```Olber’s Paradox
Why is the night sky dark?
Night Sky
If you are in a big forest and keep
walking you will bump into a tree
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If you are in a big (infinite)
universe and keep going
in a straight line you will
bump into a star.
Newton thought the Universe was
infinitely old and static
Centre of
mass
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Gravity makes the stars
collapse towards their
centre of mass
There must be more stars
pulling out to stop this
happening
And more outside these to
stop them collapsing
So the universe must be
infinitely big or it would
have collapsed
Remember Inverse Square Law
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d
2d
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out
At a distance of 2d the
over 4 times the area
So the object will have
quarter the brightness
Apparent brightness is
proportional to 1/d2
Look in any direction
Imagine spherical shells
surrounding Earth
d
2d
Shell at 2d has 4 times
the area, hence 4 times
the volume. It contains 4
times as many starts so
emits 4 times as much
light
3d
9 times as many
stars
Each shell has same brightness
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Shell at 2d has 4 time as
many stars
Remember inverse
square law
They have ¼ brightness
So apparent brightness
of each shell is the same
If the universe is infinite
Then there are an infinite number of shells.
Each shell has the same brightness
If you add the light from each you get an infinitely
bright sky
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So if the universe is infinitely big then the
sky should be bright
But the sky is dark
So the universe is not infinitely big
So it should have collapsed
What assumptions did Newton make?
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1. The universe is
infinitely old.
2. The universe is static
Note that clouds of
dust blocking light
does not solve the
problem because the
clouds would heat
energy
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1. Hubble constant
estimates age of universe