Lecture 10:

Light & Distance & Matter

Astronomy 1143 – Spring 2014

Key IdeasWe learn about properties of distant bodies because

of interaction of light & matter

We learn about the distance to objects from measuring brightness and knowing luminosity

• Brightness=apparent magnitude: energy received from an object

• Luminosity=absolute magnitude=intrinsic brightness: total energy emitted by object

Hot, dense bodies are similar to blackbodies

Wien’s Law• The hotter an object, the shorter the peak

Key IdeasSpectrum

• Electrons in atoms of an element can only absorb or emit light of specific energies

• Each element has a distinct pattern of emission or absorption lines

Kirchoff’s Laws : Emission-line, absorption-line, and continuum spectra

Pattern of lines at precise wavelengths very useful for detecting motion

Spectra of objects useful for IDing similar objects

Exploring the Universe

To map out the Universe in 3-D,we need distances to objects

Distances are also needed to figure out properties of objects

• Radius• Mass • Luminosity (esp. if not like an object we’ve seen

before)• Lookback time

The Distance Ladder

How bright is the Sun?

Issues with measuring the amount of energy that the Earth receives from the Sun:

Night

Clouds

Atmosphere

Distance of Earth from the Sun

Tilt of Earth

Define the solar constant as the solar energy received (perpendicular) at the top of the Earth’s atmosphere at 1 AU

The Solar Constant

Current measurements: 1366 W/m2

This is the apparent brightness of the Sun at the Earth.

Measures how bright an object appears to be as seen from a distance

• B is measured in units of–Energy / second / area

• Depends on the Distance to the object.

What we actually measure (observable)

Luminosity (L)

Measures the total energy output of a object (e.g. the Sun)

• L is measured in units of

–Energy / second (e.g., Watts)

• Independent of Distance

Luminosity is an intrinsic property of the light source

Spreading out light

Inverse Square Law of Brightness

2

LB =

4 d

Apparent Brightness is inversely proportionalto the square of its distance.

2-times Closer = 4-times Brighter

2-times Farther = 4-times Fainter

Relates Brightness and Luminosity:

Calculating the Sun’s Luminosity

With the distance and brightness measured, we can calculate the Sun’s Luminosity

Calculating distances from brightness + luminosity

A way to calculate distances!

If we know the luminosity of an object (for example, it is just like the Sun) and can measure the brightness,, then we can use a version of the inverse square law of brightness to get distance!

Which star is just like the Sun?

SpectrumPrism

WhiteLight

Spectra of Objects very useful

Radiation from Hot Dense ObjectsRadiation from hot, dense objects has some

specific qualities• Emits at all wavelengths (continuous spectrum)• Energy emitted depends on Temperature.• Peak wavelength depends on Temperature.

Does not depend on composition (at least ideally)

Called Blackbody Radiation

In Words:

“Hotter objects are BLUER”

“Cooler objects are REDDER”

Example: heating an iron bar

Relates peak wavelength and Temperature:

Wien’s Law

In-Class Demo: Wien’s Law

Example calcuation: Peak Wavelength for the EarthTemperature of the Earth =300 K

What is peak?

Infrared!

Examples:Person:

Body Temperature = 310 K• Peak wavelength = 9400 nm (infrared)• Typical adult emits about 100 Watts of

infrared light.

Sun:

Surface Temperature = 5770 K• Peak wavelength = 503 nm (visible)• Emits about 3.81026 Watts of visible,

infrared and UV.

Infrared Light

Visible Light

InfraredUV

Kirchoff’s Laws

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

2) A hot, low-density gas produces an emission-line spectrum.

3) A continuous spectrum source viewed through a cool, low-density gas produces an absorption-line spectrum.

ContinuumSource

Continuous Spectrum

Absorption-lineSpectrum

Emission-line Spectrum

Cloud of Hydrogen Gas

In Class Demonstration

Light: Energy and WavelengthThe wavelength ( of a photon is related to its

energy (E).

h=Planck’s constant = 4.136x10-15 eV s

c=speed of light = 3.00 x108 m/s

The larger the energy, the shorter the wavelength

When atoms emit a photon with a specific energy, they are emitting a photon with a specific wavelength.

n=1 (Ground State)

n=3 (2nd excited state)

n=2 (1st excited state)

n=4n=5

Energy Level Diagram of 1H

Ionization

n=

Emission LinesAn electron jumps from a higher to a lower energy orbital

• Emits one photon with exactly the energy difference between the orbitals.

• Bigger Jumps emit Higher Energy (bluer) photons

n=6

n=1

n=3

n=2

n=4n=5

32

62

52

42

Absorption LinesElectron absorbs a photon with exactly the energy needed to jump from a lower to a higher orbital.

• Only photons with the exact excitation energy are absorbed.

• All others pass through unabsorbed.

n=6

n=1

n=3

n=2

n=4n=5

32

62

52

42

31 =

21 =

1

23

123Unobtainium

32 =

3-1 2-1 3-2

31 =

32 =

21 =

1

2

3

123Unobtainium

Electron Jumps

Electrons that are bound to the atom can only make quantized jumps

If a photon has enough energy to ionize the atom (unbind an electron completely), then the electron is a lot less picky

For example, photons with wavelengths shorter than 91.2 nm can ionize neutral H and can therefore be absorbed

Free electrons will interact with all wavelengths of light as well!

Stars and Planets produce absorption-line spectrumThe interior of the star, or planet, which is hot and dense, produces a continuous spectrum.

The atoms in the atmosphere, which is cooler and thin, absorb photons with the “right” wavelengths.

Spectrum of the Sun

Hydrogen

Sodium

Magnesium

From the depth of the absorption lines (+ some math), we can measure the composition of the atmospheres

Types of Stars -- Colors

this star is different than

this star

and both are different than

the Sun

Different Stars

Identifying Similar Stars

We can get parallaxes to nearby stars• Measure luminosities for these stars• Can use this luminosity + brightness to get

distance for stars that are the same in nature as nearby stars

Methods• Color – provides first check• Spectra – provides detailed look

Spectra of Planet Atmospheres

Comet’s Tail is a hot, low-density Gas

Spectrum of Comet