|
Thursday, 19 November 2009 11:09 |
|
 A common question in cosmology is "why are all the galaxies receding from each other?" In
other words, the cosmological principle requires that we not be at a special place in the
Universe. Since all the galaxies are moving away from us, then they must all be moving away
from each other. This is explained if the Universe, as a whole, is expanding.
In a real sense, Hubble's law, the recession  velocity of galaxies, is an illusion. The
galaxies are not moving, the space between them is literally expanded. To see how this
produces a Doppler effect, consider a simply Universe that is a circle. To the observers in
this type of Universe, they believe they live in a 1D structure. But, in fact, they live in a
2D structure, a circle. The position of the galaxies can be measured by the distance between
them (S, see diagram below) or what are called the co-moving coordinates, an angle q between the galaxies.
|
|
Thursday, 19 November 2009 11:05 |
|
With the discovery in the early 20th century that spiral-shaped nebula were, in fact, other galaxies
external to our own, our concept of a Universe became one of in a
Newtonian universe of infinite size and mass, galaxies spread out in
infinite space. However, there is a problem with a uniform, static
Universe, any density enhancements would become unstable to gravitational collapse. Thus,
the whole Universe should have collapsed (or be collapsing) into a giant
black hole.
In the 1930's, Edwin Hubble discovered that all galaxies have a positive
redshift. In other words, all
galaxies were receding from the Milky Way. By the Copernican principle
(we are not at a special place in the Universe), we deduce that all
galaxies are receding from each other, or we live in a dynamic, expanding Universe.
This solves the problem for gravitational collapse, only small regions
will collapse to form galaxies. The rest of space keeps expanding.
|
|
Wednesday, 18 November 2009 10:46 |
|
Some balls bounce better than others.
A particular ball can be characterized by its
coefficient of restitution:
The ratio of its rebound speed Vf to its collision speedVi
when its bounces off a hard, stationary surface that can't move.
coefficient of restitution r = Vf /
Vi
Scientists have found that, for most balls, this speed ratio
remains constant over a wide range of collision speeds.
The amount of kinetic energy transformed at impact is called
the collision energy (become thermal energy).
This java applet shows you the effects due to
different coefficient of restitution.
|
|
|
|
|
|
Page 10 of 65 |
Newtonian Mountain
Kepler's Laws
Fourier series