The Expanding Universe. Tuesday, January 15. Thomas Digges (16 th century) proposed an infinite universe. Infinite universe: hard to reconcile with appearance of the night sky. Night sky is dark , with stars (small in angular size) scattered across it.
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Tuesday, January 15
Night sky is dark, with stars (small in angular size) scattered across it.
“The night sky is dark”: called Olbers’ paradox, after astronomer who discussed the subject in 1823.
Why is the darkness of the night sky paradoxical?
If stars were stuck on a celestial sphere or dome, darkness would not be paradoxical.
Only a finite number of stars on the celestial sphere.
In an infinite universe with infinite number of stars, paradox arises.
How bright do we expect the sky to be in such a universe?
Suppose there are nstars per cubic parsec of the universe.
In Sun’s neighborhood, n = 1/pc3
Suppose that an average star is a sphere with radius R.
For Sun, R = 7×105 km = 2×10-8 pc
r= radius of shell
t = thickness of shell
Area = 4 π r2
What’s the volume of the spherical shell?
Volume ≈ area × thickness ≈ 4 π r2 t
How many stars are in the shell?
Number = volume × n = 4 π r2 t n
Cross-section = π R2
What’s the cross-sectional area of all the shell’s stars?
Total = (π R2) × (4 π r2 t n)
What fraction of the shell’s area is covered by stars?
Fraction = area of stars / area of shell = (π R2 ) × ( 4 π r2 t n ) / ( 4 π r2 ) = π R2 t n
Independent of r, the radius of the shell!
For a shell 1 parsec thick, fraction covered = π R2 t n ≈ 10-15
But we’ve assumed an infinite number of shells!
1015 (one quadrillion) shells, each covering a quadrillionth of the sky with stars, will completely pave the sky with stars.
The entire night sky should be as bright as the Sun’s surface!
In a large enough forest, every line of sight ends at a tree.
My conclusion – that the sky is uniformly bright – is utter rubbish.
The night sky really is dark.
Which of my assumptions was wrong?
The universe is infinitely large.
Dubious assumption #2:
The universe is eternally old.
c = 300,000 km/sec (186,000 miles/sec).
If the universe has a finite age, then distant stars haven’t had time to send us the message “We’re here!”
Discussing Olbers’ paradox, we assumed the universe was static (neither expanding nor contracting).
This was the general assumption until the 20th century: but was it correct?
If the universe is expanding, distant galaxies will be moving away from us.
If the universe is contracting, distant galaxies will be moving toward us.
A: Look for the Doppler shift of light from the galaxy.
Wave = any periodic fluctuation traveling through a medium.
Sound wave = fluctuation in pressure.
Electromagnetic wave = fluctuation in electric and magnetic fields.
Wavelength (λ) = distance between wave crests.
Amplitude (a) = height of crests above troughs.
Describing a wave:
Visible light: wavelengths from 400 to 700 nanometers. [1 nanometer (nm) = 10-9 meters]
The Sun’s spectrum (amount of light as a function of wavelength):
Note the dark lines: from elements that absorb light at specific wavelengths.
Radial velocity = how fast object is moving toward you or away from you.
Doppler shift: If a wave source moves toward you or away from you, the wavelength changes.
Christian Doppler (1803-1853)
Wave crests are “bunched up” ahead of wave source, “stretched out” behind wave source.
If light source is moving toward you, wavelength is shorter (called blueshift).
(should be “violetshift”, more logically)
If light source is moving away from you, wavelength is longer (called redshift).
In early 20th century, astronomers were surprised to discover that all distant galaxies are redshifted!
Galaxies moving away from each other!
Note: Applies only on large scales.
The Solar System is not expanding; it’s held together by gravity.
Milky Way Galaxy is not expanding; it’s held together by gravity.
The Big Bang Model