# Day 25 - Ch. 9 - Characterizing Stars

Phys/Geog 182 Week 7 Quiz We will answer questions on a work sheet as we review the way we characterize stars. Stellar Parallax A Parsec is the distance

from us that has a parallax of one arc second (parsec = pc) 1 parsec = 206,265 A.U. or about 3.3 light-years Questions 1 and 2 Stellar Parallax

The parallax angle is an angle in the triangle with a baseline of one astronomical unit (1 A.U.) Question 1 One parsec corresponds to an angle of

1 arc second. 10 parsecs would correspond to an angle of 1/10 of an arc second. And 50 parsecs would correspond to an angle of 1/50 of an arc second. Star X is nearer and has the greater parallax angle.

Question 2 We measure the parallax angle in order to find the distance, so we can calculate the absolute magnitude. The Suns Neighborhood Each

successive circle has a radius which is 0.5 parsec larger About 21 systems are shown

(some are binaries) Inverse-Square Law for Light - question 3. Question 3

The farther star is 4 times as far away. Thus it is fainter. 4 times 4 is 16, so it is 16 times fainter. Imagine one more shell in the previous picture, with 4x4 or 16 squares.

Two unlike objects at different distances may appear the same question 4 Question 4 Just like the picture, the closer star must be dimmer, if it appears as bright as the farther star.

Thus the closer star has a lower luminosity (amount of light emitted). Apparent Magnitude of some typical objects, along with some limits for seeing through various instruments.

Each magnitude corresponds to a change in brightness of 2.5 times Question 5 Question 5 An 8th magnitude star is one magnitude

greater than a 7th magnitude star, so it is dimmer. Each magnitude corresponds to a change in brightness of 2.5 times. So the 8th magnitude star is 2.5 times dimmer than the 7th magnitude star. The absolute magnitude

is the apparent magnitude when viewed from 10 pc Our sun would appear to have an apparent magnitude of 4.8 if it were at 10 pc distance, so it has an absolute magnitude of 4.8

Question 6 Once we get the absolute magnitude from the apparent magnitude and the distance, we can get the luminosity compared to the Sun. Question 6

The concept of absolute magnitude allows us to remove the effect of differing distance. Thus we can talk about the properties of the star itself, without needing to keep in mind the location (or distance from us). Star Colors vary from red to blue question 7

Question 7 The color of a star will not change if we look at it from a different distance unless there is a dust cloud in the way. However, the angular size, parallax, apparent magnitude, and proper motion would appear to change at different

distances. spectral classification uses letters for the spectral classes: OBAFGKM (and LT) based on the stars temperature. Summary so far To measure the stars, we measure the

1. apparent magnitude 2. distance (by parallax) 3. spectrum (to find the temperature) and so we can deduce the luminosity and spectral class (OBAFGKM-LT) Stellar Sizes: from

300 times the size of the Sun to only 0.01 times the size of the Sun.

Stellar sizes Some stars are close enough and big enough to be seen as disks, for example Betelguese. Most stars look like points, so we need to deduce the size from the luminosity (based on the apparent magnitude) and the temperature by a formula: luminosity a (radius)2 x (temperature)4

(where a means is proportional to) Questions 8 and 9 Question 8 From the formula: luminosity a (radius)2 x (temperature)4 If the radius is not changed, but the temperature is increased from T to 2T

then 2T times 2T times 2T times 2T gives a number 16 times greater than T4 Question 9 From the formula: luminosity a (radius)2 x (temperature)4 If the temperature is not changed, but the radius is increased from r to 2r then

2r times 2r gives 4r2 - which is 4 times greater than r2

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