Doppler Shift

Consider a stationary point source emitting light waves

Doppler Shift

If source moves away, light appears redder than it is. If source moves towards us, light appears bluer.

Visible light

The shift in the light waves is proportional to the relative speeds of the source and

observer

Doppler Shift

Wavelength is shorter when approaching

Stationary waves

Wavelength is longer when receding

Comparison of laboratory to blue-shifted object

Comparison of laboratory to red-shifted object

Wavelength shift

=

-vc

=

Assume radial speed, v, of glowing object is small compared to speed of light, c

v << c.

is reference wavelength of medium at rest.

Frequency shift

f - fo

f=

vc

=ff

Example calculation The star Vega has a hydrogen line of

656.255nm, which is shifted from the reference value of 656.285 nm.

1. Is it moving towards us or away?2. Calculate its speed

Red shifted to LONGER wavelength so moving away. Speed is –13.7 km/s.

Rotation Rate from Doppler Shift

Spectroscopic Binary Stars

Discovery of Planets Around Remote Stars

Rotation speed of galaxy from 21-cm spectral line ofAtomic hydrogen

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.