Astronomy

Colors of Stars

A Blackbody is aideal object that completely absorbs every kind of electromagnetic radiation and reradiates the energy as quickly as it absorbs it. Charcoal is a decent blackbody in the visible. The Sun is a very good blackbody. Blackbodies are perfect radiators which obey three laws: -They emit some radiation at all wavelengths. -A hot blackbody emits more energy than a cooler blackbody at every wavelength. -The peak wavelength for hot bodies is at a shorter wavelength than the peak wavelength for cooler bodies. -Wein's Law relates the wavelength of peak radiation to the temperature of the body: hot bodies have peaks at shorter wavelengths than cool bodies. -The Stefan-Boltzmann law relates the amount of energy released to the temperature of the body: the amount of energy released depends on T4. Properties of Blackbodies 1) Every blackbody emits some radiation at every wavelength. 2) A hot body emits more radiation than a cool body at every wavelength. 3) The peak wavelength of the radiation from a hot body is at a shorter wavelength than that for a cool body.

Atoms

Atoms are composed of three fundamental particles: Protons - positive charge (+) Neutrons - no charge (0) Electrons - negative charge (-) Protons and neutrons are 1836 times more massive than electrons. The actual size of the nucleus is about a million times smaller than the orbit of the electrons. The electrons orbit around the nucleus. They are held in orbit by the electromagnetic attraction to the positively charged nucleus. The typical orbital radius for an electron is 10-10 m, about a million times the diameter of the nucleus. The protons and neutrons are contained in the nucleus of the atom. A typical atomic nucleus is 10-16 m in diameter. The nucleus is held together by the strong nuclear force. Neutrons and protons both contribute to the strong nuclear force, but only protons contribute to the electromagnetic repulsion.

Mizar

First double star seen in a telescope four star total also called a multiple star (system) -with spectroscope it can be seen that both mizar a and mizar b are spectroscopic binaries

Hubble Ultra Deep Field

From Sep. 2003 to Jan 2004, the Hubble Space Telescope pointed at a single location in the constellation Fornax for 11.3 days. The field of view was 1/100 the area of the full Moon. HST took 800 exposures over 400 orbits to build up an exposure of 1 million seconds (about 275 hours) in length.It is the deepest image of the sky ever taken. The faintest objects are four billion times fainter than what we can see with the naked eye. Only a few stars from the Milky Way are apparent in the image. Over 10,000 galaxies have been found.It would take 12.7 million such fields to cover the whole sky. If the rest of the Universe is like this randomly chosen patch, the visible universe must contain about 127 billion galaxies. Exercise -If there are 127 billion galaxies, and each galaxy contains 100 billion stars, how many stars are there in the observable universe? Use scientific notation to determine the answer. -How does this compare to the number of sand grains on the Earth? Explain your reasoning. Answer 127 billion = 127 x 109 = 1.27 x 1011 galaxies 100 billion = 100 x 109 = 2x1011 stars in each galaxy The total number of stars in the observable universe is then 12.7 sextillion stars. How does this compare to the number of sand grains on the Earth (is it very much more, about the same, very much less)? To answer this, let us try to estimate the number of grains of sand in the Sahara Desert.

Particle Nature of Light

Isaac Newton was the first person to propose that light is composed of small particles. Waves and Particles Different colors of light represent different particles. If we shine light on a solar cell, the cell generates electricity. The light knocks electrons out of the silicon atoms in the solar cell. The free electrons can wander around the circuit generating electric currents.

The Speed of Light

In a vacuum, light travels at a constant speed. In formulas, "The Speed of Light" is usually denoted by c (from the Latin celeritas, meaning speed). c = 2.99792458 x 108 m/s c = 3 x 108 m/s c = 186,282 miles per second

Nuclear Reactions

In the 1920s, Gamow, Teller and Bethe suggested that the conversion of matter into energy might power the Sun. •Such conversion is possible through nuclear reactions. •Fission reactions are those where heavy atomic nuclei are broken down into lighter nuclei. •Fusion reactions are those where light atomic nuclei come together to form heavier atomic nuclei. •The strong nuclear force holds the nucleus together. •During fusion, as the new nucleus comes together, some of the nuclear energy (called binding energy) is released.-When binding energy is released, the resulting nucleus has slightly less mass than before.-The missing mass was converted into the binding energy. •Consider converting (fusion) 4 H atoms into one He atom:•4 H atoms = 6.693x10-27 kg •1 He atom = 6.645x10-27 kg•The difference, 0.048x10-27 kg, or 0.0071 of the initial mass, is converted to energy. •Thus, converting 1 kg of hydrogen to helium converts 7.1 grams of matter to energy:-E = mc2 = 0.0071 kg x (3x108 m/s)2 = 6.4x1014 J -To produce the luminosity of the Sun, 3.83x1026W, 600 million tons of H is converted to He every second, with about 4 million tons of matter being converted into energy every second.

Mass v Weight

Weight measures the amount of force an object applies The pound is a unit of weight, not mass A mass of 1 kg produces a weight of 2.2046 lbs on the Earth An astronaut that has a weight of 150 lbs on the Earth has a weight of 25 lbs on the Moon. However, regardless of where she is, her mass is 68 kg.

Wave Nature of Light

n 1678, the Dutch physicist Christaan Huygens proposed that light travels in waves. Wasn't proven to be true until 1801, when English physicist Thomas Young clearly demonstrated the wave nature of light by passing light through two thin slits. Instead of producing two bright spots, the slits produced a series of alternating bright and dark bands.

Using Ratios and Units of Measurement

often compare two quantities by taking a ratio. Suppose that I have $100 and you have $10. If I ask you to compare the amounts of money that we each have, I am asking you to divide the two numbers. Therefore, I have ten times as much money as you do: You can also divide two equations. Often, units and constants will cancel out and simplify the comparison. Compare the area of two circles

Energy

the ability to do work -The unit of energy is the joule. -4.2 joules of energy are required to raise one gram of water one degree K. -A barrel of oil contains about 1010 joules.

Hydrostatic Equilibrium

the balance of the inward gravitational force and the outward force of fusion within a star. This balance of forces is what keeps a main sequence star stable. •The Sun is a gas throughout. -Pressure increases with temperature. •The Sun is in hydrostatic equilibrium, neither expanding nor contracting. -At each point in the Sun, the force of gravity is balanced by the pressure of the gas. •Since the weight of overlying material increases as we move inward, the temperature must increase. -A simple calculation shows that the center of the Sun must have a temperature of 15 million K, sufficient to support nuclear reactions. -The pressure is tremendous.

Apparent Brightness

the brightness of a star as seen from Earth •The apparent brightness depends on the luminosity of the star and its distance from Earth. -Apparent brightness drops as square of distance (Inverse Square Law of Light). -The apparent brightness is measured in apparent magnitudes.

P-P Chain

the chain of reactions by which low-mass stars fuse hydrogen into helium through nuclear fusion The primary source of power in the Sun is the P-P (proton-proton) chain. •In the P-P chain, protons collide directly with other protons. -To overcome the electromagnetic repul-sion, extreme temperatures are required (T must be greater than 10 million K). -The center of the Sun has a temperature of about 15 million K.

Solar Seismology

•Disturbances in the Sun create pressure waves (sound waves). •Since these waves propagate through the Sun, they can be used to probe in interior of the Sun (like earthquakes here on Earth). •On the surface, the waves appear as up and down oscillations of the solar surface. -The movement is typically a few km with time scales of 5-10 minutes.

Energy Generation

•Einstein's Special Theory of Relativity -Mass and energy are equivalent:•E = mc2 -This conversion formula describes the amount of energy that is released when we convert matter into energy. •Consider converting 1 kg of matter to energy:-E = mc2 = 1 kg x (3x108 m/s)2 = 9x1016 J -This is equivalent to 15 million barrels of oil! (1 barrel of crude oil has 6x109 J). -In 2001, the U.S. consumed about 1x1020 J of energy •This is equivalent to 17 billion barrels of oil-About 60 barrels per person •Also equivalent to total conversion of 1100 kg of matter to energy

How Do Other Stars Compare to the Sun?

•How do astronomers measure the luminosity of a star? -How does the luminosity of other stars compare to the Sun? Is the Sun more or less luminous than average? •How do astronomers measure the temperature of a star? -How does the temperature of the Sun compare to other stars? Is the Sun hotter or cooler than average?

Sun-like Star

•If the Sun were 10 pc (32.6 LY) away, it would appear as a magnitude 4.78 star, about as faint as the stars in the handle of the Little Dipper.

Inverse Square Law

•If we measure the brightness of a star in the night sky, and we know its distance (from its parallax), we can determine its luminosity using the inverse square law:3

CNO Cycle

•In stars more massive than the Sun, the CNO Cycle (carbon-nitrogen-oxygen) is responsible for most of the energy generation. •A carbon nucleus acts as a catalyst to start the reaction. At the end of the cycle, the carbon nucleus remains. •The CNO Cycle requires temperatures above 15 million K.

Energy Generation

•In the 19th century, Lord Kelvin and Hermann von Helmholtz proposed that the Sun is powered by its gradual collapse. -Collapse releases gravitational energy. -Sun would shrink by about 40 meters/yr. -Sun would be 100 million years old. -At the turn of the century, it was realized that the Earth is much older.

Energy Transport of the Sun

•In the core, the energy is transported by radiation.-The gamma rays diffuse outward, loosing energy in each encounter. •In the core, a photon can travel about 0.006 cm before being scattered .•In the outer parts of the Sun, a photon can travel about 5 cm, on average, before being scattered. -At each scattering, the photon is just as likely to head back toward the center as out to the surface. -On average, it takes 23,000 years for a photon to escape from the Sun. •In the outer part of the Sun, convection transports the energy.-Currents of hot material rise while cool material sinks.

North Celestial Pole

•In the northern hemisphere, the altitude of the north celestial pole is equal to your latitude on Earth. •This is useful for navigation. -If you measure the altitude of the north celestial pole, you can determine your latitude on Earth. •In the southern hemisphere, it is difficult, but not impossible, to find the location of the south celestial pole.

Celestial Coordinates

•Just as Earth has lines of longitude and latitude, the celestial sphere has a system of celestial coordinates: •Declination (dec): The north-south position of a star on the celestial sphere. Declination is measured in degrees, arcminutes, and arcseconds. The celestial equator is defined to have a declination of 0o .•Right Ascension (RA): The east-west coordinates of an object on the celestial sphere. R.A. is measured in hours, minutes, and seconds of time. The vernal equinox is defined to be 0h. Vega RA 18h35m DEC +38o44'

The Sun is giving off 3.8x1026 watts. If the U.S. consumes about 1x1020 joules of energy per year, for how many years could a single second of the Sun's output power the U.S.?

1.380 years 2.38,000 years 3.380,000 years 4. 3.8 million years 5. 380 million years

Kirchhoff's Laws

A luminous solid (or a highly compressed gas) emits light of all wavelengths producing a continuous spectrum. -A rarefied luminous gas emits light whose spectrum shows bright emission lines. -A continuous spectra passed through a cool gas will have certain wavelengths absorbed producing dark lines in the spectrum.

Light Gathering Power

A measure of how much light a telescope intercepts and brings to a focus. The amount of light that a telescope collects depends on the collecting area of the telescope. How does the light gathering power of the famous 200-inch Telescope on Mt. Palomar (5-meter) compare to that of the Keck 10-meter Telescope on Mauna Kea? -Lets compare the areas of the two telescopes by taking a ratio. 200-inch Telescope on Mt. Palomar Dedication ceremony, June 1948 This means that a single Keck 10-meter telescope gathers 4 times as much light as the 200-inch Palomar telescope even though it has only twice the diameter. -We would have to build 4 Palomar telescopes to match the light gathering power of a single Keck telescope.

Measuring Angles

Angles in astronomy are measured in degrees, arcminutes and arcseconds. -1 degree = 60 arcminutes -1 arcminute = 60 arcseconds -1 degree = 3600 arcseconds -1 arcsecond is the size of a U.S. quarter as seen from 5 km (3 miles) or a penny as seen from 2.2 miles.

Measuring Angles

Angles in astronomy are measured in degrees, arcminutes and arcseconds. -1 degree = 60 arcminutes -1 arcminute = 60 arcseconds -1 degree = 3600 arcseconds -1 arcsecond is the size of a U.S. quarter as seen from 5 km (3 miles) or a penny as seen from 2.2 miles. -The Sun and Moon appear to be about ½ degree in size.-Your finger held at arms length is about one degree across.-Your fist at arms length is about 10 degrees.-Your outstretched hand at arms length is about 20 degrees across. -The Sun and Moon appear to be about ½ degree in size. -Your finger held at arms length is about one degree across .-Your fist at arms length is about 10 degrees. -Your outstretched hand at arms length is about 20 degrees across.

Daily (Diurnal) Motion of the Stars

Circumpolar Stars Diurnal Paths of Stars

Electrons

Electrons orbit the nucleus in discrete orbits. When an electron falls from a higher orbit to a lower orbit, it gives off energy in the form of a photon whose wavelength is determined by the energy difference between the orbits. When an electron absorbs a photon with just the right energy, it can leap from a low orbit to a higher orbit.

Energy

Energy is the ability to do work. The unit of energy is the Joule. 4.2 Joules of energy are required to raise one gram of water one degree K. When I run at 10 mi/hr (4.4 m/s) I have a kinetic energy of 1000 Joules. A barrel of oil contains about 1010 Joules.

Measuring the Speed of Light

Galileo Galilei was the first person to attempt to measure the speed of light. In the early 1600's, Galileo and an assistant stood on two hilltops with shuttered lanterns. Galileo would open the shutter on his lantern. As soon as his assistant saw the light, he would open the shutter on his lantern. Galileo used his pulse to time the round trip travel time for the light. Galileo found that the travel time did not increase as they moved farther apart. He concluded that the travel time was too fast to be measured this way. In 1676, the Danish astronomer Olaus Romer noticed that the times that Jupiter's moons passed into, or out of, Jupiter's shadow depended on the relative positions of Jupiter and Earth. -The total difference was about 16.6 minutes. He realized that this is caused by the time it takes light to travel across the orbit of the Earth. When the Earth is closer to Jupiter, the eclipses appear to occur earlier than expected. When the Earth is farther from Jupiter, the eclipses appear to occur later than expected. Unfortunately, Romer did not know the size of the Earth's orbit, so he could not compute the speed of light in km/s. Romer's Method for Measuring the Speed of Light -This eclipse will appear to occur later than expected because the light had to travel farther (across the orbit of the Earth). In 1850, the French physicists Armand-Hippolyte Fizeau and Jean Foucault measured the speed of light using a rotating mirror. During the time it takes the light to travel from the rotating mirror to the stationary mirror, the rotating mirror moves slightly. The image of the light source will be offset after reflection. The amount of deflection indicates how much the mirror rotated in the time that it took the light to traverse the distance between the two mirrors.

Binary Stars

Half of all stars are in a binary system (some triple and quadruple) Visual Binaries are binary star systems where each star can be seen with a telescope spectroscopic binaries are those in which the stars are too close to see individually but the spectral lines show the doppler shift due to the orbital motion of the stars Optical Binaries are chance alignments where two stars appear close together but do not orbit eachother Astrometric binaries- when one star

Mass

How many atoms you have in your body

Ionization

It is possible to give the electron enough energy to completely escape from the atom. The atom is then said to be ionized. The amount of energy required to ionize an atom is called the ionization energy. The ionization energy can be provided by photons or by collisions. The resulting atom is left with a net positive charge.

Horizon and Zenith

It is sometimes useful to think of the sky as a great dome over our heads. -The horizon is where the dome meets the Earth.-The zenith is the point directly overhead. -As the Earth turns, this dome turns over our heads. It appears as if the sky is a large hollow sphere centered on the Earth.

Powers of Ten

Large Numbers 1 = one = 10 10 = ten = 10^1 100 = one hundred = 102 = 10 x 10 1,000 = one thousand = 103 = 10 x 10 x 10 10,000 = ten thousand = 104 = 10 x 10 x 10 x 10 100,000 = one hundred thousand = 105= 10 x 10 x 10 x 10 x 10 1,000,000 = one million = 106 = 10 x 10 x 10 x 10 x 10 x 10 1,000,000,000 = one billion = 109 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 1,000,000,000,000 = one trillion = 1012 Small Numbers 1 = one = 10 0.1 = 10-1 = 1/10 0.01 = 10-2 = 1/100 0.001 = 10-3 = 1/1,000 0.0001 = 10-4 = 1/10,000 0.00001 = 10-5 = 1/100,000 0.000001 = 10-6 = 1/1,000,000 0.000000001 = 10-9 = 1/1,000,000,000

Measuring Mass

Mass measures the amount of material in an object The standard measure of mass is the kilogram (kg) = 1000 grams (g) Defined by a large platinum/iridium cylinder in France

Maxwell's Equations

Maxwell studied the effects of oscillating electric charges. He found that a pattern of alternating electric and magnetic fields would spread out from the oscillating charge in a wave pattern traveling at the speed of light. Today, we call these disturbances "electromagnetic radiation.

he Bohr Model of the Atom

Neils Bohr suggested that only certain electron orbits are allowed. Orbits are given numbers n=1,2,3,4,5,...,infinity. n=1 is the ground state (ground orbit) and has the lowest energy. No lower orbit is permitted. The excited states (higher orbits) have more energy. The orbits get closer together as n increases. To change orbits, the electron must either gain or loose energy. Each type of atom has a unique set of energy levels.

Neutrino Astrophysics

Neutrinos are tiny, electrically neutral, sub-atomic particles. •Neutrinos do not often interact with matter. For example, it takes about a light year of lead to stop a neutrino. •Therefore, they escape from the Sun in about 2 seconds without interacting with any of the material in the Sun •Since they are created in the nuclear reactions in the Sun, they are a direct probe of the current conditions at the center of the Sun. •About 3.5x1016 solar neutrinos pass through your body each second (even at night).

Wavelengths of Light

The wavelength of light can be shifted by moving the source toward or away from the observer: -Blueshift = toward -Redshift = away -The change in wavelength is proportional to the velocity divided by the speed of light.

Line Series

Patterns of lines in a spectrum are called a series: The Lyman Series Absorption lines that start at n=1. Emission lines that end with n=1. All Lyman lines are in the ultraviolet. The Balmer Series Absorption lines that start at n=2. Emission lines that end with n=2. All Balmer lines are in the visible. The Paschen Series Absorption lines that start at n=3. Emission lines that end with n=3. All Paschen lines are in the infrared. The Brackett Series Absorption lines that start at n=4. Emission lines that end with n=4. All Brackett lines are in the infrared.

Power

Power is the rate at which energy is being used. The unit of power is the Watt = 1 joule/s. A 100 Watt bulb uses 100 joules per sec. The Sun is giving off about 4 x 1026 Watts. Astronomers sometimes use the term luminosity to describe the rate at which a star is giving off energy. A typical Krispy Kreme jelly donut contains over 1 million Joules of energy! If you eat a jelly donut in 100 seconds you receive 10,000 Watts of power!Since your body consumes about 100 Watts of power while at rest, it will take 10,000 seconds (3 hours) to use up all that food energy!

Scientific Notation

Scientific notation allows us to express very large or very small numbers in a compact form. This reduces errors and simplifies multiplication and division. Generally, only one number appears to the left of the decimal point. The exponent indicates how many times the decimal point was moved. 365. = 3.65 x 10^2 6,378. = 6.378 x 10^3 299,792.458 = 2.99792458 x 10^5 Multiplication To multiply two numbers in scientific notation: Multiply the numbers out front. Add the exponents. 30,000 x 20,000 = 3.0 x 10^4 x 2.0 x 10^4 = 6.0 x 10^8 Division To divide two numbers in scientific notation: Divide the numbers out front. Subtract the exponents.

Temperature

Temperature is a measurement of the internal motions of atoms and molecules in an object. The higher an object's temperature, the faster the particles are moving. The temperature of an object is the average thermal energy of the particles it contains. The standard metric unit for measuring temperature is the Celsius scale: Water freezes at 0o C Water boils at 100o C Scientists often use the Kelvin scale: A change in temperature of 1 K is the same as a change of 1o C 0 K (absolute zero) is the point at which all molecular motion ceases 0 K = -273o C = -459o F Absolute zero is the lowest possible temperature

Blackbodies:Stefan-Boltzmann Law

The amount of energy emitted depends very strongly on the temperature (T4) If we double the temperature, the energy emitted goes up by a factor of 24=16 If we triple the temperature, the energy emitted goes up by 34=81. To find the total energy emitted by the whole body (per second), we must add up the contribution from each individual square meter (i.e. multiply by the surface area). The surface area of a sphere with radius R is: The Sun has a surface temperature of around 5800 K. Therefore, each square meter emits: E=5.67x10-8 x (5800)4joule/s/m2 E=6.42 x 107 watt/m2 The radius of the Sun is 6.96x108 m, so the surface area is: A=4 p R2 = 6.09x1018 m2 The total energy emitted by the Sun is:6.42x107 x 6.09x1018 watts=3.91x1026 watts The actual luminosity of the Sun is 3.83x1026 watts. The difference is due to the fact that the Sun is not a perfect blackbody. You have a surface temperature of around 310 K. Therefore, each square meter of your body emits:E=5.67x10-8 x (310)4joule/s/m2 E=524 watt/m2 The room around you has a temperature of 290 K. Therefore, each square meter of your body absorbs: E=5.67x10-8 x (290)4joule/s/m2 E=401 watt/m2 Therefore, the net loss from your body is about 123 watts/m2. The average human body has 1-2 square meters of skin.

Astronomical Distances

The astronomical unit (AU) is defined as the average distance from the Earth to the Sun. 1 AU = 1.496 x 1011 m = 93 million miles The light year (LY) is defined as the distance light travels in one year 1 LY = 9.461 x 1015 m 1 AU = 8.3 light minutes Voyager 1 (as of 5/11/08)Most distance object launched by man Distance from Earth 105.5 AU Light travel time 14.63 hours Velocity 17.1 km/s (38,475 mph) = .0057% speed of light

The Periodic Table

The atomic number is the number of protons in the nucleus. The atomic mass is the total number of protons and neutrons. Isotopes Isotopes have the same atomic number but different atomic masses.There are 2 common forms of carbon: 12C has 6 protons and 6 neutrons 13C has 6 protons and 7 neutrons

Measuring Time

The basic unit for time measurement is the second The second used to be defined as (1/60) of (1/60) of (1/24) of the mean solar day Today, the second is defined using atomic clocks1 second = 9,192,631,770 cycles of a specific atomic transition in the cesium 133 atom1 sidereal year = 3.1558 x 107 s The standard metric unit for measuring length is the meter (m) 1 kilometer (km) = 1000 m = 103 m 1 centimeter (cm) = 0.01 m = 10-2 m 1 millimeter (mm) = 0.001 m = 10-3 m 1 nanometer (nm) = 10-9 m The meter was originally defined as one ten-millionth (10-7) of the distance from the North Pole to the Equator through Paris. From 1799 to 1960 various platinum bars served as the standard. In 1983 the meter was redefined to be the distance that light travels in a vacuum in 1/299,792,458 of a second.

Frequency

The frequency, n, is the number of waves that pass a fixed point in one second.1 Hertz = 1 wave per second c=nl The energy is directly related to the frequency: E=hn h is Planck's constant (6.626x10-34 joule s)

Altitude and Azimuth

The height of a star above the horizon is called the altitude. •The direction to the star as measured from true north is called the azimuth. -Note: True north is not the same as magnetic north. The magnetic north pole is not located in the same place as the true north pole. The altitude and azimuth of a star change during the course of night as the star rises and sets .•Angles are measured using degrees, minutes of arc, and seconds of arc.

Blackbodies: Wein's Law

The higher the temperature, the shorter the wavelength of peak radiation: -is the wavelength of the peak, in nm,and T is the temperature in Kelvins. Why does the Sun not appear green? Snow and clouds are pretty good reflectors at all visible wavelengths. Since they shine by reflected sunlight, the Sun must be the same color as snow or clouds (white)! Sunlight is a mixture of many different wavelengths (colors) and is, by definition, white! The total energy emitted per second by every square meter of a blackbody is given by: s= 5.67x10-8 joule/(s m2 K4) That is, each square meter on the surface of the black body emits this much energy per second.

Resolving Power

The smallest detail that a telescope can resolve, q Both l and D must in the same units (i.e. if D is in meters then l must be in meters). Average K-mart telescope -l = 500 x 10-9 m - D = 2 inches = 5 cm = 0.05 m -q = 2.5 arcseconds •Hale 200-inch Telescope -l = 500 x 10-9 m - D = 200 inches = 500 cm = 5.0 m-q = 0.025 arcseconds 140 Foot Telescope (radio telescope) -l = 21 cm = 1420 MHz - D = 140 feet = 42.7 m-q = 21 arcminutes Green Bank Telescope (radio telescope) -l = 21 cm = 1420 MHz- D = 100 m-q = 9 arcminutes

Rotation of the Earth

The stars move from east to west because the earth rotates from west to east.

Emission

To go from a higher level to a lower level, the electron must give up energy (emit a photon). The emitted photon has exactly the energy difference between the two levels.

Absorption

To go from a lower level to a higher level, the electron must increase in energy. It can do this by absorbing a photon that has exactly the amount of energy needed to go from the lower level to the upper level.

Nature of Light

Today, we envision light as a self-contained packet of energy, a photon, which has both wave and particle like properties. In most situations that we encounter, light acts like a wave. When dealing with atoms, light acts like a particle. Propagation of Light:Inverse-Square Law Light propagates in a straight line The brightness decreases as the square of the distance from the source If we move the source twice as far away, it is ¼ as bright If we move the source three times as far away, it is 1/9 as bright If we move it four times as far, it is 1/16 as bright The brightness of a distant source, B, is: Where L is the intrinsic luminosity (amount of light it gives off per second) and d is the distance to the object. If we double the luminosity of the source, but keep the distance the same, the brightness doubles. If we double the distance to a source, the brightness falls off by a factor of

Summary

Visible light is a form of electromagnetic radiation which also includes (in order of increasing wavelength, decreasing frequency and decreasing energy) gamma rays, X-rays, ultraviolet light, visible light, infrared radiation, and radio waves. Electromagnetic radiation consists of alternating magnetic and electric fields. It travels at the speed of light (3x108 m/s). The Earth's atmosphere is transparent at only a few places in the electromagnetic spectrum. Light can behave as both a wave and as a particle. This wave-like packet of energy is called a photon. The brightness of light drops off as the square of the distance (Inverse Square Law).

Electromagnetic Waves

Visible light is an example of an electromagnetic wave. All electromagnetic waves travel at the speed of light. The wavelength, l, is the distance from one wavecrest to the next. The wavelength determines the color of the light.

Doppler Shift

change in the apparent frequency of a wave as observer and source move toward or away from each other If a source is moving toward an observer the wavecrests will be closer together which decreases the wavelength. This causes the light to be shifted to the blue (blueshift). If a source is moving away from an observer the wavecrests will be farther apart which increases the wavelength. This causes the light to be shifted to the red (redshift). f the velocity (v) is much smaller than the speed of light (c), the change in wavelength, Dl, is: Example: An astronomer measures a Balmer emission line of hydrogen in the spectrum of a galaxy. The line is supposed to be at 676.5 nm, but appears in the spectrum at 678.5 nm. How fast is the galaxy moving, and is it moving toward or away from the Earth? Since the line is shifted to longer wavelengths, it is redshifted, which means the object is moving away from the Earth at a speed of:

Spectra

different colors of light emitted based on the chemical composition of the light source There are three kinds of spectra: -Continuous spectra which come from hot solids or compressed gasses; -Emission line spectra which come from luminous gases; and -Absorption line spectra which come from continuous spectra that have passed through a cool gas.

Super-Kamiokande

•Another neutrino detector is operating in Japan. •It uses 50,000 tons of ultra-pure water. •When a neutrino strikes a nucleus, debris from the impact produces blue light which can be detected by 11,146 photomultiplier tubes on the walls. •This experiment, which is sensitive to high energy muon neutrinos from interactions between cosmic rays and the Earth's atmosphere, has shown that neutrinos have a miniscule mass, and may oscillate from one kind to another.•It can also detect the low energy electron neutrinos from the Sun, and finds only 36% of that expected. •In 2002, Raymond Davis Jr. and Masatoshi Koshiba were awarded the Nobel Prize in Physics for their work on detecting neutrinos.

Magnitude System

•Around 150 B.C. the Greek astronomer Hipparchus compiled a catalog of nearly 1000 stars listing their positions and apparent brightness. -The brightest stars were first magnitude stars. -The next brightest were second magnitude stars .-The faintest stars he could see were sixth magnitude stars. •Fainter objects have larger apparent magnitudes. •Brighter objects have smaller apparent magnitudes.

The Motion of the Stars

•Just like the Sun and Moon the stars rise and set due to the rotation of the Earth. -They rise in the east and set in the west because Earth rotates from west to east. -Stars near the celestial poles do not rise or set. Instead they circle the poles and are called circumpolar. •In the northern hemisphere, the stars circle the pole in a counterclockwise direction.

Longitude and Latitude

•Latitude: Your north-south position on Earth. The equator is defined to have a latitude of 0o. The north pole is at 90oN and the south pole at 90oS. •Longitude: Your east-west position on Earth. An arbitrary point, the Prime Meridian in Greenwich, England marks a longitude of 0o. •Harrisonburg, Virginia is at:-Longitude 78o 52' 08.4" W-Latitude 38o 26' 56.4" N

The Sun

•Luminosity = 3.83 x 1026 W •Solar constant = 1370 W/m2 •Density = 1.41 g/cm3 •Diameter = 1.392 x 109 m = 109 Dearth = 3.6 times the Earth-Moon distance •Mass = 1.989 x 1030 kg = 332,776 Mearth

The Celestial Sphere

•North Celestial Pole: The point directly over the Earth's true north pole. -The north star, Polaris, is near the North Celestial Pole, but not exactly at the pole. It is currently about 1 degree away from the pole. •South Celestial Pole: The point directly over the Earth's true south pole .•Celestial Equator: The equator of the Earth projected onto the celestial sphere. •Meridian: A line from due north to due south that passes straight overhead. •North Celestial Pole: The point directly over the Earth's true north pole. -The north star, Polaris, is near the North Celestial Pole, but not exactly at the pole. It is currently about 1 degree away from the pole. •South Celestial Pole: The point directly over the Earth's true south pole. •Celestial Equator: The equator of the Earth projected onto the celestial sphere.•Meridian: A line from due north to due south that passes straight overhead.

Power

•Power is the rate at which energy is being used. -The unit of power is the watt = 1 joule/s. -A 100 watt bulb uses 100 joules per sec .-The Sun is giving off 3.82x1026 watts. -Astronomers use the term luminosity to describe the rate at which a star is giving off energy.

Homestake Gold Mine

•Raymond Davis Jr. devised an experiment to look for neutrinos from the Sun. A tank containing about 100,000 gallons of cleaning fluid was placed nearly a mile underground. Some neutrinos from the Sun may interact with the chlorine in the tank. •Unfortunately, the neutrinos produced by the P-P chain have low energy and are difficult to detect. •However, other nuclear reactions take place in the Sun that produce higher energy neutrinos. -These reactions happen so rarely, that they do not contribute appreciably to the total energy output, but they are sensitive to the conditions in the core of the Sun. •These neutrinos interact with a chlorine-37 nucleus to produce radioactive argon: The radioactive argon can be flushed from the tank and detected. About 1 atom of argon should be produced every day. •In fact, 1 atom of radioactive argon is produced every 3-4 days which implies that the Sun is giving off a factor of 3-4 less neutrinos than expected.

Concept Summary on how to measure solar interior

•Solar seismology and neutrinos can be used to probe the interior of the Sun. •The smaller than expected number of neutrinos coming from the Sun is probably explained by neutrinos changing type (flavor) between the core of the Sun and the Earth.

Absolute Magnitude

•The Absolute magnitude measures the brightness of a star as it would appear from a standard distance of 10 pc (32.6 LY). -The absolute magnitude depends only on the luminosity of the star since all stars are assumed to be viewed from a standard distance. -A star with a smaller absolute magnitude has a higher luminosity.

Probing the interior of the sun

•The sunlight emerging from the surface of the Sun today was generated thousands or millions of years ago.•How can we probe the nuclear reactions going on right now? -Solar seismology -Neutrino astrophysics

Neutrino Oscillation

•There are three flavors of neutrinos-Electron, Muon, and Tau neutrinos-The Sun produces only electron neutrinos.•Neutrinos are created in the Earth's atmosphere when cosmic rays strike. -Experiments show that the neutrinos oscillate from one flavor to another .-Therefore, we might be measuring too few electron neutrinos from the Sun because they changed into another kind of neutrino before reaching Earth.

Celestial Sphere

•To find due north, drop straight down from the North Celestial Pole to the horizon. •The celestial equator meets the horizon at due east and due west.

Magnitude System

•Today, the magnitude system is defined such that a difference of 5 magnitudes is exactly a factor of 100 times in brightness. -One magnitude is a difference in brightness of about 2.5 times. -Two magnitudes are 2.5x2.5=6.3 times. -Three magnitudes are 2.5x2.5x2.5=15.9 times. •Unfortunately, it turns out that many objects are brighter than first magnitude.-These have been assigned magnitudes smaller than 1, including negative numbers.•Sirius, the brightest star in the sky, has an apparent magnitude of -1.5. •The Sun has a magnitude of -26.2. •Your eye can easily see the full moon (magnitude about -13) and the faintest stars (magnitude 6). This is a difference of nearly 20 magnitudes or a range of 108. •The magnitude system is only used in visual astronomy. All other areas of astronomy define brightness in terms of energy per second per area received here on Earth. •The apparent magnitude measures the brightness of a star as seen in the night sky on Earth. -The apparent magnitude depends on the luminosity and distance to the star.