Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in...
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Transcript of Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in...
![Page 1: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/1.jpg)
Homework: Parallax
• Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs”
• By definition, d=1pc if p=1”, so convert d to A.U. by using trigonometry
• To calculate p for star with d given in lightyears, use d=1/p but convert ly to pc.
• Remember: 1 degree = 3600”• Note: p is half the angle the star
moves in half a year
![Page 2: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/2.jpg)
Our Stellar Neighborhood
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Scale Model
• If the Sun = a golf ball, then– Earth = a grain of sand
– The Earth orbits the Sun at a distance of one meter
– Proxima Centauri lies 270 kilometers (170 miles) away
– Barnard’s Star lies 370 kilometers (230 miles) away
– Less than 100 stars lie within 1000 kilometers (600 miles)
• The Universe is almost empty!
• Hipparcos satellite measured distances to nearly 1 million stars in the range of 330 ly
• almost all of the stars in our Galaxy are more distant
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Reminder: Three Things Light Tells Us
• Temperature – from black body spectrum
• Chemical composition– from spectral lines
• Radial velocity– from Doppler shift
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Luminosity and Brightness
• Luminosity L is the total power (energy per unit time) radiated by the star, actual brightness of star, cf. 100 W lightbulb
• Apparent brightness B is how bright it appears from Earth– Determined by the amount of
light per unit area reaching Earth– B L / d2
• Just by looking, we cannot tell if a star is close and dim or far away and bright
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Brightness: simplified
• 100 W light bulb will look 9 times dimmer from 3m away than from 1m away.
• A 25W light bulb will look four times dimmer than a 100W light bulb if at the same distance!
• If they appear equally bright, we can conclude that the 100W lightbulb is twice as far away!
![Page 7: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/7.jpg)
Same with stars…
• Sirius (white) will look 9 times dimmer from 3 lightyears away than from 1 lightyear away.
• Vega (also white) is as bright as Sirius, but appears to be 9 times dimmer.
• Vega must be three times farther away
• (Sirius 9 ly, Vega 27 ly)
![Page 8: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/8.jpg)
Distance Determination Method
• Understand how bright an object is (L)is (L)• Observe how bright an object appears (B)appears (B)
• Calculate how far the object is away:
B L / d2
So
L/B d2 or d √L/B
![Page 9: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/9.jpg)
Homework: Luminosity and Distance
• Distance and brightness can be used to find the luminosity:
L d2 B
• So luminosity and brightness can be used to find Distance of two stars 1 and 2:
d21 / d2
2 = L1 / L2 (since B1 = B2 )
i.e. d1 = (L1 / L2)1/2 d2
![Page 10: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/10.jpg)
The Magnitude Scale• A measure of the apparent
brightness
• Logarithmic scale • Notation: 1m.4 (smaller brighter)• Originally six groupings
– 1st magnitude the brightest
– 6th magnitude is 100x dimmer
• So a difference of 5mag is a difference of brightness of 100
• Factor 2.512=1001/5 for each mag.
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Absolute Magnitude
• The absolute magnitude is the apparent magnitude a star would have at a distance of 10 pc.
• Notation example: 2M.8
• It is a measure of a star’s actual or intrinsic brightness called luminosity
• Example: Sirius: 1M.4, Sun 4M.8– Sirius is intrinsically brighter than the Sun
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Finding the absolute Magnitude• To figure out absolute magnitude, we need to
know the distance to the star
• Then do the following Gedankenexperiment:– In your mind, put the star from its actual position to a
position 10 pc away– If a star is actually closer than 10pc, its absolute
magnitude will be a bigger number, i.e. it is intrinsically dimmer than it appears
– If a star is farther than 10pc, its absolute magnitude will be a smaller number, i.e. it is intrinsically brighter than it appears
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Measuring the Sizes of Stars
• Direct measurement is possible for a few dozen relatively close, large stars– Angular size of the disk and known distance
can be used to deduce diameter
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Indirect Measurement of Sizes
• Distance and brightness can be used to find the luminosity:
L d2 B (1)
• The laws of black body radiation also tell us that amount of energy given off depends on star size and temperature:
L R2 T4 (2)
• We can compare two values of absolute luminosity L to get the size
![Page 15: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/15.jpg)
Sizes of Stars• Dwarfs
– Comparable in size, or smaller than, the Sun
• Giants– Up to 100 times
the size of the Sun
• Supergiants– Up to 1000 times
the size of the Sun
• Note: Temperature changes!
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Classification of the Stars: Temperature
Class Temperature Color Examples
O 30,000 K blue
B 20,000 K bluish Rigel
A 10,000 K white Vega, Sirius
F 8,000 K white Canopus
G 6,000 K yellow Sun, Centauri
K 4,000 K orange Arcturus
M 3,000 K red Betelgeuse
Mnemotechnique: Oh, Be A Fine Girl/Guy, Kiss Me
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The Key Tool to understanding Stars: the Hertzsprung-Russell diagram
• Hertzsprung-Russell diagram is luminosity vs. spectral type (or temperature)
• To obtain a HR diagram: – get the luminosity. This is your y-coordinate. – Then take the spectral type as your x-coordinate, e.g.
K5 for Aldebaran. First letter is the spectral type: K (one of OBAFGKM), the arab number (5) is like a second digit to the spectral type, so K0 is very close to G, K9 is very close to M.
![Page 18: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/18.jpg)
Constructing a HR-Diagram• Example: Aldebaran, spectral type K5III,
luminosity = 160 times that of the Sun
O B A F G K M Type… 0123456789 0123456789 012345…
1
10
100
1000
L
Aldebaran
Sun (G2V)
160
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The Hertzprung-
Russell Diagram• A plot of absolute
luminosity (vertical scale) against spectral type or temperature (horizontal scale)
• Most stars (90%) lie in a band known as the Main Sequence
![Page 20: Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649ea85503460f94baca7c/html5/thumbnails/20.jpg)
Hertzsprung-Russell diagrams … of the closest stars …of the brightest stars