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Stars• Stars are very far away.• The nearest star is over

270,000 AU away! (Pluto is 39 AU from the Sun)

• That is equal to 25 trillion miles!

• At this distance it takes light 4.3 years to travel from this star. In other words the star is 4.3 light years away.

• The space shuttle travels 17,500 miles/hour, at this speed it would take over 160,000 years to get to the nearest star!

The Pleiades Star Clusterabout 400 light years away

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How Do We Know the Distance to the Stars?

Using the size of the shift due to parallax and knowing the distancefrom the Earth to the Sun we canfind the distance to nearby stars.

• The ancient Greeks realized that if the Earth moved we should see shifts in the positions of the stars over one year.

• We do see these shifts in star positions but they are very,very small.

• This shift in an object’s position due to the motion of the observer is called parallax.

• The farther an object the smaller the shift and the harder it is to find its distance.

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How Do We Know Anything About Stars?

• Since stars are so far away they almost always appear just as points of light.

• But as we already know we can learn a lot from light!

• Light can tell us about a star’s:– surface temperature– distance– motion– rotation– composition

• and if the star is part of binary star system we can determine its mass.

The Trapezium Star Clusterin the Orion Nebulaabout 1500 light years away

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Luminosity• Luminosity is the amount of energy

a body radiates each second.• Stars appear brighter or dimmer to

us for two reasons:– they are at various distances from us

and– some stars are naturally more luminous

than other stars

• If we know a stars distance and we measure its apparent brightness we can determine its luminosity.

• A stars luminosity is related to both its temperature and its radius.

• So if we also know a star’s temperature we can determine its radius.

Large stars have a higherluminosity than small stars.

Hot stars have a higher luminosity than cool stars.

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Luminosity

For stars with the same temperature,larger stars are more luminous.

For stars with the same radius, hotter stars are more luminous.

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• The inverse-square law (IS) is:

• B is the brightness at a distance d from a source of luminosity L

• This relationship is called the inverse-square law because the distance appears in the denominator as a square

The Inverse-Square Law

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LB

d

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Stellar Spectra• The temperature of a star can

be determined two ways.– from Wien’s law

– from the presence or absence of certain spectral lines.

• Strong Hydrogen lines are only seen in stars that have surface temperatures between 8,000 and 15,000 Kelvin.

• The Sun does not show strong Hydrogen lines even though it is more than 70% Hydrogen!

A) A spectrum from a star hotter than the Sun with strong Hydrogen lines.

B) A spectrum from a star like our Sun.

C) A spectrum from a star cooler than our Sun.

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Spectral Classification

• To understand the properties of stars astronomers gathered hundreds of thousands of stellar spectra.

• To understand the patterns they saw they developed spectral classification systems in order to help understand the nature of stars.

• The first system was developed in 1866 by Pietro Angelo Secchi an Italian priest and scientist. He grouped stars by their color.

• The system used today was developed by Annie Jump Cannon who ordered stars by temperature.Annie Jump Cannon

1863 - 1941

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Spectral Classes• In 1901 Cannon

developed a system where letters were assigned to stars of different temperature.

• In the 1920’s another astronomer Cecilia Payne explained why spectral lines change with temperature and confirmed the system that Cannon developed.

In order from hottest to coldest starsthe letter classification is O, B, A, F, G, K, MIn this system our Sun is a G star.

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Measuring a Star’s Composition

• To find the quantity of a given atom in the star, we use the darkness of the absorption line

• This technique of determining composition and abundance can be tricky!

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Measuring a Star’s Composition

• Possible overlap of absorption lines from several varieties of atoms being present

• Temperature can also affect how strong (dark) an absorption line is

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Example: Measuring the Radius of Sirius

• Solving for a star’s radius can be simplified if we apply L = 4R2T4 to both the star and the Sun, divide the two equations, and solve for radius:

• Where s refers to the star and refers to the Sun

• Given for Sirius Ls = 25L, Ts = 10,000 K, and for the Sun T= 6000 K, one finds Rs = 1.8R

1 22s s sR L T

R L T

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Binary Stars• Most stars in the sky

actually exist as part of a group of 2 or more stars.

• Two stars gravitationally bound are called binary stars.

• Binary stars provide a means of determining the masses of stars.

• Other properties can also sometimes be determined from binary stars.

The two stars of a binary starsystem orbit around theircommon center of mass.Using Newton’s modified formof Kepler’s 3rd Law the massof the stars can be found.

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• If both stars in a binary star system are visible this is a visual binary. The motion of the two stars can be observed directly.

• Sometimes only one point of light is seen but the spectra of this star shows two sets of lines. This is a spectroscopic binary. The motion of the two stars can found from the Doppler shift of the lines.

Example of a spectroscopic binary

Types of Binary Stars

Exampleof a visualbinary

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Eclipsing Binaries• When the orbit of a

binary is viewed edge-on from Earth the stars may actually eclipse one another. This is an eclipsing binary.

• Eclipsing binaries can give information on the radius, mass and shape of the stars.

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Summary of Measurement Methods

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The Hertzprung-Russell Diagramor The H-R Diagram

• The H-R diagram puts into one figure many of the properties of stars already discussed.

• Where a star is located on this diagram depends on – its luminosity and

– its spectral class or temperature

• Stars tend to show up in distinct groups when plotted in this way.

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Main Sequence, Giants and Dwarfs• Nearly 90% of the stars lie

along a line on the H-R diagram called the Main Sequence.

• Those stars in the upper right of the figure are very luminous but also very cool. Therefore they must be very large. These are the Red Giant stars.

• Those stars in the lower left are very hot but have low luminosity. They must be very small. These are White Dwarf stars. Betelgeuse is almost as big as the orbit

of Jupiter. Sirius B is as small as Earth.

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The Mass of Stars on the Main Sequence

• Where stars are located along the Main Sequence depends almost exclusively on the star’s mass.

• More massive stars are more luminous, they release energy at a higher rate and are located towards the upper left of the Main Sequence. (They also consume Hydrogen much faster).

• Less massive stars are located at the lower right.

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• Main-sequence stars obey a mass-luminosity relation, approximately given by:

• L and M are measured in solar units

• Consequence: Stars at top of main-sequence are more massive than stars lower down

The Mass-Luminosity Relation

3L M

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Luminosity Classes

• Another method was discovered to measure the luminosity of a star (other than using a star’s apparent magnitude and the inverse square law)– It was noticed that some stars had very narrow

absorption lines compared to other stars of the same temperature

– It was also noticed that luminous stars had narrower lines than less luminous stars

• Width of absorption line depends on density: wide for high density, narrow for low density

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Luminosity Classes

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Luminosity Classes

• Luminous stars (in upper right of H-R diagram) tend to be less dense, hence narrow absorption lines

• H-R diagram broken into luminosity classes: Ia (bright supergiant), Ib (supergiants), II (bright giants), III (giants), IV (subgiants), V (main sequence)– Star classification example: The

Sun is G2V

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Luminosity Class as Distance Estimator

• Measure spectral line widths to get Luminosity Class yields luminosity of the star

• Use inverse-square rule to find distance to a star from its luminosity and measured brightness.

• Useful for stars that are beyond the reach of the parallax method.

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Summary of the HR Diagram• Most stars lie on the main

sequence– Of these, the hottest stars

are blue and more luminous, while the coolest stars are red and dim

– Star’s position on sequence determines its mass, being more near the top of the sequence

• Three classes of stars:– Main-sequence– Giants– White dwarfs

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Summary