test 2: overview. the total energy radiated from entire surface every second is called the...

Test 2: Overview

The total energy radiated from entire surface every second is called the luminosity. Thus

Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2)

For a sphere, area of surface is 4R2, where R is the sphere's radius.

The "Inverse-Square" Law Applies to Radiation

apparent brightness 1D2

D is the distance between source and observer.

Each square gets 1/9 of the light

Each square gets 1/4 of the light

The frequency or wavelength of a wave depends on the relative motion of the source and the observer.

Types of Spectra

1. "Continuous" spectrum - radiation over a broad range of wavelengths(light: bright at every color).

3. Continuous spectrum with "absorption lines": bright over a broad range of wavelengths with a few dark lines.

2. "Emission line" spectrum - bright at specific wavelengths only.

Kirchhoff's Laws

1. A hot, opaque solid, liquid or dense gas produces a continuous spectrum.

2. A transparent hot gas produces an emission line spectrum.

3. A transparent, cool gas absorbs wavelengths from a continuous spectrum, producing an absorption line spectrum.

The pattern of emission (or absorption) lines is a fingerprint of the element in the gas (such as hydrogen, neon, etc.)

For a given element, emission and absorption lines occur at the same wavlengths.

Sodium emission and absorption spectra

Stellar Spectra

Spectra of stars are different mainly due to temperature and composition differences.

Star

'Atmosphere', atoms and ions absorb specific

wavelengths of the black-body spectrum

Interior, hot and dense, fusion

generates radiation with black-body

spectrum

The Nature of Atoms

The Bohr model of the Hydrogen atom:

_

+proton

electron

"ground state"

_

+

an "excited state"

Ground state is the lowest energy state. Atom must gain energy to move to an excited state. It must absorb a photon or collide with another atom.

But, only certain energies (or orbits) are allowed:

__

_

+

The atom can only absorb photons with exactly the right energy to boost the electron to one of its higher levels.

(photon energy αfrequency)

a few energy levels of H atom

When an atom absorbs a photon, it moves to a higher energy state briefly

When it jumps back to lower energy state, it emits a photon - in a random direction

Ionization

+

Hydrogen

_

++

Helium

"Ion"

Two atoms colliding can also lead to ionization.

_

_

Energetic UV Photon

Atom

Energetic UV Photon

13Radio Window

Optical Telescopes - Refracting vs. Reflecting

Refracting telescope

Focuses light with a lens (like a camera).

<-- object (point of light) image at focus

Problems:

- Lens can only be supported around edge.

- "Chromatic aberration".

- Some light absorbed in glass (especially UV, infrared).

- Air bubbles and imperfections affect image quality.

Chromatic Aberration

Lens - different colors focus at different places.

white light

Mirror - reflection angle doesn't depend on color.

Reflecting telescope

Focuses light with a curved mirror.

<-- object image

- Can make bigger mirrors since they are supported from behind.

- No chromatic aberration.

- Reflects all radiation with little loss by absorption.

Image of Andromeda galaxy with optical telescope.

Image with telescope of twice the diameter, same exposure time.

Resolving Power of a Mirror

(how much detail can you see?)

fuzziness you would see with your eye.

detail you can see with a telescope.

Andromeda Galaxy: (a) 10 arcminutes, (b) 1 arcminute, (c) 5 arcseconds, and (d) 1 arcsecond

Seeing

*

dome

Air density varies => bends light. No longer parallel

Parallel rays enter atmosphere

CCD

No blurring case. Rays brought to same focus.

* Sharp image on CCD.

Blurring. Rays not parallel. Can't be brought into focus.

Blurred image.

Radio Telescopes

Large metal dish acts as a mirror for radio waves. Radio receiver at focus.

Surface accuracy not so important, so easy to make large one.

angular resolution α wavelengthmirror diameter

D larger than optical case, but wavelength much larger (cm's to m's), e.g. for wavelength = 1 cm, diameter = 100 m, resolution = 20".

Jodrell Bank 76-m (England)But angular resolution is poor. Remember:

Interferometry

A technique to get improved angular resolution using an array of telescopes. Most common in radio, but also limited optical interferometry.

D

Consider two dishes with separation D vs. one dish of diameter D.By combining the radio waves from the two dishes, the achieved angular resolution is the same as the large dish.

Orbits of Planets

All orbit in same direction.

Most orbit in same plane.

Elliptical orbits, but low eccentricity for most, so nearly circular.

Two Kinds of “Classical” Planets

"Terrestrial"

Mercury, Venus,Earth, Mars

"Jovian"

Jupiter, Saturn, Uranus, Neptune

Close to the SunSmall

Far from the SunLarge

Few MoonsNo RingsMain Elements Fe, Si, C, O, N:we learn that from the spectra

Mostly RockyHigh Density (3.3 -5.3 g/cm3) reminder: liquid water is 1 g/cm3

Slow Rotation (1 - 243 days)

Mostly GaseousLow Density (0.7 -1.6 g/cm3)

Many MoonsRingsMain Elements H, He

Fast Rotation (0.41 - 0.72 days)

Dwarf Planets compared to Terrestrial Planets

"Terrestrial"

Mercury, Venus,Earth, Mars

Dwarf Planets

Pluto, Eris, many others

Close to the SunSmall

Far from the SunVery small

Few MoonsNo RingsMain Elements Fe, Si, C, O, N

Mostly RockyHigh Density (3.3 -5.3 g/cm3)Slow Rotation (1 - 243 days)

Rock and IceModerate Density (2 - 3 g/cm3)

Few MoonsNo RingsMain Elements Fe, Si, C, O, N And an icy surface

Rotation?

Early Ideas

René Descartes (1596 -1650) nebular theory:

Solar system formed out of a "whirlpool" in a "universal fluid". Planets formed out of eddies in the fluid. Sun formed at center. Planets in cooler regions. Cloud called "Solar Nebula".

This is pre-Newton and modern science. But basic idea correct, and the theory evolved as science advanced, as we'll see.

A cloud of interstellar gas

The associated dust blocks starlight. Composition mostly H, He.

a few light-years,or about 1000times bigger thanSolar System

Too cold for optical emission but some radio spectral lines from molecules. Doppler shifts of lines indicate clouds rotate at a few km/s.

Clumps within such clouds collapse to form stars or clusters of stars. They are spinning at about 1 km/s.

Now to make the planets . . .

Solar Nebula:

98% of mass is gas (H, He) 2% in dust grains (Fe, C, Si . . .)

Condensation theory: 3 steps:

1) Dust grains act as "condensation nuclei": gas atoms stick to them => growth of first clumps of matter.

2) Accretion: Clumps collide and stick => larger clumps. Eventually, small-moon sized objects: "planetesimals".

3) Gravity-enhanced accretion: objects now have significant gravity. Mutual attraction accelerates accretion. Bigger objects grow faster => a few planet-sized objects.

Result from computer simulation of planet growth

Shows growth of terrestrial planets. If Jupiter's gravity not included, fifth terrestrial planet forms in Asteroid Belt. If Jupiter's gravity included, orbits of planetesimals there are disrupted. Almost all ejected from Solar System.

Simulations also suggest that a few Mars-size objects formed in Asteroid Belt. Their gravity modified orbits of other planetesimals, before they too were ejected by Jupiter's gravity.

Asteroid Ida

The Structure of the Solar System

~ 45 AU~ 5 AU

L4

L5

L3

Asteroids and meteoroids have rocky composition; asteroids are bigger.

(above) Asteroid Ida with its moon, Dactyl

(below) Asteroid Gaspra

(above) Asteroid Mathilde

Interplanetary Matter: Asteroids

Comets are icy, with some rocky parts.

The basic components of a comet

Interplanetary Matter: Comets

Oort Cloud

The size, shape, and orientation of cometary orbits depend on their location. Oort cloud comets rarely enter the inner solar system.

Meteor Showers

Meteor showers are associated with comets – they are the debris left over when a comet breaks up.

Earth's Internal Structure

Crust: thin. Much Si and Al(lots of granite). Two-thirds covered by oceans.

How do we know? Earthquakes. See later

Mantle is mostly solid, mostly basalt (Fe, Mg, Si). Cracks in mantle allow molten material to rise => volcanoes.

Core temperature is 6000 K. Metallic - mostly nickel and iron. Outer core molten, innercore solid.

Atmosphere very thin

EarthquakesThey are vibrations in the solid Earth, or seismic waves.

Two kinds go through Earth, P-waves ("primary") and S-waves ("secondary"):

Like all waves, seismic waves bend when they encounter changes in density. If density change is gradual, wave path is curved.

S-waves are unable to travel in liquid.

Thus, measurement of seismic wave gives info on density of Earth's interior and which layers are solid/molten.

But faint P wavesseen in shadow zone,refracting off denseinner core

Curved paths ofP and S waves:density must slowlyincrease with depth

Zone with no S waves:must be a liquid corethat stops them

No P waves too:they must bend sharplyat core boundary

Earthquakes and volcanoes are related, and also don't occur at random places. They outline plates.

Plates moving at a few cm/year. "Continental drift" or "plate tectonics"

What causes the drift?

Convection! Mantle slightly fluid and can support convection. Plates ride on top of convective cells. Lava flows through cell boundaries. Earth loses internal heat this way.

Cycles take ~108 years.

Plates form lithosphere (crust and solid upper mantle).Partially melted, circulating part of mantle is asthenosphere.

When plates meet...

1) Head-on collision (Himalayas)

2) "Subduction zone" (one slides under the other) (Andes)

3) "Rift zone" (two plates moving apart) (Mid-Atlantic Ridge)

4) They may just slide past each other (San Andreas Fault)

side view

top view

=> mountain ranges, trenches, earthquakes, volcanoes

The Greenhouse Effect

Main greenhouse gases are H

2O and

CO2 .

If no greenhouse effect, surface would be 40 oC cooler!