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ps2 - Assignment 2 Due Wednesday 2006:04am PHYSICS 8.284...

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Assignment 2 PHYSICS 8 . 284 Due Wednesday 2006 February 22 11:04am Reading: Press, Chapter 2, Chapter 3.5 and Chapter 4.1 and 4.2 through 4.2.5 (http://www.lanl.gov/DLDSTP/ay45/ay45toc.html) 1-2. Assume, for the sake of simplicity, that the B filter in the Johnson UBV system has A to 4900 ˚ 100% transmission from 3900 ˚ A , and 0% transmission outside this range. A to 5950 ˚ Assume that the V filter has 100% transmission from 5050 ˚ A . Compute (by numerical integration, using Simpson’s rule with only one interval if you like) the fraction of the total flux emanating in these two idealized passbands from black bodies with each of the following temperatures: a) 10 5 K, b) 35 , 000 K, c) 9700 K, d) 6500 K, e) 4700 K, f) 2600 K. The zero-point of the UBV color system is arbitrary, and was chosen (by Johnson and Morgan) so that an A0 star would have U B = B V = 0. Compute B V colors for the black body temperatures above, choosing your zero point so that a 9700 K black body has B V = 0. Suggestion: In doing numerical integrals it’s often a good idea to take all the di- mensioned constants outside the integral and change variables so that one integrates over a dimensionless variable, e.g. let the variable of integration be x = h�/kT or y = hc/θkT . The dimensioned constants set the scale of the problem, while the dimensionless integral gives some fraction of that typical scale.
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