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The Distance to the Stars
- How far are the stars, and how do we know?
- Brightness of stars: distance vs. luminosity
Terms to Know
1. How far are the stars, and how do we know?
The ancient Greeks (as well as more "recent" astronomers,
such as Tycho Brahe) based major theories on the lack of observed
parallax of the "fixed" stars; i.e., the stars didn't appear to wiggle
back and forth as the Earth rotates on its axis and revolves in its orbit
around the Sun. But as we now know, some stars do show that wiggle,
or parallax, every year. You can use that parallax to measure the distance
to the nearest stars:
- Use the Earth's orbit around the sun as
baseline for triangulation:
Baseline = 2 A.U. (Earth's orbit)
- Formula (just simple geometry using the small-angle
approximation -- see "By the Numbers" 3.1, p. 31):
- distance (parsecs) = 1
/ angle (arcseconds)
- the 'angle' is referred to as the 'parallax'
- 1 parsec ("PARallax SECond") = 3.26 light-years
- 1 arcminute (') = 1/60th of one degree
- 1 arcsecond (") = 1/60th of one arcmin
Nearest star: Proxima Centauri 1.3 parsecs
- - actually a 3-star system, one like the Sun
- - visible to the eye
- Next closest: Barnard's star 1.8 parsecs
- - invisible to the naked eye Inference:
- Stars must come in a wide range of luminosity
- Could space be filled with dim stars that we
just can't see?
- Limitation of parallax:
- - difficult to measure parallax angle for objects
more than a few parsecs away -- most stars in the Milky Way Galaxy (and all
galaxies outside the Milky Way) are too far to use parallax for measuring
- But remember importance of parallax:
- - primary measurement of distance in astronomy.
- - the 'bottom rung' of the cosmic distance
- - with parallax, we calibrate all other methods
of determining distances to objects that are farther away.
2. Brightness of stars: distance vs. luminosity
The luminosity of a star is its intrinsic, or physical
brightness, independent of its distance. Even if you can't see the star,
its luminosity remains the same.
Recall the Inverse Square law for light: I
Types and Properties of Stars and the HR Diagram
Terms to Know
the Main Sequence
dwarf, giant, and supergiant stars
- Temperatures and luminosities of stars are observed
to be highly correlated (like weight and height for humans)
- The Hertzsprung-Russell diagram (1911-1913)
is a plot of temperature (or color -- basically the
same thing as color, for black bodies) vs. luminosity.
Every star can be plotted somewhere on the H-R diagram. It is one
of the most important graphs in astronomy, and shows the complete
life cycles of stars of all different masses, ages, temperatures,
colors, and luminosities.
90% of all stars have luminosities (or absolute magnitudes) and
temperatures (or colors) that place them in a narrow diagonal band in
the HR diagram, called the Main Sequence. This makes sense,
since stars are almost perfect black bodies, and we know that cold
black bodies are dim and red, while hot black bodies are luminous and
But there are some stars that are dim and blue,
and others that are brilliant and red! What's going on?
There must be a third characteristic coming
into play: the radius of the star! Bigger stars have more surface
area, so they appear brighter, while smaller stars have less surface
area and appear dimmer, even if they are very hot.
Which is more important: T or r?
Recall: The area of a sphere is given by A
Now remember the Stefan-Boltzmann Law?
To be more accurate, we should actually write it:
So they're both important.
Here are all the parts of the H-R diagram:
- The Main Sequence
temperature and luminosity
more luminous (and larger
size) than Main Sequence stars of same temperature
- Super Giants
even more extreme than giants
- White Dwarfs
very small, hot, and faint
- How are they all related?
- An evolutionary sequence? Sequences?
- Note 1:
Don't confuse white dwarfs with
luminosity class V ``dwarfs.''
They are NOT the same!
- Red dwarfs are the cool end of the Main Sequence,
i.e. luminosity class V, and are NOT the same as white dwarfs.
- Note 2:
Don't confuse "motion" in the
HR diagram with true motion in space! A star that stays in one place
all its life but changes temperature and luminosity will move around
in the HR diagram. Meanwhile, a star that is zooming around in the
Milky Way Galaxy could stay perfectly still in the HR diagram, if
its luminosity and temperature don't change.
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