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Review for Exam #1 Tuesday, September 29 ● Observations of the sky and how things move in it – ● ● led to Newton and Laws of Motion and Gravity Reviewed some aspects of Light, Radiation, Matter, and Forces Noticed patterns in objects in Solar System (composition, location, age, etc.) – led to theories about how Solar System formed The Celestial Sphere The sky as seen from Earth is divided into 88 constellations. It is convenient to pretend the stars are attached to a celestial sphere. The celestial sphere appears to rotate about the celestial poles (1 day). The Sun appears to move west to east relative to stars year). (1 The Moon appears to move west to east relative to stars (1 month). Celestial Sphere: A large imaginary sphere centered on Earth Season & Calendars The cause of the seasons is the tilt of the Earth’s rotation axis relative to its orbit around the Sun. The day is based on the time between one noon and the next. The year is based on the time between one vernal equinox and the next. The moon (month) is based on the time between one new moon and the next. Moon Phases & Eclipses: Key Concepts Lunar phases change as we see more or less of the Moon’s sunlit half. The Moon rotates about its axis as it revolves around the Earth. The sidereal month=27.3 days; the synodic month=29.5 days. A lunar eclipse occurs when the Moon passes through the Earth’s shadow. A solar eclipse occurs when the Earth passes through the Moon’s shadow. Solar eclipses occur when Moon is between Sun and Earth. Solar eclipses occur at NEW MOON. A lunar eclipse occurs when the Moon passes through the Earth’s shadow. Lunar eclipses occur when Earth is between Sun and Moon. Lunar eclipses occur at FULL MOON. From Ptolemy to Copernicus: Key Concepts Aristotle (4th cent BC) showed that the Earth is round. Greek astronomers developed a geocentric model for the universe. Ptolemy (2nd cent) used epicycles to explain retrograde motion of planers. Copernicus (16th cent) proposed a heliocentric model for the universe. In the model of Copernicus, retrograde motion is easily explained. The combination of small and large circles produces “loopthe-loop” motion. Tycho, Kepler, & Galileo: Key Concepts Tycho Brahe made accurate measurements of planetary motion. Planetary orbits are ellipses with the Sun at one focus. A line between planet & Sun sweeps out equal areas in equal times. The square of a planet’s orbital period is proportional to the cube of its average distance from the Sun. Galileo made telescopic observations supporting the heliocentric model. Kepler’s First Law of planetary motion The orbits of planets around the Sun are ellipses with the Sun at one focus. Kepler’s Second Law of planetary motion A line to a planet from the Sun sweeps out equal areas in equal time intervals. Kepler’s Third Law of planetary motion The square of a planet’s orbital period is proportional to the cube of its average distance from the Sun*: *A planet’s average distance from the Sun is equal to the semimajor axis of its orbit. Newton’s Laws Three Laws of Motion: (1)An object remains at rest, or moves in a straight line at constant speed, unless acted on by an outside force. (2) The acceleration of an object is directly proportional to force, and inversely proportional to mass. (3) For every action, there is an equal and opposite reaction. Law of Gravity: The gravitational force between masses M and m, separated by distance r, is proportional to the product of the masses divided by the square of the separation Applying Newton’s Laws Newton modified and expanded Kepler’s Laws of Planetary Motion. Kepler described how planets move; Newton explained why they move. Tides are caused by the difference between the Moon’s gravitational force on different sides of the Earth. Tidal forces are slowing the Earth’s rotation & enlarging the Moon’s orbit. Newton’s First Law of Motion: An object remains at rest, or moves in a straight line at constant speed, unless acted on by an outside force. Precise mathematical laws require precise definitions of terms: SPEED = rate at which an object changes its position. Example: 65 miles/hour. VELOCITY = speed plus direction of travel. Example: 65 miles/hour to the north. Newton’s Second Law of Motion: The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass. In mathematical form: Or alternatively: Newton’s Third Law of Motion: For every action, there is an equal and opposite reaction. Whenever A exerts a force on B, B exerts a force on A that’s equal in size and opposite in direction. All forces come in pairs. Kepler’s Third Law: Light Visible light is just one form of electromagnetic radiation. Light can be though of as a wave or as a particle. Light forms a spectrum from short to long wavelengths. A hot, opaque object produces a continuous blackbody spectrum. Light forms a spectrum from short to long wavelength Visible light has wavelengths from 400 to 700 nanometers. [1 nanometer (nm) = 10-9 meter] Color is determined by wavelength: Blue: 480 nm Green: 530 nm Red: 660 nm Visible light occupies only a tiny sliver of the full spectrum. Matter and Forces Matter can come in various forms that are composed of fundamental particles An element is known by it number of protons Isotopes of an element contain different number of neutrons Isotopes can be radioactive and spontaneously decay There are four fundamental forces (Gravity, Electromagnetism, Strong, and Weak) Hydrogen 1 proton 1H 2H 3He 4He Helium 2 protons Lithium 3 protons 6Li Proton: 7Li Neutron: 3H Spectra A hot, transparent gas produces an emission spectrum. A cool, transparent gas produces an absorption spectrum. Every type of atom, ion, and molecule has a unique spectrum. The most abundant elements in the universe are hydrogen and helium. The radial velocity of an object is found from its Doppler shift. Continuum Source Cloud Solar System Constituents The terrestrial planets are made primarily of rock and metal. The Jovian planets are made primarily of hydrogen and helium; also have large amounts of water, methane, and ammonia Moons (a.k.a. satellites) orbit the planets; some moons are large. The terrestrial planets are made primarily of rock and metal. Mercury, Venus, Earth, & Mars. The terrestrial planets are: low in mass (< Earth mass) high in density (> 3900 kg/m3). Water = 1000 kg/m3 Air = 1 kg/m3 Rock = 3000 kg/m3 The Earth The study of seismic waves tells us about the Earth’s interior. The Earth is layered into crust, mantle, inner core, and outer core. The Earth is layered because it underwent differentiation when molten. The crust is broken into plates that move relative to each other. Seismic waves radiating through the Earth after an earthquake: Note: S waves do not travel through the outer core! The Moon The Moon’s surface has both smooth maria and cratered highlands. The surface was shaped by heavy bombardment, followed by lava floods. The Moon has a thick crust but a tiny iron-rich core. The Moon may have been ejected when a protoplanet struck the Earth. Computer simulation of impact: Mantle of the colliding body was ejected to form the Moon. Iron core of the colliding body sank to the Earth’s center. Mercury Mercury has a 3-to-2 spin-orbit coupling (not synchronous rotation). Mercury has no permanent atmosphere because it is too hot. Like the Moon, Mercury has cratered highlands and smooth plains. Mercury has an extremely large iron-rich core. Radius of Mercury = 2400 km. Radius of iron core = 1800 km. Venus The surface of Venus is hidden from us by clouds of sulfuric acid. The atmosphere of Venus is hot because of a runaway greenhouse effect. The surface of Venus shows volcanic activity but no plate tectonics. The interior of Venus is similar to that of the Earth. The interior of Venus is similar to that of the Earth. Uncompressed density of Venus = uncompressed density of Earth = 4200 kg/m3. Venus probably has a metal core and rocky mantle, like the Earth. Mars Mars has a tenuous atmosphere, with little water vapor and few clouds. (Mars has large volcanoes and a huge rift valley, but no plate tectonics. Robotic “rovers” have given us a close-up look at Mars. Mars has two small irregular moons, Phobos and Deimos. Mars interior: Jupiter and Saturn Jupiter and Saturn consist mainly of hydrogen and helium. Jupiter and Saturn have belts and zones of clouds, plus circular storms. Jupiter and Saturn have magnetic fields created in metallic hydrogen. Differences between Jupiter and Saturn are due to Jupiter’s higher mass. All Jovian planets have rings. Jupiter and Saturn are differentiated. Moons of Jupiter and Saturn The Galilean Moons of Jupiter: Callisto: heavily cratered Ganymede: larger then Mercury Europa: covered with smooth ice Io: volcanically hyperactive The Giant Moon of Saturn: Titan: wrapped in an atmosphere 4 of the moons of Jupiter are large (> 3000 km across) and spherical (like our Moon). These are the four Galilean moons: Io, Europa, Ganymede, Callisto Titan: Saturn’s ATMOSPHERIC moon Nearly the same size as Ganymede: escape speed is the same. Twice as far from the Sun as Ganymede: temperature is lower. Titan, alone among moons, has a substantial atmosphere. Uranus and Neptune Uranus and Neptune are nearly identical in their internal structure. The rotation axis of Uranus is tilted by about 90 degrees, causing extreme seasons. Neptune has surprisingly strong storms, driven by internal heat. Triton, the giant moon of Neptune, is a cold world with nitrogen geysers. 1) 2) 3) 4) Interiors of Uranus and Neptune Gaseous atmosphere: hydrogen, helium, methane Liquid outer layer: hydrogen, helium Liquid or slushy mantle: water, ammonia Solid core: rock, metal Triton: Neptune’s Frosty Moon Surface temperature = 38 Kelvin. Covered with “frost” at poles: frozen methane, frozen nitrogen. Pluto and its moon Charon are icy worlds that resemble Triton. Eris, the troublemaker (Greek goddess of strife). The Kuiper belt, beyond Neptune, contains small, icy, Pluto-like objects. The icy Kuiper Belt Objects are leftover planetesimals. Comets are “dirty snowballs”: ice mixed with dust & carbon compounds. Most comets are in the Kuiper belt or the Oort cloud, far from the Sun. A comet or asteroid impact may have caused the extinction of dinosaurs Studies of the Outer Solar System continue. Pluto and Charon have many properties in common with Neptune’s moon Triton. • Cold surfaces (about 40 Kelvin) • Icy mantles and rocky cores (about 2000 kg/m3) • Pluto has a thin atmosphere (like Triton); Charon has none. Eris (“Xena”), the troublemaker. Discovered in 2005 by Mike Brown and collaborators. It has a moon. It is BIGGER than Pluto! Led to re-definition of what a Planet is Created new class of object called “Dwarf Planets Most comets are in the Kuiper belt or the Oort cloud, far from the Sun. Comets with short orbital periods come from the Kuiper belt, 30-50 A.U. from the Sun. We know the Kuiper belt is full of icy objects – we have seen them! Origin of the Solar System: Key Concepts How the Solar System formed: A cloud of gas & dust contracted to form a diskshaped solar nebula. The solar nebula condensed to form small planetesimals. The planetesimals collided to form larger planets. When the Solar System formed: Radioactive age-dating indicates the Solar System is 4.56 billion years old. The contraction of the solar nebula made it spin faster and heat up. (Compressed gas gets hotter.) Temperature of solar nebula: > 2000 Kelvin near Sun; < 50 Kelvin far from Sun. How does this “nebular theory” explain the current state of the Solar System? Solar System is disk-shaped: It formed from a flat solar nebula. Planets revolve in the same direction: They formed from rotating nebula. Terrestrial planets are rock and metal: They formed in hot inner region. Jovian planets include ice, H, He: They formed in cool outer region. Radioactive age-dating Radioactive decay: Unstable atomic nuclei emit elementary particles, forming a lighter, stable nucleus. Example: Potassium-40 (19 protons + 21 neutrons = 40) 89% of the time, Potassium-40 decays to Calcium-40. 11% of the time, Potassium-40 decays to Argon-40. Age of oldest Earth rocks = 4 billion years Age of oldest Moon rocks = 4.5 billion years Age of oldest meteorites (meteoroids that survive the plunge to Earth) = 4.56 billion years This is the age of the Solar System