The Life Cycles of StarsThe Life Cycles of Starsand our Sunand our Sun

Your Questions 1. Have you

ever heard of the sun song by the group They Might be Giants?

`Fun websites’:http://www.asu.edu/clas/hst/www/ahah/ Appreciating Hubble at Hyper-speed

http://www.stsci.edu/outreach/

1. How are distances between galaxies and between galaxy clusters calculated? The Hubble Flow

v = Ho d (Ho = 71 km/s/Mpc)

d

d

1

2

1. Observer 1 sees both galaxies at distance d with speed v

2. Observer 2 sees the furthest galaxy at distance 2d, with speed 2v

v

v

2. Elaborate on the difference between the Dark Matter theory and the MOdified Newtonian Dynamics theory

(MOND).

Describing Motion• Motion is when the position of an object

changes in time• If position does not change, the object is at rest• The describe motions we need to monitor

position and time• The rate at which an objects covers a given

amount of space in a given amount of time is called speed

v = d/t (when you add a direction to speed, it is called

velocity)

Acceleration • An acceleration is a

change in velocity.• Acceleration occurs when

either the magnitude or direction of the velocity (or both) are altered.

• Uniform Circular Motion is Accelerated Motion

Acceleration and Force• An object in constant velocity (or at rest) has

no force acting on it. Or: if an object is being accelerated, there must be a net force acting on it (Newton’s first law)

• Acceleration is caused by force but also related to the mass of the object (Newton’s second law)

Force = Mass x Acceleration

F = m·a

Or a = F/m

The gravitational force on an object nearthe surface of Earth is:

Fgrav = m·g (g = 9.8m/s2)

Gravity

• We can summarize the universal law of gravitation with the following statements:– Every mass attracts every other mass through the

force of gravity.– If mass #1 exerts force on mass #2, and mass#2

exerts force on mass#1, the force must depend o both masses, namely:

– The force of attraction is directly proportional to the product of the two masses.

– The force of attraction is inversely proportional to the square of the distance between the masses.

The Law of Gravity

221

d

MMGFg =

d

M1M2

G = 6.67x10-11 m3/kg/s2

2

21

2

9.8m/s=

=

=

dM

Gg

gMFg

Near Earth’s surface

… so why don’t planets just fall into the sun?

M1M2

… because they miss it!

M1M2

v

This is the concept of an orbit: M2 is being attracted by M1, which causes an acceleration, but has sufficient tangential velocity that the `fall’ becomes an orbit

Fg Fg

The same is true for galaxies:Their stars rotate around their center of mass.

If you know the distance of your star from the center, R, and its speed, v, you can calculate the mass of the galaxy contained within the radius R:

R

M(<R) = v2 R / G

And the acceleration: a= v2 / R

For the sun:M(<8kpc) = 9x1010 Msun

a = 2.5x10-8 cm/s2

…and when you reach the edges of

galaxies…

The `flat rotation curve’ seen beyond the visible edges of galaxies does not agree with the expectation that the galaxy `ends’. In this case one would expect a trend: v ~ R(-1/2)

1. DM: Fg = ma = GMm/r2 , a= GM/r2 (gravitational force) Fc = m v2 / r (centripetal force) Flat rotation curves imply `unseen’ mass in galaxies

2. MOND: F = m (a/ao) a = GMm/r2

ao = 1.2 10-8 cm s-2

Flat rotation curves stem from very small accelerations at the edges of galaxies, where the Newtonian dynamics is modified to imply: a= (Gmao)(1/2) / R and v ~ const.

Current difficulties for MOND:

1. Gravitational lensing: (still in progress; recent MOND covariant formulation)

2. Density profiles of galaxy clusters