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# homework5solutions - AST 3722C - Spring 2008 Homework #5...

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AST 3722C - Spring 2008 Homework #5 – solutions. Instructions: Solve each part of each problem below. Where math is involved, and unless otherwise indicated, show your work. 1. [2 points] You want to study the double star 32 Eridani. Star A has J2000 coordinates α A = 03 h 54 m 17 . 47 s and δ A = 02 57 14 . 5 ′′ . Star B has J2000 coordinates α B = 03 h 54 m 17 . 28 s and δ B = 02 57 09 . 9 ′′ . You want to start an observing campaign where you observe these two stars at many wavelengths across the EM spectrum, from ultraviolet to radio, with the following telescopes: wavelength telescope wavelength primary mirror regime range diameter (m) ultraviolet GALEX 135 nm to 280 nm 0.5 visible Hubble 3000 ˚ A to 9000 ˚ A 2.4 infrared (near) Keck 0.9 μ m to 2.5 μ m 10 infrared (mid) Subaru 5 μ m to 23 μ m 8 infrared (far) Spitzer 24 μ m to 160 μ m 0.85 radio (submillimeter) JCMT 0.35 mm to 0.85 mm 15 radio (millimeter) ARO 1 mm to 3 mm 12 radio (microwave) GBT 0.7 cm to 21 cm 100 (a) Calculate the separation of star A and star B, in arcseconds. The stars are close together so we can use the small-triangle formula: separation = r δ ) 2 + (Δ α ) 2 . The tricky part is that Δ α must have the same units as Δ δ . The separation in R.A. is Δ α = α A α B = 0 . 19 s = (0 . 19 × 15 × cos δ m ) in arcsec = (0 . 19 × 15 × cos( 02 57 12 . 2 ′′ )) in arcsec = 2 . 85 ′′ . I used δ m = 1 2 ( δ A + δ B ) here. The separation in Dec. is easy, just Δ δ = δ A δ B = 4 . 6 ′′ . So that means separation = r ( 4 . 6 ′′ ) 2 + (2 . 85 ′′ ) 2 = 5 . 4 ′′ . 1

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(b) For each telescope, calculate the Rayleigh criterion at both the short and long wave- length boundaries. Express your answers in arcseconds. The Rayleigh criterion is 1 . 22 × λ/D . So we have to do this for all 8 rows in the above table and at 2 wavelengths each. Note that you want to have λ have the same units as D . Then the answer comes out in radians which you can then change to arcsec. wavelength telescope wavelength Rayleigh criterion Rayleigh criterion regime in radians in arcsec ultraviolet GALEX 135 nm 3 . 29 × 10 7 0.068 ultraviolet GALEX 280 nm 6 . 83 × 10 7 0.141 visible Hubble 3000 ˚ A 1 . 52 × 10 7 0.031 visible Hubble 9000 ˚ A 4 . 57 × 10 7 0.094 infrared (near) Keck 0.9 μ m 1 . 10 × 10 7 0.023 infrared (near) Keck 2.5 μ m 3 . 05 × 10 7 0.063 infrared (mid) Subaru 5 μ m 7 . 63 × 10 7 0.157 infrared (mid) Subaru 23 μ m 3 . 51 × 10 6 0.723 infrared (far) Spitzer 24 μ m 3 . 44 × 10 5 7.105 infrared (far) Spitzer 160 μ m 2 . 30 × 10 4 47.368 radio (sub-mm) JCMT 0.35 mm 2 . 85 × 10 5 5.872 radio (sub-mm) JCMT 0.85 mm 6 . 91 × 10 5 14.260 radio (millimeter) ARO 1 mm 1 . 02 × 10 4 20.970 radio (millimeter) ARO 3 mm 3 . 05 × 10 4 62.911 radio (microwave) GBT 0.7 cm 8 . 54 × 10 5 17.615
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## This note was uploaded on 11/09/2009 for the course AST 4700 taught by Professor Fernandez during the Spring '09 term at University of Central Florida.

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homework5solutions - AST 3722C - Spring 2008 Homework #5...

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