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 System Can 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 Stars Can measure 1)orbit period (P) 3)orbit speeds (v=v 1 +v 2 )  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 From Newton’s 3rd Law:

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 10 6 M sun ! SIZE OF PLUTO’S ORBIT

The Milky Way VISIBLE LIGHT

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 Mass Mass inside an orbit can be measured using speed and distance SAME DISTANCE r:  force exerted by mass M 1 must be larger than mass M 2

Satellite Galaxies Large orbits allow us to measure Milky Way’s total mass. MAGELLANIC CLOUDS INFRARED

Mass of the Milky Way

“Massing” the Milky Way 100 billion  Sun’s mass: 100,000,000,000 (or ) 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 ORBIT SPEED 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 ORBIT SPEED 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?

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

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

Spiral Galaxies raw materials for making new stars…

Galaxy Properties SpiralElliptical Shapesflat disk + round bulge elliptical (football) Overall colorbluish (young, high-mass stars) reddish (giant stars) Gas, Dustyes – in disklittle 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.

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