Download File

Unit 10: Measuring the
Properties of Stars
Mr. Ross Brown
Brooklyn School for Law and
Technology
In this unit we will learn about:
• How we measure stars’ distances using parallax
• Why a star’s color indicates temperature & how to use
Wien’s law to determine temperature
• The difference between luminosity and brightness
• How we can measure radius using temperature
• The magnitude system of star brightness
• Stellar spectra and how it indicates surface temperature
• Luminosity classes
• How we estimate stellar masses
• The H-R diagram for inferring a star’s size and
evolutionary state
How do we measure a star’s distance
• 7 March 2016
• Do now: Why is it important to know a star’s
distance from Earth? What other things can
we calculate if we know the distance?
How do we measure a star’s distance
• For nearby stars….
– Triangulation
• Lay out a right triangle, whose one side we know
How do we measure a star’s distance
• Parallax
– Method of triangulation that uses an apparent
change in an object’s position as the observer’s
position changes.
How do we measure a star’s distance
• Parallax is small across such large distances.
Rather than measure it in degrees, we
measure it in fractions of degrees called “arc
seconds” (1/3600 of a degree, 1/60 of an arc
minute)
Homework #17
• 7 March 2016
• How is a parsec defined? How big is a parsec
compared to a light year?
How do we measure a star’s distance
• We define a parallax (p) as ½ the angle by
which it appears to shift. From this, we
measure a star’s distance (d) as 1/p where p is
in arc seconds and d is parsecs.
dpc=1/parc seconds
• One parsecs = 3.26 light-years (3.09*1013 km)
How do we use a star’s light to learn
about its properties?
• 14 March 2016 (Happy Pi Day!)
• Do now: How can we tell how hot something
is without using a thermometer or touching
it?
How do we use a star’s light to learn
about its properties?
• Temperature
– Stars are VERY hot
– Hotter  blue, cooler  red
How do we use a star’s light to learn
about its properties?
• Using color more precisely
– Wien’s Law: longer wavelength = cooler
temperature
How do we use a star’s light to learn
about its properties?
• Luminosity: the amount of energy an object
radiates
– Lightbulb = 60-75 watts
– Sun = 4* 1026 watts
– Luminosity measures how fast an object
consumes its fuel
How do we use a star’s light to learn
about its properties?
• Luminosity measured via inverse-square law
• Its distance and apparent brightness
How do we use a star’s light to learn
about its properties?
• Radius
– If two stars have the same temperature but one is
more luminous, the more-luminous star must
have a larger surface area, thus a larger radius
How do we use a star’s light to learn
about its properties?
• Stefan-Boltzmann Law
– If two stars have the same size but the surface of
one is hotter, the hotter star will have greater
luminosity
In what other ways can we measure a
star’s properties?
• 15 March 2016 (Beware the Ides of March!)
• Do now:
Which star is cooler and many
times brighter than Earth’s Sun?
a) Barnard’s Star b) Betelgeuse
c) Rigel d) Sirius
In what other ways can we measure a
star’s properties?
• Direct measurement of radius
– (Yesterday we used luminosity and StefanBoltzmann Law to arrive at radius)
– We can be more precise by using Angular Size
In what other ways can we measure a
star’s properties?
• Challenges to using angular size
– Due to distance, fuzzy images, even with
telescopes
– Large ground-based telescopes get better images,
but the atmosphere blurs them some
– Computer can de-blur it a little
In what other ways can we measure a
star’s properties?
• We need a HUGE telescope
• Or TWO telescopes, far apart, combined with
computers
In what other ways can we measure a
star’s properties?
• Star radii differ greatly
– Most are roughly the size of our Sun
– Some, like Betelgeuse, are hundreds of times
larger. These are Giants
– Smaller stars, including our Sun, are Dwarfs, or
Dwarves
In what other ways can we measure a
star’s properties?
• The Magnitude System of measuring
brightness
– 150 BCE, Greek astronomer Hipparchus
– Brightest is magnitude 1, dimmest is magnitude 6
In what other ways can we measure a
star’s properties?
• Is the Magnitude System the best system?
– Apparent magnitude is a function of luminosity
and distance
– The scale is “backward,” with the lowest number
representing the brightest stars
– Magnitude differences represent ratios
• Each magnitude represents a factor of 2.512
Homework #18
• 15 March 2016
• What is the H-R Diagram? What are its axes?
How can we differentiate between
classes of stars?
• 16 March 2016
• Do now: What are dimensions across which
we can differentiate one star from another?
How can we differentiate between
classes of stars?
• The Hertzsprung-Russell Diagram (H-R)
– 1912
– If we plot stars according to luminosity and
temperature, the follow a smooth curve
How can we differentiate between
classes of stars?
• The H-R Diagram
– Bright stars on top, dim on bottom
– Hot stars on left, cool on right
– Blue on left, red on right
• Temperature-wise, this is opposite other graphs
– The curve on which most stars (90%) are depicted
is the Main Sequence
How can we differentiate between
classes of stars?
How can we differentiate between
classes of stars?
How can we differentiate between
classes of stars?
• 17 March 2016
• Do now: On what factors does the luminosity
of a star depend?
How can we differentiate between
classes of stars?
• Luminosity depends on a star’s surface area
and temperature
– If stars are the same temperature and one is
brighter, it must have a larger radius
– This is a Giant
– Cool giants are Red Giants
– Hot stars that are dim must have smaller radii
– Dwarfs
– If it’s hot yet dim, White Dwarf
How can we differentiate between
classes of stars?
• What can we surmise about mass and density
and luminosity?
• The Mass-Luminosity Relation
• Larger mass = greater luminosity
How can we differentiate between
classes of stars?
• Luminosity Classes
How can we differentiate between
classes of stars?
– 18 March 2016
– Do now: What are the various methods we use for
determining stellar quantities?
How can we differentiate between
classes of stars?
• Methods of determining stellar quantities
– Distance
– Temperature
– Luminosity
– Composition
– Radius
– Mass
– Radial Velocity
How can we differentiate between
classes of stars?
• The Method of Standard Candles
– Think about oncoming headlights as you drive
How can we differentiate between
classes of stars?
• Method of Standard Candles
– If we know luminosity and brightness, we can
calculate distance
How can we differentiate between
classes of stars?