Tools We Will Need on our Journey through the

Universe

Don’t Panic…but it IS physics and math

Quick Review of Scientific Notation

Powers of Ten

Scientific Notation• 10n means 10 x 10 x 10 x 10 … [n times]• 10-n means 1/(10 x 10 x 10 ….) [n times]

There are 1010 – 1011 stars in our Galaxy, and a similar number of galaxies in the Universe

Units for Distance, not Time

Kilometer (km) = .621 miles

Light-year (lt-yr) = The distance light travels in one year in a vacuum.

1 lt-yr = 9.5 x 1012 km

Parsec = 3.3 light-years (Mpc = 1,000 pc)

arc-second = (1 degree/3600)

Forces in the Universe

Weak

Strong

Electromagnetic

Gravitational

Strong Force

The strong interaction is very strong, but very short-ranged. It acts only over ranges of order 10-13 centimeters and is

responsible for holding the nuclei of atoms together. It is basically attractive, but can be effectively repulsive in some

circumstances.

Weak Force

The weak force is responsible for radioactive decay and neutrino

interactions. It has a very short range and, as its name indicates, it is very weak.

Electromagnetic Force

The electromagnetic force causes electric and magnetic effects such as the repulsion

between like electrical charges or the interaction of bar magnets. It is long-

ranged, but much weaker than the strong force. It can be attractive or repulsive, and

acts only between pieces of matter carrying electrical charge.

Light is Electromagnetic!

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The Wave Nature of LightProvides us with Important Probes for Understanding

Our Universe

c = 3 x 108 m/s

It’s not just a good idea, it’s the law!

Let There Be Light!

A Brief Review of ...

VLA COBE IRAS EUVE Chandra CGRO

Seeing the Light

HST/Keck

Looking back through space and time

Constellation-X

NGST, FIRST

Explorer

MAP, Planck

LISA, GLAST

OWL

Big Bang inflation

first stars, galaxies,

and black holes

clusters and groups of galaxies

microwavebackground

matter/radiationdecouplingEarly Universe Gap

First Stars Gap

Falloff and Shift

Two things we must understand:

1.) Intensity of light falls off as we move away from the source

2.) Wavelength of light we see shifts as source moves

Light at a Distance

Objective:

Your detector in orbit around Earth has

measured a certain amount of energy from

the direction of a faraway source.

Your job is to determine how much energy

the source actually emitted. Assume the source emits energy equally in all directions.

Think About It!

A light emits equally in all directions.

What does this mean about the amount of light you will measure in any given square cm as you move further and further away from the light source?

• At r1, the light per unit area, L1 = L/4(r1)2. •And at r2, the light per unit area, L2 = L/4(r2)2.

• Solving each equation for L gives us

L= L1 x 4(r1)2 = L2 x 4(r2)2.

Think of it in terms of a ratio... the amount of light per unit area at r2 relative to the amount of light per unit area at r1 is then

L2/L1 = (r1)2/(r2)2.

Add the Mathematics!

Conclusion

•We say that the intensity, or amount of light per square cm, changes as 1/distance squared (i.e., 1/r2) away from the source.

•How does this help us to achieve our Objective? If we measure X amount of energy per square cm in our detector, then we know that the source must have emitted energy equal to 4r2 times X!

Now Confirm It…Low-TechWant to convince yourself that light really does fall off as 1/r2? Here is a quick, easy, low-tech way!

Materials:

tape measure

flashlight - with a well focused emission of light - light end no more than 5cm in diameter

graphics calculator

Look!

Dist.(cm)

Diameters measured in cm D1 D2 D3

mean D(cm)

Radius(cm)

Area(cm2)

46.5 20.5 21.5 21 21 10.5 346.3668.5 30.5 31 31 30.8 15.42 746.6786 39 39.5 38.5 39 19.5 1194.5995 42 43 44 43 21.5 1454.6

Keep Looking!

Light

y = 0.1526x2.0118

0

200

400

600

800

1000

1200

1400

1600

0 20 40 60 80 100

Distance from Source

Area of Projected Circle

Doppler Shift

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If source approaches, light appears bluer than it is.

If source recedes, light appears redder than it is.

Doppler Shift

Wavelength is shorter when approaching

Stationary waves

Wavelength is longer when receding

What It Looks Like

Comparison of laboratory to blue-shifted object

Comparison of laboratory to red-shifted object

Doppler Shift / Redshift

Redshift, z, is a non-relativistic approximation to the Doppler shift

=

vc

=z =

Historical Note

Using the Doppler shift, Edwin Hubble

observed that the

Universe is expanding!

What Hubble Found

Compared to modern measurements, Hubble’s

results were off by afactor of ten!

The Hubble constant

Ho = 558 km s -1 Mpc -1

is the slope of these graphs

Hubble’s Law

v = Ho * d Ho is called the Hubble constant. It is generally believed to be around 65 km/sec/Mpc…plus or minus about 10 km/sec/Mpc.

Note: The further away you are, the faster you are moving!

Implications of Hubble’s Law

To get a rough idea of how far away a very distant object is from Earth, all we need to know is the object's velocity.

The velocity is relatively easy for us to measure using the Doppler effect, or Doppler shift.

Distance = velocity/(Hubble constant)

Caveat!

Space between the galaxies expands while galaxies stay

the same size

The Tools of All Astronomy

• Light Curves – examining how bright something is as a function of time

• Images – examining what something looks like spatially

• Spectra – examining how much energy an object emits as a function of energy

Kinds of Spectra

Another Way to Look at a Spectrum

The Atom’s Family

Bohr atom

Electrons in fixed orbits around… Protons and neutrons in the nucleus Only certain electron orbits are allowed Electrons jump between orbits to make photons of

specific energies

Periodic TableElectrons fill shells labeled s, p, d, f, etc.

New

shells are added

The Atom’s Family

Quantum atomElectrons are clouds of probability densityNo two electrons can have identical

quantum numbers Pauli exclusion principle

Heisenberg Uncertainty principle limits knowledge our simultaneous knowledge of:position & momentumenergy & time

x p = h/2>

Gravitational Force

The gravitational force is weak, but very long ranged. Furthermore, it is always attractive, and acts between any two

pieces of matter in the Universe since mass is its source.

Remember the Tortoise and the Hare?

Gravity has basic properties that set it apart from the other forces: (1) it is long-ranged and thus can act over cosmological distances; (2) it always supplies an attractive force between any two pieces of matter in the Universe.

Thus, although extremely weak, it always wins over cosmological distances and is the most important force for the understanding of the large scale structure and evolution of the Universe.

So, let us deal with GRAVITY

We’ll need a bit of a history lesson:•Brahe•Kepler•Newton•Einstein

Pay close attention, gravity has many

implications!

Tycho Brahe

A wild Dane, but he made and recorded large quantities of accurate measurements of the motions of the planets around the Sun.

1546 - 1601

Began working with Johannes Kepler in 1600.

Kepler’sKepler’s Three Laws of PlanetaryThree Laws of Planetary MotionMotion

Landmarks in the history for astronomy and mathematics, for in the effort to justify them Isaac Newton was led to create modern celestial mechanics. The three laws are:

1) The planets move abort the sun in elliptical orbits with the sun at one focus.

2) The radius vector joining a planetto the sun sweeps over equal areas in equal intervals of time.

The empirical discovery of these laws from Tycho Brahe's mass of data constitutes one of the most remarkable inductions ever made in science.

T12/ T2

2 =R13/ R2

3

orT2=k.R3

3) The square of the time of one compete revolution of a planet about its orbit is proportional to the cube of the orbit's semi-major axis

Isaac Newton

Born 1642, the year Galileo diedLoner, tinkerer, paranoid1665-1666 Plague was very good for himSuffered mental breakdown 1675Math, Chemistry, Theology, ParliamentDied 1727Has his picture on the British pound note

He put the physics and mathematics toKepler’s Laws!

Was there really an apple?

We know: he was on a farm

We don’t know anything else

Newton’s Laws of MotionFirst Law

- A body remains in its state of motion unless acted upon by an outside force

Second Law - A body acted upon by an external force will change its

momentum in the direction of the force such that the greater the force the greater the change in momentum (F= ma)

Third Law - Forces always occur in pairs, i.e. for every action there is an

equal and opposite reaction

Universal Law of Gravitation

All objects in the Universe attract each other with a force that varies directly as the product of their masses and inversely as the square of their separation from each other.

F = G m m

rgravity 1 2

2

Albert Einstein

E = m c2

• Energy can be neither created nor destroyed. It can just change from one form to another. Light, heat, kinetic, potential, etc. etc. etc.

Besides having great hair, he taught us a few fundamentally important things:

• No object can move faster than the speed of light.

• Space and time are linked together.