Martin D. Weinberg UMass Astronomy [email protected]/astron100-mdw/lectures/lec20.pdfModern relation Age of the Universe Expansion of the Universe Cosmological

Read: Chaps 20, 21 11/18/14 – slide 1

A100–Exploring the Universe: Measuring the Universe

Martin D. Weinberg

UMass Astronomy

[email protected]

November 18, 2014

Announcements

⊲ Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae

Hubble’sMeasurement

Modern relation

Age of the Universe

Expansion of theUniverse

CosmologicalPrinciple

Thought question

What is expanding?

Thought question

Measurement in anexpanding universe

Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 2

Exam #2 scores posted in Mastering. See class web site

for answer key.

⊲ See TAs after class today for exams

http://courses.umass.edu/astron100-mdw

Announcements

⊲ Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 2


for answer key.


Galaxies

⊲ How did Hubble prove that galaxies lie far beyond

the Milky Way?

⊲ What is Hubble’s Law?

⊲ How do distance measurements tell us the age of

the Universe?

⊲ How does the universe’s expansion affect our

distance measurements?


Announcements

⊲ Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 2


for answer key.


Galaxies

⊲ How did Hubble prove that galaxies lie far beyond

the Milky Way?

⊲ What is Hubble’s Law?

⊲ How do distance measurements tell us the age of

the Universe?

⊲ How does the universe’s expansion affect our

distance measurements?

Your questions?


Measuring distances to galaxies

Read: Chaps 20, 21 11/18/14 – slide 3

Measuring distances to galaxies

Read: Chaps 20, 21 11/18/14 – slide 3

The Distance Ladder

Tully-Fisher relation

Announcements

Measuring distances

⊲ Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 4

Entire galaxies can also

be used as standard can-

dles because galaxy lu-

minosity is related to ro-

tation speed

3 types of astronomical distance measurements

Announcements

Measuring distances

Tully-Fisher

⊲ 3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 5

1. Direct mesurements: Measuring the distance directly.

Example:

Radar

“Time of flight”

2. Standard rulers: Size = Distance × θ (angle on the sky).

Need to know the true size of the object.

Expanding supernova remnants

3. Standard candles: Lapparent = Ltrue/D2.

Need to know the true luminosity of an object.

Main-sequence fitting

Tully-Fisher

Cepheid variables

The Distance Ladder: Summary

Announcements

Measuring distances

Tully-Fisher

3 types

⊲ Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 6

We measure galaxy distances using

a chain of interdependent

techniques


Announcements

Measuring distances

Tully-Fisher

3 types

⊲ Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 7

The distance-measurement chain begins with parallax

measurements that build on radar ranging in our solar

system

Using parallax and the relationship between luminosity,

distance, and brightness, we can calibrate a series of

standard candles

We can measure distances greater than 10 billion light

years using white dwarf supernovae as standard candles


Announcements

Measuring distances

Tully-Fisher

3 types

⊲ Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 8

The distance-measurement chain begins with parallax

measurements that build on radar ranging in our solar

system

Using parallax and the relationship between luminosity,

distance, and brightness, we can calibrate a series of

standard candles

We can measure distances greater than 10 billion light

years using white dwarf supernovae as standard candles

The “Puzzle” of Spiral Nebulae

Read: Chaps 20, 21 11/18/14 – slide 9

Before Hubble, some scientists argued

that spiral nebulae were entire galaxies

like our Milky Way, while others main-

tained they were smaller collections of

stars within the Milky Way

The debate remained unsettled until

someone finally measured their dis-

tances

Physical nature of “cloudy objects” debated

Read: Chaps 20, 21 11/18/14 – slide 10

Rosse’s sketch

Lord Rosse (Irish nobleman) observed M51 with 72 inch mirror


Read: Chaps 20, 21 11/18/14 – slide 10

Artist’s conception


How it appeared to naked eye in early telescopes


Read: Chaps 20, 21 11/18/14 – slide 10

Hubble Space Telecope


How it appeared to naked eye in early telescopes

How it appears with the Hubble Space Telescope

The “Puzzle” of Spiral Nebulae

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

⊲ Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 11

Hubble settled the debate by measuring the distance to the

Andromeda Galaxy using Cepheid variables as standard

candles (late 1920’s. . . )

Hubble’s Law

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

⊲ Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 12

The spectral features of virtually all galaxies are

redshifted . . . they are all moving away from us!

Hubble’s Law

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

⊲ Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 12

The spectral features of virtually all galaxies are

redshifted . . . they are all moving away from us!

By measuring distances to galaxies, Hubble found that

redshift and distance are related in a special way

Hubble’s Measurement

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae

⊲Hubble’sMeasurement

Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 13

Edwin Hubble (1929) measured distances to 25 galaxies

⊲ Distances from Cepheid variables

⊲ Velocities from redshift of spectral lines:

z =v

c=

λ− λ0

λ0

=∆λ

λ0

⊲ v = c× z = cz

He found:

recession velocity increases linearly with distance!


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 14

How to really do it . . .


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 14


Spectra of cooler stars show very strong absorption lines due

to singly-ionized calcium:


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 14


Spectra of cooler stars show very strong absorption lines due

to singly-ionized calcium:

H K

These strong absoption line stand out in the spectrum!


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 15


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 15


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 15

v = Hod Ho = 70 km/s/Mpc

New distance indicator: d = zc/Ho

Example:

Redshift of a galaxy is z = 0.1

Recession velocity: v = zc = 30, 000 km/s

Distance:

d =zc

Ho

=30, 000 km/s

70 km/s/Mpc= 429Mpc

Hubble’s Law

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


⊲ Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 16

Hubble’s Law: velocity = H0 × distance

Hubble’s Law

Read: Chaps 20, 21 11/18/14 – slide 17

Redshift of a galaxy tells us

its distance through

Hubble’s Law:

distance =velocity

H0

=zc

H0

Hubble’s Law

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


⊲ Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 18

Hubble

Ultra Deep Field

Distances of farthest galaxies are measured from redshifts

Age of the Universe

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

⊲Age of theUniverse



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 19

How do distance measurements tell us

the age of the Universe?

Thought question

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation




Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 20

Your friend leaves your house. She later calls you on her cell

phone, saying that she’s been driving at 60 miles an hour

directly away from you the whole time and is now 60 miles

away. How long has she been gone?

(A) 1 minute

(B) 30 minutes

(C) 60 minutes

(D) 120 minutes

Thought question

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation




Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 20

Your friend leaves your house. She later calls you on her cell

phone, saying that she’s been driving at 60 miles an hour

directly away from you the whole time and is now 60 miles

away. How long has she been gone?

(A) 1 minute

(B) 30 minutes

(C) 60 minutes

(D) 120 minutes

Expansion of the Universe

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe

⊲Expansion of theUniverse


Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 21

Observations suggest:

1. The expansion rate appears to be the same everywhere!

2. The Universe has no center and no boundary!

(as far as we can tell)


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe

⊲Expansion of theUniverse


Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 22

One example of something that expands but has no center or

edge is the surface of a balloon

The Cosmological Principle

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe


⊲CosmologicalPrinciple

Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 23

The Universe looks about the same no matter

where you are within it

Matter is evenly distributed on very large scales in the

Universe

There is NO center and no edges

Not proved but consistent with all observations to date


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 24

Philosphically consistent with the lessons learned from

Ptolemy to Copernicus

⊲ We don’t want to make the same mistake again!


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 24




Copernican view: nothing special about Earth’s position

in the Universe


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 24




Copernican view: nothing special about Earth’s position

in the Universe

This is often called the Copernican Principle


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 25

Observations support the idea that the Universe is both

isotropic and homogeneous

Homogeneous: At large scales, the Universe looks the

same everywhere

⊲ There is no preferred location

⊲ I.e. no center

Isotropic: At large scales, the Universe looks the same in

all directions on the sky

⊲ There is no special direction

⊲ I.e. no axis


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 26

Homogeneous– looks the same independent of location

Isotropic– looks the same independent of direction

In 3 dimensions In 2 dimensions


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 27

Isotropy and homogeneity are related:

Isotropy +Copernican

Principle=⇒ Homogeneity

⇓

Isotropy +Isotropy around

another point=⇒ Homogeneity


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 28

The universe is homogeneous

and isotropic when viewed on a

large enough scale.

The Cosmological Principle derives from the Copernican

Principle

But not demanded by any physical model

It can not be proven in a mathematical sense

However:

⊲ Supported by numerous observations

⊲ Great weight from purely empirical grounds

The Cosmological Principle: Newton’s version

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 29

To prevent one part of the Universe from collapsing

(i.e. into a black hole)

⊲ Homogeneous

⊲ Isotropic

⊲ Infinite in size

⊲ No center

Infinite in time

(i.e. no beginning or end of time)

⊲ Always has been

⊲ Always will be

The Cosmological Principle: Newton’s version

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 29

To prevent one part of the Universe from collapsing

(i.e. into a black hole)

⊲ Homogeneous

⊲ Isotropic

⊲ Infinite in size

⊲ No center

Infinite in time

(i.e. no beginning or end of time)

⊲ Always has been

⊲ Always will be

⇒ Known as the Perfect cosmological principle.

⇒ Inconsistent with expansion!

Thought question

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



⊲ Thought question

What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 30

What is the Universe expanding into?

(A) Nothingness

(B) Extra dimensions of space and time

(C) The Universe is not really expanding, it is stretching

Thought question

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe




What is expanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 30

What is the Universe expanding into?

(A) Nothingness

(B) Extra dimensions of space and time

(C) The Universe is not really expanding, it is stretching

What is expanding?

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

⊲What isexpanding?

Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 31

The spaces between faraway galaxies stretch

What is not expanding or stretching

What is expanding?

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question


Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 31



⊲ You and I are not expanding

⊲ The Earth is not expanding

⊲ The Sun isn’t expanding

⊲ The entire Milky Way galaxy is not expanding

What is expanding?

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question


Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 31



On small scales, the effect of the Universe’s stretching is

completely overwhelmed by other forces

What is expanding?

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question


Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 31





⊲ The atomic forces which hold people’s bodies

together

⊲ The Earth’s gravity

⊲ The Sun’s gravity

⊲ The Galaxy’s gravity

What is expanding?

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question


Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 31





On very large scales, the effect of the universe’s

stretching becomes noticeable above the effects of local

gravity and other forces which tend to hold things

together

What is expanding?

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question


Thought question


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 31





On very large scales, the effect of the universe’s

stretching becomes noticeable above the effects of local

gravity and other forces which tend to hold things

together

This is often called the Hubble Flow

Thought question

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?



Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 32

You observe a galaxy moving away from you at 0.1 light-years

per year, and it is now 1.4 billion light-years away from you.

How long has it taken to get there?

(A) 1 million years

(B) 14 million years

(C) 10 billion years

(D) 14 billion years

Thought question

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?



Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 32




(A) 1 million years




Thought question

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?



Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 32




(A) 1 million years




Hubble’s constant tells us age of universe be-

cause it relates velocities and distances of all

galaxies:

Age =Distance

Velocity≈

1

H0

Measurement in an expanding universe

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question

⊲

Measurement inan expandinguniverse

Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 33

How does the Universe’s expansion affect our distance

measurements?


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question

⊲


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 33


measurements?Distances between faraway

galaxies change while light

travels


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question

⊲


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 33


measurements?Distances between faraway

galaxies change while light

travels

Astronomers think in terms

of lookback time rather than

distance


Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question

⊲


Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 34

Expansion stretches photon wavelengths, causing a

cosmological redshift directly related to lookback time

Summary

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


⊲ Summary

Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 35

How did Hubble prove that galaxies lie far beyond the

Milky Way?

⊲ He measured the distance to the Andromeda galaxy

using Cepheid variable stars as standard candles

What is Hubble’s Law?

⊲ The faster a galaxy is moving away from us, the

greater its distance:

velocity = H0 × distance

How do we observe the life histories of galaxies?

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

⊲ Galaxian history

Looking back

Read: Chaps 20, 21 11/18/14 – slide 36

Observing galaxies at different distances shows how they age

Looking back

Announcements

Measuring distances

Tully-Fisher

3 types

Summary

Spiral Nebulae


Modern relation

Age of the Universe



Thought question

What is expanding?

Thought question


Summary

Galaxian history

⊲ Looking back

Read: Chaps 20, 21 11/18/14 – slide 37

Deep observations

show us very

distant galaxies as

they were much

earlier in time

(Old light from

young galaxies)

Documents

Martin D. Weinberg UMass Astronomy [email protected]/astron100-mdw/lectures/lec20.pdfModern relation Age of the Universe Expansion of the Universe Cosmological