Midterm Cheat Sheet PDF

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Cheat Sheet for Midterm Exam...

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Significant Digits  Earth’s radius = 6370 km = 6,370,000 m = 6.37x106 m.  1mm = 0.001 m = 10-3 m. 1 au = average distance between earth and sun = 1.5 x 1011 m Constellations: group/pattern of stars.  Section of the sky (Like postal codes) Asterism: recognizable group or pattern of stars.  Landmarks on earth. Big/Little Dipper, Winter Circle Stars in a constellation or asterism might not be physically close to each other. They are far so seem close. Angular Size & Distance  Measured in degrees; 1o= 60’ arcmins, 1’ = 60’’ arcsecs

Farthest North in Summer Solstice and South in Winter Reasons Why Summer is warmer than winter:  Sun is above the horizon for longer each day.  Angle of sun: sun reaches closer to the zenith. Sidereal period: The length of any cycle of motion measured with respect to the stars. Sidereal year is

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Sidereal day: 23 h 56 m 4 s. Solar day: 24 hours Sidereal Month: 27.3 days. Synodic/Lunar Month:

Object ¿ ¿ Object Distance  Angular Size = Sunset

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Zenith: The point directly overhead. (Altitude = 90o) Horizon: All points 90o away from the zenith; Altitude = 0o Meridian: A line pass through the zenith and connecting the N and S points on the horizon; Sun @ 12pm meridian Altitude: Angular distance from the horizon. (If altitude is negative, that means something is below the horizon.) Azimuth: Direction, expressed as an angle measured to the right of north. (east is 90o, south is 180o, west is 270o) Celestial Sphere: an imaginary sphere surrounding the earth, containing the stars, planets, sun, etc. Celestial Pole: A point on the celestial sphere directly above one of the earth’s poles. Celestial Equator: A circle around the celestial sphere directly above earth’s equator. Declination: Angular distance from the celestial equator, + if north, - if south. Declination = latitude [-90, 90]. Right ascension: an angle measured eastward from the vernal equinox. RA = longitude (0-24 hours)  Whatever your latitude is on the earth, that is also the angular distance of the NCP above the horizon. Circumpolar star: a star that never sets, but always stays above the horizon. Move in circles near celestial pole.  Circumpolar stars have declinations > 90o-your latitude Rotation: The motion of an object that spins around an axis through that object. Earth rotates on its axis. Revolution: Orbital motion of one body around another. Ecliptic: Circle marking the sun’s apparent path around the celestial sphere.  Earth’s (equator ) is tilted 23.5o relative to the ecliptic. Vernal Equinox: The intersection of sun’s path and the celestial equator. Spring in NH, and Autumn in SH.  Prime meridian of the celestial sphere.  South to North Autumnal Equinox: Intersection of sun’s path and the celestial equator. Autumn in NH, and Spring in SH.  North to South Winter Solstice: Winter in NH and Summer in SH Summer Solstice: Summer in NH and Winter in SH

Sunrise

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At full moon, the moon rises at sunset and sets at sunrise. At 3rd quarter, moon rises at midnight and sets at noon. Terminator: is the boundary between the illuminated and dark side. Earth’s terminator = sunrise/sunset. Solar Eclipses: New moon, Lunar Eclipses: Full moon The moon must be at the nodal points for eclipse to occur Umbra: The sun is completely blocked. (Total Eclipse) Penumbra: The sun is partially blocked. (Partial Eclipse) Annular Eclipse: Ring, angular diameter of moon < suns. Tidal Locking: Earth’s gravity pulls more strongly on one side of the moon than the other, keeping one side locked. In NH (Toronto) Looking in east stars should come up: / The moon phases from NH and SH are opposite but the name is same each day. (New moon and Full moon same day) Spectroscopy: Break light into its different wavelengths, and compare the amount of light emitted at different wavelengths Stefan-Boltzmann Law: hotter objects emit more radiation Wien’s Law: hotter objects emit photos with higher average energy. Betelgeuse is redder in color than Rigel. It is a cooler star. Conversions: 1 au = 1.49598 x 1011 m = 1.49598 x 108 km 1 light year = 9.46 x 104 m, 1 parsec = 3.26 light year 2

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Newto n s Version= A =

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Earth’s spinning causes day and night Zodiac constellations: Constellations through which the sun moves throughout the year along the ecliptic. The mass of an object is measured in terms of number of particles it contains. The weight is the force with which you push down on a scale due to the gravitational attraction. Venus appears smallest at full phase Planets visible with unaided eye: Mercury, Venus, Mars, Jupiter, & Saturn. Mercury & Venus wander back and forth from west to east. After sunset evening star Before sunrise morning star If RA of Mercury Venus > Sun = “evening stars”. Sun moves slowly eastward along the ecliptic. Geocentric: Earth is fixed at the center of the universe.  Could not explain retrograde motion Earth, Moon, Mercury, Venus, Sun, Mars, Jupitar, Saturn Heliocentric: Earth moves around the sun.  Aristarchus of Samos, Nicholas Copernicus Sun, Mercury, Venus, Earth, Mars, Jupitar, Saturn, Uranus, Neptune

Parallax: An apparent change of position caused by viewing from different places and angles. The farther away an object is, the smaller the parallax. Epicycles: Each planet moves on a smaller circle, epicycle.  Claudius Ptolemaeus explained retrograde motion with epicycles. Centre of each epicycle moves on a larger circle, the deferent. (Still in geocentric)  Change in brightness; brighter when closer. Occam’s Razor: Chose the theory with least assumptions.

Eccentricity: [0,1] how un-circular an ellipse is. 0 = circle Perihelion: The planet’s orbit when it is closest to the sun.  Earth reaches early January. Fastest @ Perihelion Aphelion: The planet’s orbit when it is farthest to the sun. Major axis: The longest distance across the ellipse which equals perihelion distance + aphelion distance. Semimajor axis: Half of major axis. Eccentricity: a2 e 2=a2 −b2 , a = semi-major axis, b = semi-minor axis, e = eccentricity.

r max −r min 2a

Retrograde motion: Inner planets moving faster and overtaking outer. Opposite of prograde/direct motion. Superior planets: Planets that orbit farther away from sun. Inferior planets: Planets that orbit closer to the sun. Retrograde motion occurs when Earth and superior planet are at opposition (same side of the sun) look @ diagram. Newton’s Laws: I. Law of inertia: An object at rest remains at rest unless a force acts on it; Object in motion will continue in a straight line at constant velocity. II. The Force Law: Two objects attract each other with a force proportional to the product of their masses and inversely proportional to the square of their distance. a.

Kepler’s Laws of Planetary Motion: (Used Tycho’s theory) I. The orbits of planets are ellipses with sun at one focus. II. A line from a planet to the sun sweeps over equal areas in equal intervals of time. III. A planet’s orbital period squared is proportional to its average distance from the sun cubed. P 2years =a3AU

e=

F N =masskg × acceleration m s2

III. When one body exerts a force on a second body, the second body exerts an equal and opposite force back. Earth & Moon both accelerate but moon accelerates more due its smaller mass. Earth only wobbles slightly. Barycenter: Combined center of mass of Earth and Moon  The center of mass is closer to the bigger (Earth) Conservation of angular momentum: As the spread of mass decreases, the rotation rates must increase.  How fast an object rotates or revolves?  How much mass it has?  How spread out that mass is? Equations

1 Kinetic Energy= m v 2 Work =F ×d Momentum=mv 2 GmM on earth=mgh , g Graviation Potential Energy= r L2 Angular Momentum=L=Iω, KE= 2I I =moment of interia . ω=angular speed∧direction Gravitational Force ( F g ) =

G m1 m2 r

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∨F g=m1 g ∨ g =

Gm r

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Wave: a periodic motion that can carry energy without carrying matter along with it. Wavelength: ( λ ¿ distance between two wave crests. Frequency: Number of waves per second c=λ × freq Photoelectric effect: light is composed of particles that have wave properties, creating what is now called the wave-particle duality. E photon=hf Amount of energy by light can be quantified by intensity. Electromagnetic waves in a vacuum travel at speed of light       

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Light = electromagnetic radiation Amount of energy carried by light=intensity W/m2 Newton: Light consists of particles (corpuscles) Wave: periodic motion that can carry energy without carrying matter along with it. Wave speed depends on the medium Frequency depends on the source The change in direction as light travels from one medium into another is called refraction, and the resulting spread of colors is called spectrum/spectra. Huygens proposed that light travels in the form of waves. The shorter the wavelength, the more the light is refracted. Speed of light (c) = 3.0 x 105 km/s Einstein proposed that light travels as waves enclosed in discrete packets now called photons.

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Planck ' s Constant × speed of ligh Wavelength ' −34 Planck s Constant(h)=6.67 ×10 J

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If one photon is not able to eject an electron from a metal, then billions of photons with that energy will still be unable to remove that electron. Frequency: Number of waves per second

c=λ × freq 

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Photoelectric effect: light is composed of particles that have wave properties, creating what is now called the wave-particle duality. E photon =hf 2 types of telescopes

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Refracting: collect light through lenses. Reflecting: collect light through mirrors. (Modern) Longer wavelengths = redder light, short = blue Since not all light can get through Earth’s atmosphere, we build observatories in space. Spectroscopy: breaking light from an object into its different wavelengths and comparing the amounts of light(intensity) emitted at different wavelengths. Spectrum of light source = comparing intensities at different frequencies. 3 types of spectra:  Continuous (thermal)  Blackbody radiation  Depends on the temperature  Stefan-Boltzman Law: hotter objects emit more radiation than cooler ones.  Wien’s Law: Hotter objects emit photons with a higher average energy.  Emission (line)  Absorption (line) If the source is moving toward us, the spectral lines will be shifted to higher frequencies (blueshif).  Redshift, lower freq is moving away Terrestrial Planets: Mercury, Venus, Earth, Mars  Small, rocky, dense Jovian Planets: Jupiter, Saturn, Uranus, Neptune  Large, gassy, less dense  Have more moons, hydrogen and helium  All have rings Asteroid belt is a region at distances approx. 2-4 au from the Sun, between the orbits of Mars and Jupiter. Kuiper belt 30-50 au from the Sun.  Methane and ammonia contained  Pluto part of it  Small period comets Oort Cloud 2000-50,000 au from the Sun  Long period comets Nebular Hypothesis: planets were formed out of a cloud of material. Explains how the matter that formed the solar system collapsed into a disk.  Protosun at the center heats up due to the energy released in collapse  Colliding dust grains in the disc begin to stick together and form planetesimals, some which eventually grow into protoplanets large enough to start pulling in more planetesimals gravitationally.

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All the angular momentum in the solar system came from the initial spin of the collapsing cloud.  Process stops when the sun “turns on” Evidence of planets around other stars  Direct visual observation  Effects of planets on the motion of a star, or on each other  Effects of planets on the apparent brightness of a star Orion Nebula: a region where new stars are being formed Exoplanet (extrasolar planet): planet outside of our own solar system.  Detected by:  Direct Imaging  Radial Velocity or Doppler Method  Astrometric Method  Transit Method  Gravitational Microlensing  Other indirect methods Direct imaging: photographing a planet (via light reflected from its star)  Can get atmospheric composition from the spectrum of reflected light  Use IR to reduce star’s brightness  Best when planet is large and far from its star. Radial Velocity: Use Doppler effect to detect small wobble of a star as the star and planet orbit in their barycenter.  Earliest successful methods  Can get mass and orbital radius  Best when planet’s orbit viewed almost edge-on from Earth  Large planets, close to star, “HOT JUPITERS” Astrometric Method: measure small changes in the star’s position on the celestial sphere.  Sideways motion  Far from star, obit viewed face-on  Orbit is large (large semimajor axis) Transit Method: like eclipse where the planet moves in front of the star.  Light curve: planet’s size and orbital period  Detect absorption lines as part of star’s light passes through planet’s atmosphere -> Chemical composition  Need nearly edge-on Gravitational Microlensing: based on the bending of light by a gravitational field.

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 Detect planets very far from us  Detect low mass planets  Only rough estimate of the distance TESS (Transiting Exoplanet Survey Satellite) Habitable zone: based on the assumption that life requires liquid water. Nice Model seeks to explain:  Formation and present orbits of the planets  Structure and composition of the solar system  Collection of small objects like asteroid, Kuiper belt and oort cloud  Late Heavy Bombardment: period of increased frequency of meteor impacts that is inferred from craters on the Moon and other bodies. Orbital Resonance: when two objects have orbital periods in simple whole-number ratios (2:1), there are small interactions that recur during each orbit. Larger semimajor axis = larger total energy Seismology: earthquakes = s waves and p waves  S waves cannot travel through liquids  S waves could not travel through the middle of the Earth hence core is liquid Small solar system bodies (SSSB) When a meteoroid strikes the Earth’s atmosphere, the event is called a meteor aka shooting star  Meteorite a piece of meteoroid that survives the atmosphere and lands on the surface. Capture Theory: moon formed somewhere else in the solar system and then was drawn into orbit around Earth by gravitational forces. Collision-ejection theory: earth was struck by a Mars-sized planetesimal forming Theia.  Also making the earth tilted at its axis Synchronous rotation of the moon is a result of tidal locking Earth’s rotation = Moon’s revolution, results in sidereal month = sidereal day Mercury: 2 years = 3 sidereal days = 1 solar day Venus rotates in the opposite direction Runaway greenhouse effect: heat trapped inside the atmosphere boiled away what was left of the oceans Metallic Hydrogen: Under high pressures, hydrogen becomes an electrical conductor and behaves like a liquid metal.  Strong magnetic field Belts: darker bands of lower pressure Zones: lighter bands of higher pressure Patterns of winds can be understood based on the interaction of convection and the planet’s rotation.

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Convection – pattern of circulation where heat rises and looses its heat and sinks Winds spiral around high and low pressure areas due to the Coriolis effect  Sidewise deflection of trajectories due to rotation In N hemisphere, air circulates counterclockwise around low-pressure areas, clockwise around high. Reversed in S hemisphere. Roche limit: minimum distance at which a solid object held together by its own gravity can orbit without being pulled apart by tidal forces. Moons of Jupiter: Io, Europa, Ganymede, Callisto  Io closest, all heated up by tidal forces Two sides of Europa  Trailing Hemisphere is redder  Leading Hemisphere has sulfur compounds Classical Kuiper Belt contains the greatest concentration of stuff Boundaries for Kuiper belt marked by orbits in 3:2 and 2:1 resonance with Neptune’s. A less dense zone farther out is called the scattered disc from Kuiper belt Planet – an object which  Orbits the Sun (or a star)  Is large enough to be pulled into a nearly spherical shape by its own gravity – hydrostatic equilibrium  Cleared away other objects from its orbit path. Dwarf planets meet 1, and 2 but not 3 Tidal locking – continuous ‘day’ and ‘night’ side Heat-Pipe Tectonics allow for carbon cycle to exist as long as tidal heating persists (plate tectonics replace)...