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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