homework3solutions - AST 3722C - Spring 2008 Homework #3...

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Unformatted text preview: AST 3722C - Spring 2008 Homework #3 – solutions • 1. [1 point] You want to observe Comet 17P/Holmes tonight and you look up online that it’s equatorial position at 9 p.m. (EST) will be α = 03 h 26 m 58 . 4 s and δ = +39 ◦ 12 ′ 19 . 7 ′′ (2000.0). You are also told that the comet is moving 31.9 arcsec per hour in R.A. and -12.1 arcsec per hour in Declination. Calculate the equatorial coordinates of the comet at 10 p.m. Since 10 p.m. is 1 hour after 9 p.m., the comet has moved 31.9 arcsec in R.A. and -12.1 arcsec in Dec. The latter is easier; you just have to remember that a negative Dec motion means the comet moves south. Let δ 10 be the Declination at 10 p.m. δ 10 = δ + offset = δ − 12 . 1 ′′ = +39 ◦ 12 ′ 19 . 7 ′′ − 12 . 1 ′′ = + 39 ◦ 12 ′ 07 . 6 ′′ R.A. is harder. We need to convert that 31.9 arcsec into an equivalent amount of change in R.A. You cannot just divide by 15; you have to account for the cos δ factor. Recall that R . A . distance in arcsec = R . A . distance in seconds × 15 × cos δ mean where δ mean is the average of the Declinations that are appropriate to the problem. In this case, δ mean = 1 2 × ( δ + δ 10 ). Therefore R . A . distance in seconds = R . A . distance in arcsec 15 × cos δ mean = 31 . 9 15 × cos(+39 ◦ 12 ′ 13 . 1 ′′ ) = 31 . 9 15 × . 7749 = 2 . 74 . The comet is moving east (since the rate is positive). Let α 10 be the R.A. at 10 p.m. So: α 10 = α + offset = α + 2 . 74 s = 03 h 26 m 58 . 4 s + 2 . 74 s = 03 h 26 m 61 . 1 s (now carry over) = 03 h 27 m 01 . 1 s . 1 • 2. [2 points] The nearest star system to the Sun is the α Centauri system, which has 3 stars – A, B, and C (a.k.a Proxima). A and B are easy to see, but C is pretty faint. A has equatorial coordinates (2000.0) of α = 14 h 39 m 36 . 5 s and δ = − 60 ◦ 50 ′ 02 . 3 ′′ . B has equatorial coordinates (2000.0) of α = 14 h 39 m 35 . 1 s and δ = − 60 ◦ 50 ′ 13 . 8 ′′ . (a) Given these coordinates, what was the angular separation of these stars? I didn’t put it in the problem but let a subscript X refer to star X. You should remember from previous homework that in situations like this, you can use the small-spherical triangle approximation. You just have to be careful of using cos δ factor. So: separation = radicalBig ( δ A − δ B ) 2 + (( α A − α B ) × 15 × cos δ mean ) 2 . In the second term above, the 15 and the cos δ mean allow us to convert the difference in R.A. from seconds to arcsec. In this case, δ mean is just 1 2 × ( δ A + δ B ). First we deal with the Declinations: δ A − δ B = − 60 ◦ 50 ′ 02 . 3 ′′ − ( − 60 ◦ 50 ′ 13 . 8 ′′ ) = − 60 ◦ 50 ′ 02 . 3 ′′ + 60 ◦ 50 ′ 13 . 8 ′′ = 11 . 5 ′′ ....
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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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homework3solutions - AST 3722C - Spring 2008 Homework #3...

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