Need 2 out of 3 to measure TOTAL MASS:
1) orbit period (P)
2) orbit size (A or r = radius)
3) orbit speed (v)
For circular orbits,
Kepler’s Third Law:
Example #1: Solar SystemCan measure
1) orbit period (P)
2) orbit size (A or r = radius)
Kepler’s Third Law:
Examples: planets around Sun, moons around planets, spacecraft around other objects
Binary Stars
• main way to accurately measure star properties• neither star is “stationary”• some stars pull gas off companion star
MOST STARS ARE IN BINARY STAR SYSTEMS!
Example #2: Binary StarsCan measure
1) orbit period (P)
3) orbit speeds (v=v1+v2)
can’t see orbit size!
Substitute for A:
Center of Mass
“balance point” must be closer to more massive object:
Center of Mass• If center of mass is to remain
between two moving objects, less massive object must move faster in exact opposite direction
Doppler Effect Technique
• gravitational tug of planet causes star to move
• measure Doppler effect of star’s light
597 planets detected so far
Thought Question:
Where will the planet be when the star has its largest blueshift?
D.
C.
B.
A.
TO EARTH
The Center of the Milky Way
Near galactic center:
•moving stars appear to be orbiting something dark…
…almost 4 x 106 Msun!
SIZE OF PLUTO’S ORBIT
Example #3: Galaxies
Examples: stars orbiting in galaxies, galaxies orbiting other galaxies
Can’t wait long enough to measure orbit period (P)…
Can measure:
2) orbit size (r = radius)
3) orbital speed (v)
Substitute for P:
Measuring MassMass inside an orbit can be measured using speed and distance
SAME DISTANCE r:
force exerted by mass M1 must be larger than mass M2
Satellite Galaxies• Large orbits allow us to measure Milky Way’s
total mass.
MAGELLANIC CLOUDS
INFRARED
“Massing” the Milky Way
100 billion Sun’s mass:
100,000,000,000 (or 1011)
About 300,000,000,000 stars!!
About 50 for every person on Earth…
Thought Question:If a galaxy rotates like a solid body, how will the
orbit speeds of stars change with distance from the center? In other words, what would the graph look like?
DISTANCE FROM CENTER
OR
BIT
SP
EE
D A. B.
D.C.
E.
Rotation Curves
SOLID BODY ROTATION:
• all parts of a rotating object take same time P to rotate once
• parts that are farther from center must move faster:
Thought Question:If most of the mass of a galaxy is at its center,
how should the speeds of orbiting stars change with distance? In other words, which of these graphs is most likely:
DISTANCE FROM CENTER
OR
BIT
SP
EE
D
A.
B.
C.
D.
E.
Rotation Curves“KEPLERIAN”
ROTATION:• gravity of a single
mass keeps objects in orbit
• objects move at a certain speed to stay in a circular orbit
• orbital speed decreases with distance:
Rotation Curves“FLAT” ROTATION:• For galaxies,
rotation speed doesn’t change much with distance.
• To maintain speeds, there must be MUCH extra mass present:
Dark Matter?
…but “bright matter” is fairly concentrated and orbit speeds are still large far from center!
“Dark matter”?
very abundant and very spread out?
Spiral Galaxies
• What are the main colors?
• How can you describe the general shape?
• Do you see signs of gas clouds?
Types of Galaxies
Pinwheel Galaxy (M101)
Types of Galaxies
Spiral Galaxies
•What are the main colors?
• How can you describe the general shape?
• Do you see signs of gas clouds?
Sombrero Galaxy (M104)
Elliptical Galaxies
•What colors are visible?
• How do you describe the general shape?
• Do you see signs of gas clouds?
Types of Galaxies
M87
Thought Question:The light from a galaxy you are studying has a
strong bluish tint. What kind of star is probably releasing most of the light you see?
A. low-mass main sequence stars
B. high-mass main sequence stars
C. giant stars
D. supergiant stars
E. white dwarfs
Temperature
Luminosity
Star Census
Most luminous and common stars are usually either:
• blue (high-mass main sequence stars)
OR
• red (red giant stars)
and this colors a galaxy…
Thought Question:What type of star are you likely to find in a galaxy
today ONLY if there are large amounts of gas and dust that can be used to form stars NOW?
(Hint: what kind of stars will only be around for a short time?)
A. low-mass main sequence stars
B. high-mass main sequence stars
C. white dwarfs
D. neutron stars
Galaxy Properties
Spiral Elliptical
Shapes flat disk + round bulge
elliptical (football)
Overall color bluish (young, high-mass stars)
reddish (giant stars)
Gas, Dust yes – in disk little or none
Where?
Review Question:A racecar completes a lap at a constant speed. A
track official with a radar gun monitors the racecar’s motion. Where does the official measure the lowest speed?
E. It’s the same everywhere.