homework9solutions - AST 3722C - Spring 2008 Homework #9...

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Homework #9 – solutions Astrometry. Star RA Dec. PG 1047+003 10 h 50 m 02 . 79 s 00 00 36 . 7 ′′ PG 1047+003 A 10 h 50 m 05 . 65 s 00 01 11 . 1 ′′ PG 1047+003 B 10 h 50 m 09 s 00 02 00 ′′ 1. (1 pt) Use the values above to calculate the angular separation in Dec., the separation in R.A., and the total separation between star ’003A’ and star ’003’. How is 003 positioned compared to star 003A; i.e., is it farther north or south? Is it farther east or west? Star 003 is 34.4 arcsec farther north in Declination, and it is 2.86 seconds farther west in R.A. . But we need that in arcseconds. So, the separation is 2.86 seconds × 15 × cos δ mean = 2.86 seconds × 15 × cos( 00 00 53 . 9 ′′ ) = 42.9 arcsec farther west . The total separation can be found from the Pythagorean theorem: 54.99 arcseconds . 2. (1 pt) The “position angle” (PA) is the direction on the plane of the sky one travels to connect two objects. For example, if object X is due north of object Y, object X has a PA of 0 . If object X is due southwest of object Y, object X has a PA of 225 . PA increases in a counterclockwise sense (i.e. it use the right hand rule). Use the given R.A. and Dec. to ±gure out the PA of star 003 with respect to 003A. The easiest way to visualize this is to setup a little drawing: The angle θ is the PA. Note how it is de±ned from north through east (as implied by the question). So you should see that star 003 has to have a PA with respect to star 003A of something between 270 and 360 . To do the geometry, I’ve also put in the angle 2 π θ . So you can probably tell that tan(2 π θ ) = 42 . 9 / 34 . 4. And since we’ve set things up explicitly, we are pretty much automatically taking care of the arctan ambiguity. This means θ = 308.7 degrees . 3. (1 pt) In the CCD image, star 003A is the middle of the three stars in that diagonal. Star 003 is the bottom-right one. Find the pixel locations of those two stars in the image. (If you’re using the spreadsheet, be careful! Your answer for each star has to be an ordered pair of numbers, not an alphanumeric string.) If you used the spreadsheet, you would have found star 003A at entry DJ409. The pixel value there is 4478, which is the highest of any pixel that the star is on. In terms of pixels this location is pixel (114,193) . Star 003 is at entry EX453. The pixel value there is 4060, which is the highest of any pixel that the star is on. In terms of pixels this location is pixel (154,149) . 1
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homework9solutions - AST 3722C - Spring 2008 Homework #9...

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