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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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the expanding universe

The Expanding Universe

Tuesday, January 15

slide3

Infinite universe: hard to reconcile with appearance of the night sky.

Night sky is dark, with stars (small in angular size) scattered across it.

slide4

“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?

slide5

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.

slide6

In an infinite universe with infinite number of stars, paradox arises.

How bright do we expect the sky to be in such a universe?

slide7

ASSUMPTIONS:

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

slide8

You are here

r= radius of shell

t = thickness of shell

slide9

What’s the surface area of the spherical 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

slide10

What’s the cross-sectional area of a single star?

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?

slide11

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!

slide12

A single shell will cover only a tiny part of the sky with stars.

For a shell 1 parsec thick, fraction covered = π R2 t n ≈ 10-15

But we’ve assumed an infinite number of shells!

slide13

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!

slide14

Olbers’ Paradox for Trees:

In a large enough forest, every line of sight ends at a tree.

slide15

My conclusion – that the sky is uniformly bright – is utter rubbish.

The night sky really is dark.

Which of my assumptions was wrong?

slide16

Dubious assumption #1:

The universe is infinitely large.

Dubious assumption #2:

The universe is eternally old.

slide17

The speed of light (c) is large but finite.

c = 300,000 km/sec (186,000 miles/sec).

slide18

If the universe has a finite age, then distant stars haven’t had time to send us the message “We’re here!”

slide19

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?

slide20

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.

slide21

Q: How can we tell if a galaxy is moving toward us or away from us?

A: Look for the Doppler shift of light from the galaxy.

we can think of light as a wave traveling through space
We can think of light as a wave traveling through space.

Wave = any periodic fluctuation traveling through a medium.

slide23

Ocean wave = fluctuation in height of water.

Sound wave = fluctuation in pressure.

Electromagnetic wave = fluctuation in electric and magnetic fields.

slide24

λ

a

Wavelength (λ) = distance between wave crests.

Amplitude (a) = height of crests above troughs.

Describing a wave:

the color of visible light is determined by its wavelength
The color of visible light is determined by its wavelength.

Visible light: wavelengths from 400 to 700 nanometers. [1 nanometer (nm) = 10-9 meters]

slide26

Hydrogen

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 of an object is found from the doppler shift of its light
Radial velocity of an object is found from the Doppler shift of its light.

Radial velocity = how fast object is moving toward you or away from you.

slide28

Doppler shift: If a wave source moves toward you or away from you, the wavelength changes.

Christian Doppler (1803-1853)

slide29

The reason for Doppler shifts:

Wave crests are “bunched up” ahead of wave source, “stretched out” behind wave source.

slide30

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).

slide32

In early 20th century, astronomers were surprised to discover that all distant galaxies are redshifted!

Galaxies moving away from each other!

slide33

“The Universe is expanding.”

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.

thursday s lecture
Thursday’s Lecture:

The Big Bang Model

Reading:

Chapter 3

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