The%20Life%20Cycles%20of%20Stars%20and%20our%20Sun

1
The Life Cycles of Starsand our Sun

2
Your Questions

1. Have you ever heard of the sun song by the group
   They Might be Giants?

3
Fun websites
http//www.asu.edu/clas/hst/www/ahah/
Appreciating Hubble at Hyper-speed
http//www.stsci.edu/outreach/
4
1. How are distances between galaxies and between
galaxy clusters calculated? The Hubble Flow
v Ho d (Ho 71 km/s/Mpc)

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

d
v
1
d
v
2
5
2. Elaborate on the difference between the Dark
Matter theory and the MOdified Newtonian Dynamics
theory (MOND).
6
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)

7
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

8
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 (Newtons first law)
• Acceleration is caused by force but also related
  to the mass of the object (Newtons second law)

Force Mass x Acceleration
F ma
Or a F/m
9
The gravitational force on an object nearthe
surface of Earth is Fgrav mg (g
9.8m/s2)
10
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 mass2
  exerts force on mass1, 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.

11
The Law of Gravity
G 6.67x10-11 m3/kg/s2
d
M2
M1
12
so why dont planets just fall into the sun?
M2
M1
13
because they miss it!
v
Fg
Fg
M2
M1
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
14
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(ltR) v2 R / G
And the acceleration a v2 / R
For the sun M(lt8kpc) 9x1010 Msun a 2.5x10-8
cm/s2
15
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)
16

• 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.

17
Current difficulties for MOND

• Gravitational lensing
• (still in progress recent
• MOND covariant
• formulation)

2. Density profiles of galaxy clusters