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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 12

Fig. 12.01: 

Fig. 12.01 Triangulation: finding distances

Fig. 12.01a: 

Fig. 12.01a

Fig. 12.01b: 

Fig. 12.01b

Fig. 12.02: 

Fig. 12.02


A parallax is the apparent shift in an object's position with respect to some back ground (for close stars the background is far away stars) when viewed from two different locations, you need to measure the distance between these locations.   The rest is trigonometry.

Fig. 12.02a: 

Fig. 12.02a


The max. base line for the earth is 2 AU. This allows us measure distances out to about 250 parsecs A parsec is the distance when the parallax is one second of arc. This is a distance of 3.26 ly

Fig. 12.02b: 

Fig. 12.02b


The shift in the star’s position w/respect to the background stars 6 months apart. p is the angle in arcsecond, d is the distance in parsecs. dpc=1/parcsec

Fig. 12.02c: 

Fig. 12.02c

Fig. 12.03: 

Fig. 12.03 The wavelength λ (in nm) of Max. brightness Gives the surface temp. (in K)

Fig. 12.04: 

Fig. 12.04 Inverse square law: the surface area goes up as the Square of the radius.

Fig. 12.04a: 

Fig. 12.04a Flux is the amount of energy per second passing through a square meter of area, watts/m2

Fig. 12.04b: 

Fig. 12.04b


The flux radiated from an object (like a star) decreases as the square of the distance, because the area of a sphere increases as the square of the radius of that sphere. examples, flux at the earth (a distance of 1 AU) is 1370 watts/m2 what would be the flux at a distance of 2 AU?  1370/22 at 3 AU 1370/32

Fig. 12.04c: 

Fig. 12.04c

Fig. 12.05: 

Fig. 12.05

Fig. 12.05a: 

Fig. 12.05a

Fig. 12.05b: 

Fig. 12.05b


In order to find Luminosity (total energy output per second) of star we need to measure its flux and find its distance from earth. Why is luminosity of a star important?  Fundamental understanding of stars. The luminosity of the sun will be our standard Lsun=4x1026 W


Apparent Magnitude originally from 1 to 6, 1 is brightest, 6 faintest modern values, extend into negative values Sirius: magnitude -1.4     Venus: can be as bright as -4 6 is the limit of what you can see with the unaided eye Absolute Magnitude what is the magnitude of an object when it is 10 parsecs away (32.6 light years)  (the closest star to our sun is about 4 light years away) this is called Absolute Magnitude, sun 4.8, Sirius 1.4, Polaris (the pole star) -4.6

Fig. 12.07: 

Fig. 12.07


Spectral Classification of Stars Recall Balmer lines are in the visible region of the spectrum which makes them very useful for optical telescopes now and one hundred years ago (when this classification scheme was first thought of) Also, recall that Balmer absorption lines occur from a hydrogen electron being in the second excited state (there must be enough energy around to get the electron to jump up from the ground state) 


Therefore when Balmer absorption lines are weak (when they don't appear very dark) we know something about the star. Temperature is a measure of the average kinetic energy of a substance, so when we see weak Balmer lines in stars cooler than the sun, we can conclude that the kinetic energy is not strong to put a large number of hydrogen electrons into the 2nd excited state (2nd energy level).  For hotter stars than the sun, however we see very intense Balmer absorption lines (very dark). When stars get even hotter than this the lines get weaker again. Why? The hydrogen atoms in these stars are so energetic that electrons are striped away, the hydrogen becomes ionized (a different spectrum, not Balmer lines).

Fig. 12.07a: 

Fig. 12.07a


Remember that the relative strength of the Balmer lines can give us the temperature of a star.

Fig. 12.07b: 

Fig. 12.07b

Fig. 12.07c: 

Fig. 12.07c

Fig. 12.08: 

Fig. 12.08

Fig. 12.09: 

Fig. 12.09


The spectral sequence from hotter to colder from the work at Harvard, which started over one hundred years ago, ended up being: O  B  A  F  G K M  it's further divided by numbers 0 to 9 between the letters For example:  B0, B1, B2, B3, B4, B5, B6, B7, B8, B9, A0, A1, A2, ... B0 is hotter than B1 and so forth.  

Fig. 12.10: 

Fig. 12.10

Fig. 12.11: 

Fig. 12.11


This classification shows surface temperature ranges O stars 25,000 Kelvin and up (color: bluish-white) B stars 11,000-25,000 K (color: bluish-white) A stars 7500-11,000 K (color: bluish-white) F stars 6000-7500 K (color: bluish-white to just white) G stars 5000-6000 K (color: white to yellowish) Recall our sun has a surface temp. of about 5800, so our sun is a G type star, G2 in fact. K stars 3500-5000 K (color: yellowish to orange) M stars 3500 K and lower  (red)

Fig. 12.12: 

Fig. 12.12 The Doppler effect tells us relative motion of the stars The speed of a star along our line of sight is radial velocity

Fig. 12.12a: 

Fig. 12.12a

Fig. 12.12b: 

Fig. 12.12b

Fig. 12.13: 

Fig. 12.13


Binary stars are common in our galaxy. Upward of 40% of all the stars we see are in binary systems. This gives us a way to determine the mass of stars using Kepler’s 3rd law.

Fig. 12.14: 

Fig. 12.14

Fig. 12.14a: 

Fig. 12.14a

Fig. 12.14b: 

Fig. 12.14b

Fig. 12.15: 

Fig. 12.15

Fig. 12.16: 

Fig. 12.16


Eclipsing binary stars also give us detail about the diameter of a star, which we get from the amount of time of the eclipse.

Fig. 12.16a: 

Fig. 12.16a

Fig. 12.16b: 

Fig. 12.16b

Fig. 12.17: 

Fig. 12.17


The Hertzsprung-Russell Diagram H-R Diagram for short Note: surface temperature starting on the left of the diagram is the hottest (O type stars)  Main Sequence stars, White Dwarfs, and Giants and SuperGiants G type stars are not very common in our galaxy, only about 4%, M stars are by far the most abundant 70%. 

Fig. 12.18: 

Fig. 12.18

Fig. 12.19: 

Fig. 12.19


Two stars that are the same temperature, i.e. same peak color, can have greatly different luminosities. How can this be? Greater luminosity means greater surface area, we can distinguish between giant stars, and dwarf stars and average size stars, using the H-R diagram.

Fig. 12.20: 

Fig. 12.20

Fig. 12.20a: 

Fig. 12.20a


Main sequence stars obey the mass-luminosity relation. In solar units L=M3

Fig. 12.20b: 

Fig. 12.20b

Fig. 12.21: 

Fig. 12.21

Fig. 12.21a: 

Fig. 12.21a

Fig. 12.21b: 

Fig. 12.21b

Fig. 12.21c: 

Fig. 12.21c

Fig. 12.22: 

Fig. 12.22

Fig. 12.23: 

Fig. 12.23


Periodic variable stars are used to determine distance On the H-R diagram they are in an unstable position, the so called instability strip.

Fig. 12.24: 

Fig. 12.24

Fig. 12.25: 

Fig. 12.25

Fig. bf12.01: 

Fig. bf12.01

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