Lecture 10: Light & Distance & Matter Astronomy 1143 – Spring 2014
Key Ideas We 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 Ideas Spectrum 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/m 2 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 Apparent Brightness is inversely proportional to 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?
Spectrum Prism White Light Spectra of Objects very useful
Radiation from Hot Dense Objects Radiation 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 Earth Temperature 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 3.8 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.
Continuum Source Continuous Spectrum Absorption-line Spectrum Emission-line Spectrum Cloud of Hydrogen Gas
In Class Demonstration
Light: Energy and Wavelength The wavelength ( of a photon is related to its energy (E). h=Planck’s constant = 4.136x eV s c=speed of light = 3.00 x10 8 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 (2 nd excited state) n=2 (1 st excited state) n=4 n=5 Energy Level Diagram of 1 H Ionization n=
Emission Lines An 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=4 n=5 3232 6262 5252 4242
Absorption Lines Electron 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=4 n=5 3232 6262 5252 4242
3 1 = 2 1 = Unobtainium 3 2 =
3 1 = 3 2 = 2 1 = Unobtainium
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 spectrum The 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