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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:

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Page 1: 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:

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:

Page 2: 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

Page 3: 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:

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!

Page 4: 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 #2: Binary StarsCan measure

1) orbit period (P)

3) orbit speeds (v=v1+v2)

can’t see orbit size!

Substitute for A:

Page 5: 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:

Center of Mass

“balance point” must be closer to more massive object:

http://astro.unl.edu/classaction/animations/binaryvariablestars/centerofmass.html
Page 6: 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:

Center of Mass• If center of mass is to remain

between two moving objects, less massive object must move faster in exact opposite direction

Page 7: 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:

Doppler Effect Technique

• gravitational tug of planet causes star to move

• measure Doppler effect of star’s light

597 planets detected so far

Page 8: 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:

Thought Question:

Where will the planet be when the star has its largest blueshift?

D.

C.

B.

A.

TO EARTH

Page 9: 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:

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

Page 10: 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:

The Milky WayVISIBLE LIGHT

Page 11: 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 #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:

Page 12: 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:

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

Page 13: 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:

Satellite Galaxies• Large orbits allow us to measure Milky Way’s

total mass.

MAGELLANIC CLOUDS

INFRARED

Page 14: 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:

Mass of the Milky Way

Page 15: 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:

“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…

Page 16: 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:

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.

Page 17: 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:

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:

Page 18: 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:

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.

Page 19: 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:

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:

Page 20: 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:

Rotation Curves“FLAT” ROTATION:• For galaxies,

rotation speed doesn’t change much with distance.

• To maintain speeds, there must be MUCH extra mass present:

Page 21: 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:

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?

Page 22: 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:

• A very long exposure of a small “blank” portion of sky

Galaxies

Page 23: 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:
Page 24: 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:

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)

Page 25: 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:

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)

Page 26: 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:

Elliptical Galaxies

•What colors are visible?

• How do you describe the general shape?

• Do you see signs of gas clouds?

Types of Galaxies

M87

Page 27: 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:

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

Page 28: 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:

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…

Page 29: 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:

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

Page 30: 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:

Spiral Galaxies

raw materials for making new stars…

Page 31: 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:

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?

Page 32: 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:

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.

Page 33: 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:

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


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