Question

1. A red photon has a wavelength of 660 nm. How fast must a star be moving toward the Earth for a red photon emitted by the star to change its color to an orange photon of wavelength 620 nm? You may, if you wish, express your answer either in m/s or in terms of the speed of light c (e.g., "0.021c"). [You'll need to do a little bit of algebra. Keep in mind that, by convention, the velocity is negative if the motion is toward the observer. Assume that the speed is less than 0.2c, then check whether this assumption is correct.] [4 points; from Chapter 5] 2. Astronomers observe two stars, A and B. a. Star A has a parallax of 0.04 arcseconds. Calculate the distance to star A in parsecs (pc). b. Star B has a spectrum that is identical to that of star A, indicating that the two are the same type of star with the same luminosity. However, the brightness of star B as observed from the Earth is only 0.0001 times that of star A. Calculate the distance to star B. [4 points; from Chapter 6]

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Answer 1

2

a)

$\theta$ = angle = 0.04 arcseconds

d = distance

we know that

distance = 1/angle

d = 1/$\theta$

d = 1/0.04

d = 25 parsec

b)

B_b = brightness of B = 0.0001 x brightness of A = 0.0001 B_a

B_b /B_a = 0.0001

d_a = distance to A = 25 parsec

d_b = distance to B

using the equation

d²_b/d_a² = B_a /B_b

d²_b/25² = 1/0.0001

d_b = 2500 parsec