6/25 How do we get information from the telescope? 1. Galileo drew pictures. 2. With the invention of photography, we began taking pictures of the view in the telescope. With telescopes that would rotate to correct for the rotation of the Earth, we could take long time exposures. As we will learn, such exposures allowed us to calculate the relative brightnesses of stars. Photographic film is not efficient only a few percent of the light is detected by the film. 3. Photoelectric Effect light striking a metal surface drives electrons out of the metal. Put a battery across the device, and get an electric current. The greater the electric current, the brighter the light. First accurate measurement of brightnesses of stars problem: only a single star could be in the field of view (if more, total brightness of all stars). 4. Now we use Charge-Coupled Detectors or CCD s. Advantage of photography with a complete field of stars at once but with 80 to 90% efficiency. Goes straight to a computer and analyzed there. The brightness of all stars in the view can be analyzed at once. Observations in Non Visible Parts of EM Spectrum Radio Astronomy detecting radio waves from space found the cosmic microwave background radiation. Note, in the picture, that this is a Cassegrain radio telescope! Infrared absorbed by water in the atmosphere can be observed from space or high mountains or weather balloons. Allows us to see through gas and dust in the universe because its relatively long wavelength is not scattered by gas and dust. Can see past the gas and dust near the center of our galaxy to see the center and to see stars in the process of being born inside clouds of gas and dust. Ultraviolet largely absorbed by the ionosphere must be observed from space. Used to view the Sun and we note the existence of a region around the Sun without gas and dust local bubble explosion nearby in the past? X Rays must be viewed from space used for detecting exotic objects such as neutron stars and black holes also observing the Sun. Gamma Rays must be viewed from space discovered gamma ray burster seem to be associated with supernovae. What We Can Deduce About Stars Without Knowing the Distance Black Body Radiation A black body is one that absorbs all electromagnetic radiation from radio waves to gamma rays
that strike it. A white body is one that reflects the entire electromagnetic spectrum. White bodies cannot radiate the reflect all energy and have no energy to radiate. Black Bodies can radiate stars radiate like black bodies. They don t look black because they are hot. The amount of radiation from a star given by its luminosity L in watts depends on the temperature (Stefan-Boltzmann Law): where e = emissivity (0 for a perfect white body, 1 for a perfect black body), = Stafan- Boltzmann constant = 5.67 10 8 W/m 2 K 4, A is the surface area of the star, and T is its absolute temperature. (Aside: Temperature Temperature is a measure of how fast the atoms in a system are moving. There is a minimum temperature: 1. Extract heat from a body and its molecules will slow down. 2. If we extract enough heat, molecular motion will stop. Once this is done, the temperature of the body can no longer be lowered. 3. The body is at absolute zero. An absolute temperature takes absolute zero as zero on its scale. The kelvin scale is an absolute temperature scale measure temperature in kelvins = K. The size of the kelvin is the same size as the Celsius degree. On the kelvin scale, the freezing point of water 0 C is 273 K and the boiling point of water 100 C is 373 K. For high temperature, kelvin and Celsius temperatures are roughly the same and roughly ½ of the Fahrenheit temperature.) If we increase the temperature of a star the wavelength at which it emits its maximum radiation shifts toward shorter wavelengths (becomes bluer). Governed by Wien s displacement law:
Example: Wavelength at which the Sun emits most of its energy. Astronomers measure the black body radiation curve for a star. Read off the wavelength at which maximum occurs. Use Wien s law to get the temperature of the star. Astronomers can measure the temperatures of stars. Spectra of Stars: Types of Spectra: 1. Continuous Spectrum rainbow is a continuous spectrum black body spectrum discussed above. 2. Emission Spectrum See lines of color at isolated wavelengths separated by dark regions spectrum from a low-density gas. 3. Absorption Spectrum See a continuous spectrum with missing lines spectrum produced when a continuous spectrum passes through a low-density gas. To understand the last two, we must understand the atom and how it emits light. We will use the solar system model of the atom with the nucleus like the Sun at the center and electrons like planets in orbit about it. Since hydrogen is the most common element in the universe and the simplest atom (a single proton as the nucleus and a single electron in orbit) we will concentrate on that atom. Quantum mechanics tells us that the electron can only exist in certain allowed orbits. Lowest orbit or energy state is called the ground state of the atom.
Higher orbits are excited states. Electrons want to be in the lowest state the ground state. If an electron is in an excited state, it will eventually jump down to a lower state. When it does so, it lowers its energy and lowers the energy of the atom. However, the principle of conservation of energy tells us that the total energy of an isolated system is constant something must happen to conserve energy when the energy of the atom decreases. What happens: a particle of light called a photon is created and emitted by the atom. The energy of the emitted photon is the same as the energy lost by the atom when the electron jumps from the higher state to the lower state. Since the electron in the atom can only be in certain energy states, the energies of the emitted photons will have only certain discrete values. The frequency/wavelength of a photon is related to its energy by the Planck energy relation: So we will only see discrete wavelengths or discrete colors. Produces the emission spectrum of an atom. Each atom and molecule as its own distinct spectrum. If the spectrum of that atom or molecule appears in the light from a distant object, we know that the element associated with the atom or substance associated with the molecule is in that object. Stars exhibit absorption spectra continuous spectrum emitted by the star s visible surface then passes through the stars gaseous atmosphere. If a photon in the continuous spectrum light has the same
energy as an energy difference in a hydrogen atom, it will cause the electron to jump from a lower state to higher state and be absorbed in the process. This photon will be missing in the spectrum that reaches us here on Earth missing line. Since each atom has its own spectrum, we can use the absorption spectrum of a star to determine what it is made of. Note that this spectrum can also be used to measure the temperature of a star. In a cool star, only the lower states will be substantially excited and they will appear bright in the spectrum while higher states will be dim. In hotter stars, the higher state transitions will produce bright lines in the spectrum as well. The relative brightness of the lines in the spectrum indicate the temperature. Doppler Effect Apparent change in the wavelength or frequency of light due to the relative motion of the source and observer. Since, in our frame of reference, we are at rest and the source the star is moving, we will look at that case. If we drop stones into a pond, all in the same location, it will produce ripples the distance between ripples will be the wavelength. The source the star is at the point where the stone enters the water. Now drop stones and move along the branch between each drop this will correspond to a moving source. The ripples in front of the source are closer together meaning a shorter wavelength or a shift toward the blue blueshift. Ripples behind the source are farther apart meaning a shift toward the red or a redshift. Since as the speed of the source gets faster, the waves in front are scrunched up more and spread out more in back. There must be a relation between the speed of a star and the shift in wavelength of the light from the star. Note that the Doppler effect only gives us information about that part of the velocity of an object that is either directly toward us or away from us radial velocity. If the speed of the object is not too great, the relation can be written:
or Example: Suppose the spectral line in a star is measured to be 656.3 nm. In the lab, it is measured to be 656.15 nm. What is the radial velocity of the star? We know we have the right line in the spectrum because the spectrum lines of an element are all shifted by the same amount. Solar System Chapters 4,5, and 6 Creation of the Solar System Started with a cloud of gas and dust. Slowly rotating. Something (more later) caused this cloud to begin contracting under its own gravity. As the cloud contracts, the rate of spin increases (conservation of angular momentum/ice-skater) Centrifugal force impedes contraction perpendicular to spin axis but not parallel to the spin axis. Causes the cloud to form into a disk shape. Contraction at the center of the cloud causes it to heat up eventually becomes the Sun. Heat out from the center pushes lighter elements hydrogen (H) and helium (He) away from the central regions and into the outer part of the disk. Leaves heavier elements in the interior. Over time, collisions take place that produce larger and larger objects when they get to asteroid size, they are called planetesimals.
Eventually, one of these planetesimals gets large enough to dominate and eventually gets big enough to be a planet. Process took about 500 million years. Still many collisions but, eventually, the planet swept up all the material and the collisions became much less frequent. In the inner solar system with few volatiles, rocky planets formed Mercury, Venus, Earth, and Mars. Volatile materials did exist in the outer part of the disk gas giants were created: Jupiter, Saturn, Uranus, and Neptune.