The Life Cycles of Stars
and 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)
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
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 near
the 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
Near Earth’s
surface
M 1M 2
Fg  G
2
d
G=
6.67x10-11
Fg  gM 2
m3/kg/s2
M1
g G 2
d
2
 9.8m/s
d
M1
M2
… so why don’t planets just fall
into the sun?
M1
M2
… because they miss it!
v
Fg
M1
Fg
M2
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
The same is true for galaxies:
Their stars rotate around their
center of mass.
R
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:
M(<R) = v2 R / G
For the sun:
M(<8kpc) = 9x1010 Msun
a = 2.5x10-8 cm/s2
And the acceleration:
a= v2 / R
…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
Fc = m v2 / r
(gravitational force)
(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