Astr 3000 Contemporary Astronomy
Fall 2017  Assignment 12  Answers
Assignment

Stars A and B are equally bright, but star B is 6 times further away

Set P_{A} = P_{B} = 1

d_{A} = 1

d_{B} = 6d_{A} = 6

then I_{A} = P_{A} / d_{A}²
= 1

and I_{B} = P_{B} / d_{B}²
= 1/36

Which one is dimmer from our point of view? Since
I_{B} < I_{A} star B is dimmer

By how much? by a factor of 36

Star C has only half the brightness of star D, and is 3 times further away

Set P_{D} = 1

P_{C} = ½P_{D} = ½

d_{D} = 1

d_{C} = 3d_{D} = 3

then I_{D} = P_{D} / d_{D}²
= 1

and I_{C} = P_{C} / d_{C}²
= ½ / 3² = 1/18

Which one is dimmer from our point of view? Since
I_{C} < I_{D} star C is dimmer

By how much? by a factor of 18

Star E has five times the brightness of star F, and is 3 times further
away

Set P_{F} = 1

P_{E} = 5P_{F} = 5

d_{F} = 1

d_{E} = 3d_{F} = 3

then I_{F} = P_{F} / d_{F}²
= 1

and I_{E} = 5 / 3² = 5/9

Which one is dimmer from our point of view? Since
I_{E} < I_{F} star E is dimmer

By how much? by a factor of 9/5 = 1.8

Star G is six times the radius of star H, and has a surface temperature
twice as high

Set r_{H} = 1

r_{G} = 6r_{H} = 6

T_{H} = 1

T_{G} = 2T_{H} = 2

then P_{H} = r_{H}² T_{H}^{4}
= 1

and P_{G} = r_{G}² T_{G}^{4}
= 6² 2^{4} = 576

Which one produces the most amount of light? Since
P_{G} > P_{H} star G has the higher luminosity (power)

By what factor? by a factor of 576

Star K is six times the radius of star L, but has a surface temperature
only half that of star L

Set r_{L} = 1

r_{K} = 6r_{L} = 6

T_{L} = 1

T_{K} = ½T_{L} = ½

then P_{L} = r_{L}² T_{L}^{4}
= 1

and P_{K} = r_{K}² T_{K}^{4}
= 6² ½^{4} = 2.25

Which one produces the most amount of light? Since
P_{K} > P_{L} star K has the higher luminosity (power)

By what factor? by a factor of 2.25

Compared to star M, star N is three times bigger and eight times further
away. The surface temperature of start M is 4000 K, whereas the surface
temperature of start N is 5000 K

Set r_{M} = 1

r_{N} = 3 r_{M} = 3

T_{M} = 1 (in units of 4000 K)

T_{N} = 5000 K = 5/4 T_{M}

d_{M} = 1

d_{N} = 8d_{M} = 8

then I_{M} = r_{M}² T_{M}^{4}
/ d_{M}² = 1

and I_{N} = r_{N}² T_{N}^{4}
/ d_{N}² = 3² (5/4)^{4} / 8² = 0.34

Which one is dimmer from our point of view? Since
I_{N} < I_{M} star N is dimmer

By how much? by a factor of 0.34
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