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• Linear size = how big something really is– Meters, inches, light years, feet• Angular size = how big something looks– Degrees, arcminutes, arcseconds, milliarcsecondsCircle = 360 degrees1 degree = 60 arcmin1 arcmin = 60 arcsec1 arcsec = 1000 mas
- can appear big or
- small in the sky because they are really big or small or because they are
- very close or far away
- 2x distance = ½ as big, 10x distance = 1/10 as
Distances in the Solar System
- • Can use angular size to find distances to planets• Transits of Venus and Mercury• Can also bounce radar waves off planets to find distance
- – Example: Laser measurements indicate the averagedistance to the Moon is 385,000 kilometers (+- 3 cm!)Distances in solar system often measured inAstronomical Units – average distance fromEarth-Sun150 million km or 93 million milesJupiter – 5 AU from Sun, Pluto – 40 AU
Distances to the Stars
One proof of a heliocentricUniverse is stellar parallax.– Greeks, Tycho Brahe saw no parallax.– Copernicus: stars too far away.• Nearest star: Proxima Centauri– Parallax angle = 0.76 arcsec– Tycho’s precision = 1 arcmin
• What is the distance of anobject with a parallax angle of1 arcsec?Distance = 206,265 AU• This distance is 1 parsec (pc)1 pc = 206,265 AU = 3.26 ly• 1 lightyear = distance light travels inone year.
Distance (in parsecs) = 1 / parallax (in arcsec)
If Star A has a parallax of 2 arcseconds, and StarB has a parallax of 0.25 arcseconds:
a. Star A is closer to us than Star B. Both are fartherfrom us than 1 pc.
b. Star A is closer to us than Star B. Both are closer to usthan 1 pc.
c. Star A is closer to us than 1 pc. Star B is farther than 1pc.
d. Star B is closer to us than 1 pc. Star A is farther than 1pc.
e. Star B is closer to us than Star A. Both are fartheraway than 1 pc.
• How bright arethey really?• What is due todistance?• What is due toluminosity?• Luminosity:– Total energyradiated everysecond.
Brightness = Howintense is the light Isee from where I am.– Magnitude is thetechnical term for this.• Luminosity = howmuch light is the thingreally giving off.
Brightness vs. Distance
• Inverse square lawBrightness = 1/distance22x distance = ¼ as brightWhat is the brightness at10x distance?Size and distance?How much smaller does object appear at 10x distance?
• The SMALLER thenumber the BRIGHTERthe star!– Every difference of 1magnitude = 2.5x brighter ordimmer.– Difference of 2 magnitudes= 2.5x2.5 = 6.25x brighter ordimmer
Star light, starbright
Sirius is magnitude -1.5Polaris is magnitude 2.5• Is Sirius really moreluminous than Polaris?• Not necessarily, Sirius isjust closer.• Example: light bulbs.
Magnitude and Brightness
• Apparent magnitude - how bright a star appearsto be from Earth; mv• Absolute magnitude - intrinsic luminosity of astar; Mv– brightness at a given distance(10 pc = 32.6 light years)– Difference between apparent and absolutemagnitude can give you distance to star
Apparent and Absolute
Apparent Magnitude = brightness (magnitude) of astar as seen from Earth. m– Depends on star’s total energy radiated (Luminosity) anddistance• Absolute Magnitude = brightness (magnitude) of astar as seen from a distance of 10 pc. M– Only depends on a star’s luminosity
Cepheid variables – pulsating starsthese stars change brightness over time in aregular way – can be used to find distance
Period of pulsation related to luminosity: the longer the period, the brighter the star
How Big Are Stars?
-We can’t see the stars’diameters through a telescope.Stars are so far away that wesee them just as points of light.
- If we know a star’s temperature and its luminosity,we can calculate its diameter.
- -Luminosity depends on….
- TEMPERATURE -the hotter a star is,the brighter it is.DIAMETER –the bigger a star is,the brighter it is.Stars range in size from about the size of the Earth tohundreds of times the Sun’s diameter
We see stars have differentluminosities and differenttemperatures.• Stars have different sizes.• If you know a star’s– Distance– Angular size• You can find its real size.
How hot are stars?• Thermal radiationand temperature.• Different starshave differentcolors, differentstars aretemperatures.• Different temp,different tracecompositions
The Composition of Stars
90% hydrogen atoms10% helium atomsLess than 1%everything else(and everythingelse is made in stars!)
Everything comes from the Stars
Elements that make up the human body are mostly carbon, hydrogen,oxygen (hydrocarbons) and calcium.• Trace amounts of sodium, potassium play a crucial role in the process ofhuman thought.• Food is mostly also C, H, O and trace amounts of heavy elements (zinc isused to grow pineapples!).• The air we need to breathe is oxygen and nitrogen.• Most of what we use for living is also C, H, O, and metals like iron,aluminum, etc.• Let’s not forget silicon. It makes beaches, glass, and email possible
Abundance of Elements in the Sun
Chemical elements arecreated• in the EarlyUniverse• in Stars• in Supernovae• The Galaxy is enrichedin chemical elementsthrough interstell
- How do you weigh a star?• Kepler’s Laws – devised for the planets.• Apply to any object that orbits another object.• Kepler’s Third Law relates:– Period: “how long it takes to orbit something”– Semimajor axis: “how far you are away from that something”– Mass: “how much gravity is pulling you around in orbit”• Where M is the Total Mass.• Can calculate the mass of stars this way.
- period squared = distance cubed / mass
Most stars in the skyare in multiplesystems.• Binaries, triplets,quadruplets, etc….– Sirius– Alcor and Mizar– Tatooine• The Sun is in theminority by beingsingle.
You can watch how stars go around each other and figure out theirmasses from Kepler’s third law
Masses of Stars
- The more massive the star, the more luminous it is.The more massive the
- star, the hotter it is.• Between 1/100th and 100x the mass of the Sun•
- Smallest stars: brown dwarfs, too small for fusion tohappen – just a
- “dull glow”Gliese 623b:1/10 mass of Sun,60,000x fainterJust barely a
Most stars aroundthe sun aredimmer…
And smaller than thesun…