has 6 times the diameter of a 2-m telescope and therefore 36 times the area. It gathers light 36 times faster. What the 2-m telescope can gather in 1 hour, the 12-m can gather in (60 min)/36 = 1.7 minutes. 4. The angular resolution of a telescope gets poorer as wavelength increases. The angular resolution in arc-seconds is proportional to the wavelength. (a) 3.5 μ m = 3,500 nm. 3,500/700 = 5, so the wavelength is 5 times longer. The resolution should be 5 times poorer or 0.05" × 5 = 0.25". (b) Similarly, for the ultraviolet, 140 nm/700 nm = 0.2 and 0.05" × 0.2 = 0.01". 7. The Hubble Space Telescope has a mirror diameter of 2.4 m. Observing at 400 nm, it can therefore achieve an angular resolution of 0.25(0.4 μ m)/(2.4 m) = 0.042". If the stars in the previous problem have an angular separation of 0.033" at 200 light-years, then the distance at which their separation will be 0.042" is (0.033/0.042)(200 light-years) = 160 light-years. 9. Use the last formula in More Precisely 1-4 and use arc seconds instead of degrees. 57.3° = 206,000". Diameter = 380,000 km(3" / 206,000") = 5.5 km; Diameter = 380,000 km(0.05" / 206,000") = 0.092 km = 92 m; Diameter = 380,000 km(0.001"/ 206,000”) = 1.8 m. 10. This is exactly the same problem as the previous problem but with a new distance, 2.5 million light years. Diameter = 2.5 million LY (3"/ 206,000") = 36 Ly; the other two answers are 0.6 Ly and 0.012 Ly ( = 760 A.U.) 11. The Arecibo telescope is 300 m in diameter. Comparing the areas of the two telescopes, square their diameters. (300) 2 / (105) 2 = 8.2, so Arecibo collects 8 times more radio waves and is 8 times more sensitive.

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## This note was uploaded on 11/01/2009 for the course PHYS 229 taught by Professor Mehmetyali during the Fall '09 term at Sabancı University.

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Unassigned%20Problems%202 - Chapter 5 Problems 2. max =...

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