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:
2p r
v=
P
4p
3
P =
A
G(M + m)
2
2
v
r
M
P
m
Example #1: Solar System
Can measure
1) orbit period (P)
2) orbit size (A or r = radius)
Kepler’s Third Law:
4p
3
P =
A
G(M + m)
r
M
2
2
P
Examples: planets around Sun, moons around planets,
spacecraft around other objects
m
Binary Stars
MOST STARS ARE IN
BINARY STAR
SYSTEMS!
• main way to accurately measure star properties
• neither star is “stationary”
• some stars pull gas off companion star
Example #2: Binary Stars
Can measure
1) orbit period (P)
3) orbit speeds (v=v1+v2)
 can’t see orbit size!
Substitute for A:
v2
M2
M1
v P
(M1 + M 2 ) »
2pG
3
v1
P
Center of Mass
“balance point” must be
closer to more massive
object:
r2 m1
=
r1 m2
v1t
Center of Mass
m1
• If center of mass is to remain
between two moving objects,
less massive object must
move faster in exact opposite
direction
r1
v 2 r2 m1
= =
v1 r1 m2
r2
m2
v 2t
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?
B.
TO EARTH
C.
A.
D.
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
The Milky Way
VISIBLE LIGHT
Example #3: Galaxies
Can’t wait long enough to measure orbit period (P)…
Can measure:
2) orbit size (r = radius)
v
3) orbital speed (v)
M
Substitute for P:
rv
»
G
2
M total
Examples: stars orbiting in galaxies, galaxies orbiting
other galaxies
r
m
Measuring Mass
Mass inside an orbit can be
measured using speed and distance
rv
M»
G
2
v1
M1
r
v2
m
M2
SAME DISTANCE r:
 force exerted by mass M1 must be larger than mass M2
r
m
Satellite Galaxies
•
Large orbits allow us to measure Milky Way’s
total mass.
INFRARED
MAGELLANIC
CLOUDS
Mass
of the
Milky
Way
“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:
ORBIT SPEED
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?
A.
B.
D.
C.
DISTANCE FROM CENTER
E.
2p r
v=
P
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
2pr
v=
move faster:
P
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:
ORBIT SPEED
A.
GM
v=
r
C.
E.
B.
D.
DISTANCE FROM CENTER
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:
GM
vc =
R
Rotation Curves
“FLAT” ROTATION:
• For galaxies,
rotation speed
doesn’t change
much with
distance.
• To maintain
speeds, there
must be MUCH
extra mass
present:
vr
M»
G
2
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?
Galaxies
• A very long
exposure of
a small
“blank”
portion of
sky
Types of Galaxies
Spiral Galaxies
• What are the
main colors?
• How can you
describe the
general shape?
• Do you see
signs of gas
clouds?
Pinwheel Galaxy (M101)
Types of Galaxies
Spiral
Galaxies
•What are the
main colors?
• How can you
describe the
general
shape?
Sombrero Galaxy (M104)
• Do you see
signs of gas
clouds?
Types of
Galaxies
Elliptical Galaxies
•What colors are
visible?
• How do you
describe the
general shape?
• Do you see signs
of gas clouds?
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
Star
Census
Luminosity
Most luminous
and common
stars are usually
either:
• blue
(high-mass main
sequence stars)
OR
• red
(red giant stars)
Temperature
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
Spiral Galaxies
raw materials
for making
new stars…
Galaxy Properties
Spiral
Elliptical
Shapes
flat disk + round
bulge
elliptical
(football)
Overall color
bluish (young,
reddish (giant
high-mass stars) stars)
Gas, Dust
yes – in disk
Where?
little or none
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.
Review Question:
A star with a radius like that of the Sun and a
surface temperature twice that of the Sun will
have a luminosity how many times as great at
the Sun?
A. 4
B. 9
C. 16
D. 64
E. 144