Dark Matter Online Game - Primer
Outline:
• Explanation of theory
• Explanation of observation
• Problem
Theory
To move in a circle, there must be a force pulling the object towards the center of the circle.
Consider a car on a level curve.
Friction between the road and the tires allow the car to turn.
If there is a lot of friction, cars can turn sharply or go around curves at high speeds.
If the road is slippery – less friction – the car has to slow down.
If we apply this idea to stars that are some distance from the center of the galaxy:
• The farther away a star is, the weaker the force of gravity that is pulling the star toward the center of
the galaxy.
• Just like a car with less friction, a star that is far away from the center of the galaxy has less gravity
and must move slower.
So theory predicts that stars that are farther away move slower.
Here is the math:
Fnet = ma
GMm/r2 = mv2/r
So v = root(GM/r)
Observation
When something that emits waves is moving, the observed wavelength and frequency are different than
when it is stationary.
Consider a race car – if it was standing still and rev’ing its engines, it would sound a certain way. It has a
particular pitch.
If the race car was driving towards you, the approaching sounds waves would get bunched together. You
would hear a higher pitch. If it was driving away from you, the sound waves are spread out and you would
hear a lower pitch.
This is called the Doppler Shift.
The same principle applies to light emitted from moving stars. When moving towards you, the light waves
are more bunched together. We call this Blue Shift since blue has shorter wavelengths.
When a star is moving away, the waves are spread out more – we call that a Red Shift, since red has a
longer wavelength.
By looking at the colours/wavelengths of star light we can measure their blue shift or red shift. From the
shifts we can find the speed of the stars.
So by observation of the wavelengths of light coming off stars, we can calculate the speed of the stars.
The Problem
The observed speeds (from Doppler shifts) is faster than the theory predicted!
Galaxies are faster and therefore more massive than traditional observations indicate.
Or the visible mass of the observed stars only provides some of the centripetal force needed for these
observed velocities.
When physicists calculate the mass of a galaxy by looking at the number and size of the galaxy’s stars,
they get a value for mass that is much lower than they expect for these high velocities.
From the Doppler shift, physicists get a value for speed – this is the speed the stars are moving. When that
speed is used to get a value for the mass of the galaxy the mass is large. It is larger than the mass of the
observed matter in the galaxy.
So there must be some mass in the galaxies that is unaccounted for.
Physicists have tried to come up with explanations for the missing mass.
A theory for this mass is dark matter: matter that doesn’t interact with light or radiation – hence invisible to
our traditional ways of seeing matter. Since it doesn’t interact with light and is invisible to us, it has been
called dark matter.
However, since dark matter has mass, it does affect spacetime. From the observed speeds of stars,
physicists can estimate the amount and distribution of dark matter in galaxies.