ASTR114 Lecture 10 Review PDF

Scientific Notation One power of ten is one order of magnitude! Also referred to as 1 dex in logarithmic units. Log_base_x(N)=base_x to the what power will give you N? Example: Log10(10)=1.Positive This isexponents one dex, or andone order ofabbreviations common Just count the zeros! magnitude. 101 = 10 = ten 102 = 10x10 = 100 = hundred 103 = 10x10x10 = 1,000 = thousand (kilo- k) 104 = 10,000 = ten thousand 105 = 100,000 = hundred thousand 106 = 1,000,000 = million (Mega- M) 107 = 10,000,000 = ten million 8 Scientific Notation Negative exponents and common abbreviations Count the zeros (including the one to the left of the decimal place)! 10-1 = (1/10) = 0.1 = one tenth 10-2 = (1/100) = 0.01 one hundredth (centi) 10-3 = 0.001 = one thousandth (milli) 10-4 = 0.0001 = one ten thousandth 10-5 = 0.00001 = one hundred thousandth 10-6 = 0.000001 = one millionth (micro) 10-7 = 0.0000001 = one ten millionth Units UNITS & SCIENTIFIC NOTATION In astronomy (and science in general) we use SI (Systeme Internationale) units. The SI system uses length, mass, time, and temperature as its basic properties. The basic units for these properties are: 1. length: the meter (m) (about a yard, 3 feet) 2. mass: the kilogram (kg) (2.2 pounds) 3. time: the second (s) 4. temperature: the Kelvin (K) (same increments as Celsius, but 273 degrees higher). Kelvin is the absolute temperature scale; 0K corresponds to an average kinetic energy of zero for particles in the system — a temperature which is impossible to achieve in any actual real physical system due to quantum mechanics UNITS & SCIENTIFIC Astronomers use numbers that are often very large or small and writing out the numbers is cumbersome. NOTATION The distance to the nearest star: 40,000,000,000,000 km The radius of an atomic nucleus: 0.0000000001 m We use scientific notation to express numbers compactly. The distance to the nearest star is: 4 x 1013 km (4 times 10 to the 13 km) The Parsec: A unit of distance, not time… Parsec: Distance to an object from the sun with a parallax angle of 1 arc second (equivalent to 1/60th of a degree). Where this parallax is defined from an earth observer between Summer/Winter… A pc is *roughly* the average distance between stars in the Milky Way…and the most common distance unit in astronomy… In order to get a feel for parallax angular shift, hold your index finger in front of One “Astronomical Unit” (AU): average distance between Sun and Earth 93,000,000 miles 150,000,000 km 1.5 x 108 km Distance Light Travels in One Year is a “Light- year” (LY) 9.46 x 1012 km 63,000 AU or 6.3x 104 AU 0.307 parsecs (pc) The Cosmic Perspective We live on planet Earth —> A rocky world orbiting the sun (a relatively average “G-type” star) roughly 93 million miles (1 AU) away at a speed of roughly 19 miles/second We live in an outer edge of one of the spiral arms of our galaxy (known as the milky way — a relatively normal spiral galaxy) Our galaxy is one of trillions in the observable universe And our universe may be one of Question What determines the size of the “Observeable Universe”? Answer —> The Speed of Light! The Speed of Light Einstein discovered the speed of light is finite, and is given by: C = 300,000 km/s This is true according to any observer, and is the fastest any form of matter or energy can travel Consequently, when we observe distant objects either with our eyes directly or through telescopes, we are seeing the light which was emitted some time previously The further away the object, the further back in time we are seeing it We see the Universe as it once was, not as it is Motions of the Night Sky, Seasons, & Eclipses Star Trails over the Grand Canyon | Image Credit: Babak Tafreshi (TWAN) The Celestial Sphere Stars at different distances all appear to lie on the celestial sphere. The 88 official constellations cover the entire celestial sphere. The Ecliptic The ecliptic is the circular path that the Sun traces out in the celestial sphere through the year. It can also be thought of as the plane in which the Earth orbits the Sun. The Earth’s axis is tilted by The Celestial Sphere North celestial pole is directly above Earth's North Pole. South celestial pole is directly above Earth's South Pole. Celestial equator is a projection of Earth's equator onto sky. Celestial Coordinates Celestial Coordinates Right Ascension (R.A.) is measured in hours, minutes, and seconds east of the March equinox on the celestial sphere. Declination (Dec) is measure in degrees, arcminutes, and arcseconds, north or south of the celestial sphere. Celestial sphere rotates 360 deg in 24 hrs. —> 1 hr of RA is 360/24=15 degrees. Similarly, 1 minute of RA is 15 arcminutes (60 minutes per hour, 60 arc minutes per deg) Celestial Coordinates RA & Dec are what astronomers use to locate objects in the sky RA & Dec are fixed for fixed objects — anything which does not appear to move with respect to the International Celestial Reference Frame (ICRF, which is just the instantiation of the ICRS) RA & Dec change for objects moving along the plane of the sky for an Earth observer. This How do we perceive Earth’srotation? The Sun appears to rise and set each day. Stars in the night sky appear to rotate around us. Earth rotates from west to east, so stars appear to circle from east to west. Finding the North Star Our View FromEarth Stars near the north celestial pole are circumpolar and never set. We cannot see stars near the south celestial pole. All other stars (and Sun, Moon, planets) rise in east and set in west. The Celestial Sphere: Observer- Centered Terms… The north celestial pole is the point where a line extending out of the Earth’s north pole would intersect the celestial sphere. South celestial pole: the projection of the Earth’s geographic south pole into space. Why Do the Constellations We See Depend on Latitude and Time of Year? (Not Longitude) They depend on latitude because your position on Earth determines which constellations remain below the horizon. The Sky Varies as Earth Orbits the Sun Constellations depend on time of year because Earth’s orbit changes the apparent location of the Sun among the stars. As the Earth orbits the Sun, the Sun appears to move eastward along the ecliptic. At midnight, the stars on our meridian are opposite the Sun in the sky. Three Views You should be able to go back and forth between three different views of the sky: 1) Above Earth 2) Above the viewer 3) Viewer’s perspective The LocalSky An object's altitude (above horizon) and direction along horizon (azimuth) specify its location in your local sky. Azimuth is the angular distance of an object from the local North, measured along the horizon. An object which is due North has azimuth = 0 degrees; due East is azimuth = 90 degrees; due South is azimuth = 180 degrees; due West is azimuth = 270 degrees. We Measure The Sky Using Angles How Doesthe Orientationof Earth’s Axis Change with Time? Although the axis seems fixed on human time scales, it actually precesses over about 26,000 years. –Polaris won't always be the North Star. –Positions of equinoxes shift around orbit; for example, spring equinox, once in Aries, is now in Pisces! Earth’s axis precesses like the axis of a spinning top The Celestial Sphere: Observer-Centered Terms… Most stars rise above the horizon in the East, follow circular arcs through the sky, and set in the West. This follows a 24 hour cycle. The Celestial Sphere: Observer-Centered Terms… Stars near enough to the celestial pole in your hemisphere never set and are said to be circumpolar. They still follow a 24 hour cycle. A Different View The zenith and horizon move with the observer The celestial poles and equator are oriented relative to the Earth The observed altitude of the celestial poles changes as the observer The Celestial Sphere at different locations on Earth… As Seen From North America, Polaris and Other Stars of the Same Constellation (1 of 2) a. are in the Big Dipper. b. are seen only in winter. c. are seen only in summer. d. never set. Copyright © 2024 Pearson Education, Inc. All Rights Reserved As Seen From North America, Polaris and Other Stars of the Same Constellation (2 of 2) a. are in the Big Dipper. b. are seen only in winter. c. are seen only in summer. d. never set. Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Long WasThis Exposure? (1 of 2) a. A few seconds b. A few minutes c. A few hours d. A few days Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Long WasThis Exposure? (2 of 2) a. A few seconds b. A few minutes c. A few hours d. A few days Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Are Different Stars Seen in Different Seasons? (1 of 2) a. Because of Earth’s axis tilt b. Because stars move during the year c. Because Earth orbits the Sun, the stars that are behind the Sun are not visible d. Because of precession Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Are Different Stars Seen in Different Seasons? (2 of 2) a. Because of Earth’s axis tilt b. Because stars move during the year c. Because Earth orbits the Sun, the stars that are behind the Sun are not visible d. Because of precession Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Causes The Seasons? Seasons depend on how Earth's axis affects the directness of sunlight & how concentrated light energy is Why Does It Tend to Be Warmer During Summer Than During Winter? (1 of 2) a. In summer, the entire Earth is closer to the Sun. b. In summer, the tilt of Earth’s axis means that one part of Earth is closer to the Sun. c. In summer, the Sun is up for more hours. d. In summer, the Sun climbs higher in the sky so its rays hit the ground more directly. e. Both c and d are correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Does It Tend to Be Warmer During Summer Than During Winter? (2 of 2) a. In summer, the entire Earth is closer to the Sun. b. In summer, the tilt of Earth’s axis means that one part of Earth is closer to the Sun. c. In summer, the Sun is up for more hours. d. In summer, the Sun climbs higher in the sky so its rays hit the ground more directly. e. Both c and d are correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved When It Is Summer in the United States, in Australia It Is (1 of 2) a. winter. b. summer. c. spring. d. fall. Copyright © 2024 Pearson Education, Inc. All Rights Reserved When It Is Summer in the United States, in Australia It Is (2 of 2) a. winter. b. summer. c. spring. d. fall. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Doesn't Distance Matter? Variation of Earth– Sun distance is small— about 3%; this small variation is overwhelmed by the effects of axis tilt. Variation in any season of each hemisphere — Sun distance is even smaller! Solstices and Equinoxes ◦ Summer solstice Sun farthest north (highest in the sky, more direct, longest day), ~June 21. ◦ Fall (autumnal) equinox Sun on the equator (roughly equal night and day), ~Sept 21. ◦ Winter solstice: Sun farthest south (lowest in the sky, less direct, shortest day), ~Dec 21. ◦ Spring (vernal) equinox Sun on the equator (roughly equal night and day), ~Mar 21. ◦ Equinoxes are the only two days when the Sun precisely rises East and sets West. Position of Sun with Latitude The Sun can be directly overhead at the Tropic of Capricorn (latitude = +23.5 deg.) and the Tropic of Cancer (latitude = -23.5 deg), but is never directly overhead north or south of the tropics. Highest (tropic of cancer at noon): 90 – 23.5 + 23.5 = 90 deg When Is the Sun Directly Overhead at Noon in the Continental United States? (1 of 2) a. March 21 b. June 21 c. July 21 d. Never Copyright © 2024 Pearson Education, Inc. All Rights Reserved When Is the Sun Directly Overhead at Noon in the Continental United States? (2 of 2) a. March 21 b. June 21 c. July 21 d. Never Copyright © 2024 Pearson Education, Inc. All Rights Reserved The Moon (the 2nd brightest object Revolves in thethe around sky) Earth every 29.5 days. The word moon is the origin of the word month. – Some cultures still follow a moon month (kinda) It rotates about its axis every 29.5 days. Therefore, the same side always Moon Not to scale! The Moon is actually 30 Earth- diameters away from us. The Moon’s orbit is also tilted relative to the path of the Sun in the Phases sky While half of the Moon is always lit by the Sun, we see different amounts of the lit half from Earth depending on where the Moon is located in its orbit. If You Were on the Moon, Earth Would (1 of 2) a. show no phases. b. show phases the same as the Moon (when it is full Moon, it is full Earth, etc.). c. show phases opposite to the Moon (when it is full Moon, it is new Earth, etc.). —Make a sketch to decide! Copyright © 2024 Pearson Education, Inc. All Rights Reserved If You Were on the Moon, Earth Would (2 of 2) a. show no phases. b. show phases the same as the Moon (when it is full Moon, it is full Earth, etc.). c. show phases opposite to the Moon (when it is full Moon, it is new Earth, etc.). —Make a sketch to decide! Copyright © 2024 Pearson Education, Inc. All Rights Reserved The “Meridian Times” are when the Moon is at its highest point in the sky (i.e. above due South). Examples: The meridian time for the First Quarter moon is 6pm. The meridian time for the Full Moon is midnight. The meridian time for the New Moon is Noon. The Meridian time for the Waxing Crescent Moon is 3pm. Eclipse Requirements: Orbital Alignment Eclipse Requirements: Orbital Alignment Eclipse Requirements: Orbital Alignment Eclipse Requirements: Shadows 2,3,4 are in the penumbra Why don’t eclipses occur all the time? The Moon’s orbit is inclined 5 degrees with respect to the ecliptic. Eclipses can occur only when the plane of the Moon’s orbit crosses the ecliptic. Total solar eclipses only occur when Moon is closest to the Earth. Lunar Eclipses When there is a Full Moon and the Moon intersects the ecliptic, you get a lunar eclipse. Lunar Eclipses Occur when the shadow of the Earth falls on the Moon. Occur only when the Moon is Full. Solar Eclipses: Moon’s Shadow When there is a New Moon and the Moon intersects the ecliptic, you get a solar eclipse. The Sun and Moon have very nearly the same angular size in the sky because though the Moon is ~400 times smaller than the Sun it is ~400 times closer to Earth than the Sun. The distance between the Moon and Earth varies a little bit, and if the Moon is far enough away during a solar eclipse, you can get an “annular eclipse” Not All New Moons Cause Solar Eclipses The Moon’s orbit is inclined by about 5 degrees relative to the ecliptic so most new moons are not perfectly between the Earth and Sun. Tides Tides are strongest when gravitational forces line up, i.e., the earth-sun-moon system is in a straight line The History of Astronomy: From Ancient Civilizations to the Scientific Revolution Eratosthenes Measured Earth’s Diameter/Circumference Using Geometry/Trigonometry Eratosthenes learned that at noon on the Summer Solstice in Syene, Egypt, shadows disappeared at the bottom of wells. The Sun must have been at the zenith at noon for this to be possible. Syene happens to sit almost exactly on the Tropic of Cancer. Radius = distance between Syene & Alexandria/angle theta from Column’s shadow in Alexandria. Theta can be learned from basic trigonometry using the length of the shadow and height of the column. The Celestial Sphere as Reality During the Greek Empire, many believed the celestial sphere to consist of a crystalline material with the stars as embedded gems. This appealed to philosophical sensibilities at the time that spheres and circles were “perfect” and that all motion in nature should be “perfect”. This geocentric way ofthinking elevated Earth to a special place in the cosmos… the unmoving center of everything. These ideas were supported by major Greek intellects such as Pythagoras, A More Elaborate Cosmology was Needed The Sun, Moon, and five known planets each had their own spheres that moved relative to the one containing the stars. Largely influenced by the thinking of Aristotle and Plato who were driven more by beauty and philosophy than observational consequences. 71 Additional Shortcomings of Geocentrism Mars and the other planets often display retrograde motion. This further complicates the cosmology. How can this work with just perfect spherical motion? This happens when one planet laps another! Retrograde Motion in the actual heliocentric model This is one example of how planets “wander” against the background (fixed) stars (they move too but their apparent motion is practically undetectable for early astronomers) Ptolemaic Model Alfonso X, the King of Castile: “If the Lord Almighty had consulted me before embarking upon Creation, I should have recommended something simpler.” Why Does the Celestial Sphere ModelWork So Well? The Pivotal Role of Galileo He pioneered the use of telescopes for astronomical investigations With a telescope he built, Galileo discovered 4 moons of Jupiter: Io, Europa, Ganymede, and Callisto, now called the Galilean Satellites Discovery of the Galilean Satellites proved that things could orbit the other planets and that not everything orbited Earth He was able to confirm a crucial prediction of Copernicus’ heliocentrism involving the phases of Venus (we’ll discuss this in upcoming Galileo and the Leaning Tower of Pisa Aristotle taught that heavy objects fall faster than the lighter ones, and in direct proportion to their weight. Galileo tested this, finding that objects fall at the same rate regardless of their weight. Galileo realized that he could turn the power ofthe telescope toward the heavens. Galileo Galilei, Father of Modern Science ^Telescope used by Galileo (26mm diameter Galileo Galilei, Father of Modern Science https://astro.unl.edu/classaction/animations/renaissance/ venusphases.html ClassAction —> Animations —> Phases of Venus ClassAction —> Animations —> Ptolemaic Phases of Galileo Galilei, Father of Modern Science What Did Tycho Do That Advanced Astronomy Significantly? (1 of 2) a. He realized that orbits didn’t have to be circles; they could be ellipses. b. He made more accurate observations than anyone before him. c. He thought of the idea ofcircles moving on circles (epicycles) to explain planetary motion. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Did Tycho Do That Advanced Astronomy Significantly? (2 of 2) a. He realized that orbits didn’t have to be circles; they could be ellipses. b. He made more accurate observations than anyone before him. c. He thought of the idea ofcircles moving on circles (epicycles) to explain planetary motion. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Could You Distinguish Between Ptolemy’s Earth- Centered Model and a Sun-Centered Model by Observing Venus With a Telescope? (1 of 2) a. Yes. Venus would show phases in only the Sun-centered model. b. No. Venus shows phases in both models. c. Yes. In the Sun-centered model, Venus goes through a full set of phases, while in the Ptolemaic model, Venus only shows new and crescent phases. d. Yes. Venus would show phases in only the Ptolemaic Earth- centered model. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Could You Distinguish Between Ptolemy’s Earth- Centered Model and a Sun-Centered Model by Observing Venus With a Telescope? (2 of 2) a. Yes. Venus would show phases in only the Sun-centered model. b. No. Venus shows phases in both models. c. Yes. In the Sun-centered model, Venus goes through a full set of phases, while in the Ptolemaic model, Venus only shows new and crescent phases. d. Yes. Venus would show phases in only the Ptolemaic Earth- centered model. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Kepler’s 1st Law of Planetary Motion The orbits of the planets are ellipses with the Sun at one of the two foci The sum or r and r’ is a fixed The eccentricity e determines how “squashed” an ellipse is A circle is an ellipse with eccentricity equal to zero and a radius equal to the semimajor axis An eccentricity ofone means the ellipse has been squished completely flat to a line Kepler’s 2nd Law of Planetary Motion The line segment connecting the Sun and planet sweeps out equal amounts of area in equal amounts of time Therefore, a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun. Kepler’s Second Law A planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun. Kepler’s 3rd Law of Planetary Motion The square of a planet’s orbital period is proportional to the cube of its semimajor axis P ∝ a 2 3 The farther away a planet is from the Sun, the longer it (P = period = time to complete one orbit takes to orbit. a = Semi-major axis = half the Closer orbits go faster (shorter period) distance of the long cross-section of the Farther orbits go slower ellipse (longer period) Closer orbits go faster On the Shoulders of Giants: Newton & His Laws Isaac Newton Realized the same physical laws that operate on Earth also operate in the heavens Discovered laws of motion and gravity Newton’s 1st Law of Motion THIS IS A STATEMENT Objects maintain a fixed velocity OF THE CONSVERVATION OF unless acted upon by a force MOMENTUM Velocity can be zero, i.e. objects at rest stay at rest This law was heavily influenced by the thinking and observations of Galileo This is unintuitive given that on Earth, objects released at rest will fall to the ground, and objects that are pushed along the floor, for instance, will be stopped by friction Sometimes referred to as the law of inertia Velocity isa Vector Which just means it has a magnitude (speed) and a If you’re traveling direction, commonly10 depicted m/s, that with is your an speed, arrow but if you’re traveling 10 m/s due north, that is your velocity A force can change a velocity by changing the speed and/ or the direction Change from some force Initial Resultant velocity velocity How do we describe motion? The acceleration of gravity Galileo showed g is the same for all objects on Earth! Which of the Following Represents a Situation in Which a Car Is Undergoing Acceleration? (1 of 2) a. Hitting the gas pedal b. Hitting the brake pedal c. Turning the steering wheel d. All of the above Copyright © 2024 Pearson Education, Inc. All Rights Reserved Which of the Following Represents a Situation in Which a Car Is Undergoing Acceleration? (2 of 2) a. Hitting the gas pedal b. Hitting the brake pedal c. Turning the steering wheel d. All of the above Copyright © 2024 Pearson Education, Inc. All Rights Reserved Newton’s 2nd Law of Motion The total force applied to an object is proportional to the rate of change of that object’s velocity and the constant of proportionality is that object’s The “dot” notation was Force is a vector as ormass created by Newton and denoted by bold font means “rate of change”. F = m Rate of change of velocity v is also called acceleration Mass is the constant Velocity is a vector as of proportionality Momentum and Force A net force changes momentum, causing an acceleration and change in velocity Momentum = mass x velocity Rotational momentum of a spinning or orbiting object is known as angular momentum Question: For each of the following is there a net force? 1. A car coming to a stop 2. A bus speeding up 3. An elevator moving at constant speed 4. A bicycle going around a curve 5. A moon orbiting Jupiter Momentum and Force Momentum = mass x velocity A net force changes momentum, causing an acceleration — change in velocity Rotational momentum of a spinning or orbiting object is known as angular momentum Question: For each of the following is there a net force? 1. A car coming to a stop: Y 2. A bus speeding up: Y 3. An elevator moving at constant speed: N 4. A bicycle going around a curve: Y 5. A moon orbiting Jupiter: Y Moving in Circles Angular momentum describes objects that are spinning or moving in circles. A special force, a torque, is needed to change an object’s angular momentum. (This is the case in the precession of Earth’s rotational axis — or nutation, caused by interaction of the bulge of excess mass around Earth’s equator and its gravitational interaction with the sun) Acceleration Around a Newton’sCurve second law of motion tells us that an object going around a curve has an acceleration pointing toward the inside of the curve. This is known as a centripetal acceleration, where ac = v2/r Changing an Object’s Momentum Requires a. of (1 gravity. 2) b. applying a force. c. friction. d. None of the above is correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Changing an Object’s Momentum Requires a. of (2 gravity. 2) b. applying a force. c. friction. d. None of the above is correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Changing an Object’s Angular Momentum Requires (1 of 2) a. gravity. b. applying a torque. c. friction. d. None of the above is correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Changing an Object’s Angular Momentum Requires (2 of 2) a. gravity. b. applying a torque. c. friction. d. None of the above is correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved A Long-Handled Wrench Turns a Bolt More Easily Than a Short-Handled One. Why? (1 of 2) a. A long handle applies more torque. b. A long handle applies more force. c. A long handle is heavier. d. A long handle is easier to grip. Copyright © 2024 Pearson Education, Inc. All Rights Reserved A Long-Handled Wrench Turns a Bolt More Easily Than a Short-Handled One. Why? (2 of 2) a. A long handle applies more torque. b. A long handle applies more force. c. A long handle is heavier. d. A long handle is easier to grip. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Newton’s Second Law, F = Ma, (Force = Mass times Acceleration), Means That With No Net Force (1 of 2) a. objects will be at rest. b. an object will slow to a stop. c. an object will move in a straight line at a constant speed. d. an object will move in random directions. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Newton’s Second Law, F = Ma, (Force = Mass times Acceleration), Means That With No Net Force (2 of 2) a. objects will be at rest. b. an object will slow to a stop. c. an object will move in a straight line at a constant speed. d. an object will move in random directions. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Newton’s 3rd Law of Motion Every force is accompanied by another force of equal magnitude but opposite direction Why Do Objects Move at Constant Velocity if No Force Acts on Them? Objects continue at constant velocity because of conservation of momentum. The total momentum of interacting objects cannot change unless an external force is acting on them. Interacting objects exchange Conservation of Angular Momentum Angular momentum = mass x velocity x radius The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it. This conservation of orbital angular momentum applies to the planets in our solar system Universal Law of Gravitation Constant of proportionalit y Force and mass are directly proportional. As mass increases force increases Force and distance are inversely proportional. As distance increases force decreases. Universal Law of Gravitation Every mass attracts and is attracted to every other mass in the Universe Mass enters into the law in the numerator so more massive objects produce bigger gravitational forces The gravitational force between two masses is proportional to the inverse square of the distance between their masses, so halving the distance between two masses quadruples the gravitational force between them The gravitational constant G is a small number, requiring very large masses in order to produce substantial gravitational forces True or False: Your Gravitational Force on the Earth Is the Same as the Earth’s Gravitational Force on You (1 of 2) a. True b. False Copyright © 2024 Pearson Education, Inc. All Rights Reserved True or False: Your Gravitational Force on the Earth Is the Same as the Earth’s Gravitational Force on You (2 of 2) a. True b. False Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Do All Objects Fall at the Same Rate? Inertial and gravitational mass equivalency… In the international space station, how strong is the force, compared to the force on Earth’s surface? a. About 1% as strong. b. About 10% as strong. c. About 50% as strong. d. About 90% as strong. e. 100% (equally) as strong. In the international space station, how strong is the force, compared to the force on Earth’s surface? a. About 1% as strong. b. About 10% as strong. c. About 50% as strong. d. About 90% as strong. e. 100% (equally) as strong. So, why do astronauts appear weightless? Bathroom Scale When you get on a standard scale it registers your weight as 150 lbs. When you get on a standard scale holding a large book it registers your weight as 153 lbs. Does the bathroom scale read your weight? Weight = Gravitational force you experience. Can only change with diet and exercise. Or moving to another planet. Apparent weight = What the bathroom scale reads. Changes all the time. The Elevator Problem Apparent Weight True Weight a=0 The Elevator Problem Apparent Weight True Weight a = up The Elevator Problem Apparent Weight True Weight a = down The Elevator Problem What if the elevator cable snaps? Apparently Weightless !.. True Weight a=g Falling In Orbit Orbiting is just falling while missing the Earth Astronauts experience weightlessness in orbit despite still feeling acceleration from gravity because they are in free fall How is mass different from weight? Mass—a measure of the amount of matter in an object Weight—the force that a scale exerts upon an object You are weightless in free-fall, but not massless (you are never massless). Newton’s form of Kepler’s Third a 3 Average Orbital period distance Law P∝ 2 between the two (M1 + objects M2 ) Masses of the two objects Mass does matter when you’re comparing systems with very different masses. Kepler’s 3rd Law worked for all the planets because their masses were insignificant compared to the mass of the Sun, so the system mass is always pretty much just the Escape Velocity Escape velocity is when the kinetic energy of an object is enough to escape its gravitational potential So, K.E > G.P.E Using the full form for G.P.E… 2 RE 1 mv2 > GmME v> 2GME RE Energy Is Conserved: Energy (like momentum) can be neither created nor destroyed, but it can change form or be exchanged between objects. Conservation of Energy: the total energy content in an isolated system is always the same. The total energy content of the Universe was determined in the Big Bang and remains the same today. In science, the standard unit of energy is the joule. ENERGY IS CONSERVED, IT CAN BE NEITHER CREATED OR DESTROYED —> BUT TRANSFORMS FROM ONE FORM TO ANOTHER Basic Types of Energy Kinetic (motion) – Movement of object – Thermal Energy – Sound Radiative (light) Potential (stored) – Gravitational – Mechanical Kinetic Energy K.E. = (1/2) * mass * velocity2 Thermal Energy (Kinetic) Thermal Energy the collective kinetic energy of many particles (for example, in a rock, in air, in water). Thermal energy is related to temperature but it is NOT the same. Temperature is related to the average kinetic energy of the many particles in a substance. Temperature Scales: Kelvin is absolute temperature scale; Celsius is Kelvin - 273 degrees Gravitational Potential Energy Stored energy that can be turned into other forms Gravitational potential energy is greatest when the twoobjects arefurthest away, i.e. the ball and the center of the Earth below On Earth, this energy depends on the following: –Object’s mass (m) –strength of gravity (g) –its height above the ground (h) Energy is Conserved (assume frictionless slope & no drag) K.E. = 1/2*m*v2 P.E. = m*g*h Joule is unit of energy for MKS unit system (meter, kilogram, Energy Can be Transferred between Forms! In space, an object or a gas cloud has more gravitational energy when it is spread out than when it contracts. A contracting cloud converts Mass-Energy: A Subtype of Potential Energy When You Are Standing Still on a Ladder, We Say That You Have (1 of 2) a. more kinetic energy than when you were on the ground. b. more gravitational potential energy than when you were on the ground. c. more radiative energy than when you were on the ground. d. more heat energy than when you were on the ground. Copyright © 2024 Pearson Education, Inc. All Rights Reserved When You Are Standing Still on a Ladder, We Say That You Have (2 of 2) a. more kinetic energy than when you were on the ground. b. more gravitational potential energy than when you were on the ground. c. more radiative energy than when you were on the ground. d. more heat energy than when you were on the ground. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Which Is an Example of Changing Gravitational Potential Energy into Kinetic Energy? (1 of 2) a. Eating food and releasing the energy b. Riding a bicycle c. Falling off a ladder Copyright © 2024 Pearson Education, Inc. All Rights Reserved Which Is an Example of Changing Gravitational Potential Energy into Kinetic Energy? (2 of 2) a. Eating food and releasing the energy b. Riding a bicycle c. Falling off a ladder Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is the Primary Cause of the Tides on Earth? (1 of 2) a. Gravity from Earth’s core b. Gravity from the Moon pulling on the oceans c. Gravity from the Moon pulling harder on one side of Earth than the other d. Gravity from the Moon and/or the Sun pulling harder on one side of Earth than the other Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is the Primary Cause of the Tides on Earth? (2 of 2) a. Gravity from Earth’s core b. Gravity from the Moon pulling on the oceans c. Gravity from the Moon pulling harder on one side of Earth than the other d. Gravity from the Moon and/or the Sun pulling harder on one side of Earth than the other Copyright © 2024 Pearson Education, Inc. All Rights Reserved Light & Matter Electric Charge and Coulomb’s Law If I take a charge q and place it here it will feel a force towards q the other charge Q with magnitude Q This force law is called Coulomb’s Law and it is mathematically identical to Newton’s gravitational law. Charge, unlike mass, can be positive or negative so Coulomb force can be attractive or repulsive. Moving Charges When electric charges are accelerated, e.g. when electric current is moved through a loop of wire, magnetic field is generated. Charges interact with magnetic fields differently than with electric fields. Moving Charges When electric charges are accelerated, e.g. when electric current is moved through a loop of wire, magnetic field is generated. Charges interact with magnetic fields differently than with electric fields. Electricity and Magnetism are Interconnected Stationary charges produce electric fields Moving charges produce magnetic fields Time-varying electric fields create magnetic fields Time-varying magnetic fields create electric fields Maxwell’s Biggest Result With a mathematical framework in place to describe electromagnetic fields, Maxwell found that accelerating charges produce electromagnetic waves The electric and magnetic fields are perpendicular to one another and transverse to the direction in which the wave is propagating The waves travel at a fixed speed through vacuum that is set by certain natural constants that can be measured with experiments on circuits in a lab. Electromagnetic waves travel at the speed of light. Light is electromagnetic waves! Wave Basics Wavelength vs. Frequency Heinrich Hertz is the frequency commonly expressed in hertz or cycles per second is the speed of light commonly expressed as Flux vs. Distance As the light that a light source puts out radiates outward, you can think of that light as being spread out over increasingly large spheres. The area of spheres grows as the square of the sphere’s radius, so the flux of the light falls off as the inverse square of the sphere’s radius. Light: Particles or Waves? Particle: Wave: Double Slit Experiments Photoelectric Effect ROY G BIV Blackbody Radiation Wien’s Law states that the peak wavelength of the blackbody spectrum is inversely proportional to temperature Blackbody Radiation The Stefan-Boltzmann law says that the total energy a blackbody emits across all wavelengths is power of temperature. proportional to the fourth The Sun as a Blackbody How do Light and Matter There are Interact? three basic ways: 1)Matter can EMIT light, 2)ABSORB light, or 3)REFLECT (also called “SCATTER”) light. Types of Light Emission Light can be emitted as “lines” or as “continuum”. Lines are single-color emission, like a laser. Continuum has many colors, like a rainbow. Dense objects like the Earth and stars and people emit To understand spectral lines, we need to understand atomic theory Atoms have a dense nucleus of protons and neutrons. Electrons surround the nucleus in a “cloud.” Electron Cloud Atom Nucleus ~“Femtometer” Each type of atom has a unique set of energies. Electrons can have certain energies; other energies are not allowed. Atoms can absorb or emit photons. Energy is conserved – the photon energy is gained by atom or a photon is created and atom loses Spectral “Fingerprints” The wavelengths at which atoms emit and absorb radiation form unique spectral fingerprints for each atom. – We can learn what something is made of by looking at the wavelengths of its emission and absorption lines. 2 18 10 11 Elemental Emission Spectra Flame tests are just one way to see different colors coming from different elements. If you make sealed tubes of different elements and heat them they will glow. They glow noticeably different colors like the colors in a neon sign. Their emission spectra show patterns of spectral lines Absorption Spectra Suppose you take continuous spectrum light like that produced by a blackbody and pass it through a sealed tube of cool gas. You will find that the same spectral lines the gas emits when heated are now missing from the previously continuous spectrum. This is referred to as the absorption spectrum of the gas. The dark lines in the otherwise continuous solar spectrum are the absorption spectrum of relatively cool gas in the Sun’s upper atmosphere backlit by the continuous blackbody radiation from the Sun’s hotter denser core. In this way, we can learn what elements are in the Sun’s atmosphere without ever touching it! Continuous Spectrum The spectrum of a common (incandescent) light bulb spans all visible wavelengths! The Sun's spectrum is (almost) continuous. Emission Line Spectrum A thin or low-density cloud of gas emits light only at specific wavelengths, producing a spectrum with bright emission lines. Again, what causes emission lines? Absorption Line Spectrum A cloud of gas between us and something producing a continuous spectrum can absorb light of specific wavelengths, leaving dark absorption lines in the spectrum. Doppler Shift A spectral line associated with a source moving towards you will appear to have a slightly shorter wavelength than what is known from a laboratory. We call this a blueshift If the source is moving away from you, the spectral line will appear to have a longer wavelength than what is known in the lab and is said to have a redshift The amount that the wavelength appears to change depends on the rest-frame wavelength and the radial velocity A Red Sweater Appears Red Because (1 of 2) a. the sweater is absorbing red light. b. the sweater is transmitting red light. c. the sweater is reflecting red light. d. the sweater is reflecting all colors except red. Copyright © 2024 Pearson Education, Inc. All Rights Reserved A Red Sweater Appears Red Because (2 of 2) a. the sweater is absorbing red light. b. the sweater is transmitting red light. c. the sweater is reflecting red light. d. the sweater is reflecting all colors except red. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is Light? (1 of 2) a. A wave, like sound only much faster b. A particle c. The absence of dark d. A kind of energy with some of the properties of waves and some properties of particles Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is Light? (2 of 2) a. A wave, like sound only much faster b. A particle c. The absence of dark d. A kind of energy with some of the properties of waves and some properties of particles Copyright © 2024 Pearson Education, Inc. All Rights Reserved Compared to Red Light, Blue Light Has (1 of 2) a. shorter wavelengths and lower energy. b. longer wavelengths and lower energy. c. shorter wavelength and higher energy. d. longer wavelength and higher energy. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Compared to Red Light, Blue Light Has (2 of 2) a. shorter wavelengths and lower energy. b. longer wavelengths and lower energy. c. shorter wavelength and higher energy. d. longer wavelength and higher energy. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is Found in the Nucleus of a Helium Atom? (1 of 2) a. Protons with a positive charge and neutrons with a neutral charge b. Protons with a positive charge, neutrons with a neutral charge and electrons with a negative charge c. Electrons with a negative charge d. Neutrons with a positive charge and electrons with a negative charge Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is Found in the Nucleus of a Helium Atom? (2 of 2) a. Protons with a positive charge and neutrons with a neutral charge b. Protons with a positive charge, neutrons with a neutral charge and electrons with a negative charge c. Electrons with a negative charge d. Neutrons with a positive charge and electrons with a negative charge Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Kind of Spectrum Does Hot Gaseous Hydrogen Produce? (1 of 2) a. Emission line b. Absorption line c. Continuous d. Infrared Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Kind of Spectrum Does Hot Gaseous Hydrogen Produce? (2 of 2) a. Emission line b. Absorption line c. Continuous d. Infrared Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Happens to Thermal Radiation (a Continuous Spectrum) if You Make the Source Hotter? (1 of 2) a. It produces more energy at all wavelengths and the peak of the spectrum shifts to shorter wavelengths. b. It produces more energy at all wavelengths and the peak of the spectrum shifts to longer wavelengths. c. It produces less energy at all wavelengths and the peak of the spectrum shifts to shorter wavelengths. d. It produces less energy at all wavelengths and the peak of the spectrum shifts to longer wavelengths. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Happens to Thermal Radiation (a Continuous Spectrum) if You Make the Source Hotter? (2 of 2) a. It produces more energy at all wavelengths and the peak of the spectrum shifts to shorter wavelengths. b. It produces more energy at all wavelengths and the peak of the spectrum shifts to longer wavelengths. c. It produces less energy at all wavelengths and the peak of the spectrum shifts to shorter wavelengths. d. It produces less energy at all wavelengths and the peak of the spectrum shifts to longer wavelengths. Copyright © 2024 Pearson Education, Inc. All Rights Reserved The Hottest Star Is One That Appears (1 of 2) a. orange. b. red. c. yellow. d. white or bluish-white. e. They are all the same temperature; they just look different colors. Copyright © 2024 Pearson Education, Inc. All Rights Reserved The Hottest Star Is One That Appears (2 of 2) a. orange. b. red. c. yellow. d. white or bluish-white. e. They are all the same temperature; they just look different colors. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Telescopes 194 Refraction Refraction is the bending of light when it passes from one substance into another. Your eye uses refraction to focus light. This is also why prisms separate white light into n = index of refraction colors, the refractive index n=1 in a vacuum, >1 in medium is often wavelength v = c/n, λ = λ 0/n dependent in media, Velocity of light slows in media, meaning different colors of and wavelength decreases Image Formation in refractor The focal plane is where light from different directions comes into focus. The image behind a single (convex) lens is actually upside down! Everything is upside down and backwards! Focal length: distance between objective lens and the Reflecting Telescope Reflecting telescopes can have much greater diameters. Longer focal length can be achieved in smaller space due to mirror redirection– smaller telescopes Most modern telescopes are reflectors. Recording Images — IMAGES ARE FOCUSED ONTO TELESCOPE PHOTO-SENSITIVE DETECTORS A camera focuses light like an eye and captures the image with a detector. The CHARGE COUPLED DEVICE (C C D) detectors in digital cameras are similar to those used in modern telescopes. Light is converted to electrons and current via the photoelectric effect. Astronomers often use computer software to combine, sharpen, or refine images. What Are the Two Most Important Properties of a Telescope? 1. Light-collecting area: Telescopes with a larger collecting area can gather a greater amount of light in a shorter time. This is sometimes referred to as a telescope’s “sensitivity” 2. Angular resolution: Telescopes that are larger are capable of taking images with greater detail. Angular Resolution (1 of 3) The minimum angular separation that the telescope can distinguish Angular Resolution (2 of 3) Ultimate limit to resolution comes from interference of light waves within a telescope. Larger telescopes are capable of greater angular resolution because there is less interference. Angular Resolution (3 of 3) The rings in this image of a star come from interference of light waves. This theoretical limit on angular resolution is known as the diffraction limit. This diffraction limit depends only on the wavelength of light This image is from the and diameter of the Hubble Space Telescope. telescopes collecting area Angular Resolution This diffraction limit is given by the Rayleigh criterion: θ = 1.22 λ D This is defined by having two overlapping diffraction patterns (“airy disks”) not overlap for two distant This image is from the point sources of Hubble Space Telescope. light Visible Light — “atmospheric seeing” Characterized by wavelengths between 400 and 700 nanometers. By definition it can traverse our atmosphere, though not without some distortion, so space-based instruments can still be important. Earth’s atmosphere degrades images. This is why stars twinkle! Limits the angular resolution of ground-based optical telescopes to ~ 1 arc second Space-based telescopes do not have this problem. How Does Earth’s Atmosphere Affect Ground- Based Observations? The best ground-based sites for astronomical observing are as follows: – calm (not too windy) – high (less atmosphere to see through) – dark (far from city lights) – dry (few cloudy nights) — Summit of Maunakea, water vapor is also an issue Hawaii The best observing sites are atop remote mountains. in radio astronomy Light Pollution (1 of 2) Scattering of human-made light in the atmosphere is a growing problem for astronomy. Transmission Through Earth’s Atmosphere Only radio and visible light pass easily through Earth's atmosphere. We need telescopes in space to observe other forms. Space telescopes like Hubble also let us obtain higher angular resolution images without adaptive optics and avoid Radio Characterized by wavelengths longer than about 0.1 meters. The atmosphere is transparent to radio waves until their wavelength begins to exceed approximately 30 meters. For radio telescopes we can use reflective surfaces instead of mirrors or lenses How DoWe Observe Radio Light? A standard satellite dish is essentially a telescope for observing radio waves. A radio telescope is like a giant mirror that reflects radio waves to a focus. This is the Five-hundred-meter Aperture Spherical Telescope (FAST) in China. Radio Telescopes - Arrays Interferometric arrays combine the signals from many telescopes to increase the resolution. Very Large Array (VLA) The angular resolution is equal to a telescope with diameter the size of the array, but light collecting power is only as good as What Do Astronomers Do with Telescopes? Imaging: Taking pictures of the sky Spectroscopy: Breaking light into spectra Time Monitoring: Measuring how light output varies with time Imaging (1 of 2) Astronomical detectors generally record only one color of light at a time. Several images must be combined to make full- color pictures. Imaging (2 of 2) Astronomical detectors can record bands of light our eyes can’t see. Color is sometimes used to represent different energies of nonvisible light. Spectroscopy (1 of 2) A spectrograph separates the different wavelengths of light before they hit the detector. Spectroscopy (2 of 2) Graphing relative brightness of light at each wavelength shows the details in a spectrum. Higher spectral resolution requires more light. – Larger telescopes – Longer exposures Time Monitoring A light curve represents a series of brightness measurements made over a period of time. Multimessenger Astronomy We can also gain knowledge by collecting other signals using different sorts of – neutrinos — neutral charged fundamental “telescopes” particle – cosmic rays — high-energy particles coming from the universe! Pulsar Timing Arrays – gravitational waves — stretching and squeezing of spacetime Aerial view shows the Laser IceCube South Pole Interferometer Gravitational-Wave Neutrino Observatory Observatory (LIGO) Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Advantages Come From Putting a Telescope in Space? (1 of 2) a. Wavelengths of light that do not penetrate Earth’s atmosphere can be seen. b. Images may be sharper, without moving air to blur them. c. You are closer to the stars, for a better view. d. All of the above are correct. e. Both a and b are correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Advantages Come From Putting a Telescope in Space? (2 of 2) a. Wavelengths of light that do not penetrate Earth’s atmosphere can be seen. b. Images may be sharper, without moving air to blur them. c. You are closer to the stars, for a better view. d. All of the above are correct. e. Both a and b are correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Are the Two Most Important Properties for Optical Telescopes? (1 of 2) a. High magnification and high angular resolution b. High magnification and low angular resolution c. Low magnification and large collecting area d. A large collecting area and high angular resolution e. A large collecting area and low angular resolution Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Are the Two Most Important Properties for Optical Telescopes? (2 of 2) a. High magnification and high angular resolution b. High magnification and low angular resolution c. Low magnification and large collecting area d. A large collecting area and high angular resolution e. A large collecting area and low angular resolution Copyright © 2024 Pearson Education, Inc. All Rights Reserved An Intro to The Solar System: Our Planets See cool interactive infographic at NASA website: https://solarsystem.nasa.gov/solar- system/our-solar-system/overview/ Planet Mnemonic Mercury My Venus Very There are eight major planets with nearly circular orbits. Earth Educated Dwarf planets such as Pluto Mars Mother are smaller than the major planets, Jupiter Just and some have quite elliptical Saturn Served Us orbits. Uranus Nachos Planets all orbit in same direction and nearly in same plane. Neptune Tasty nachos! * * 13 uto B3 Pl * Not planets :( U 03 20 s nu ne ra tu U ep N tu rn Giants r te Sa pi Ju Asteroids* h s rt ar Terrestrial M Ea ry cu er planets s nu M Ve The The Sun — NOT A PLANET Over 99.8% of solar system’s mass Made mostly of H/He gas (plasma) Converts 4 million tons of mass into energy each second Venus– Why you so Hot? Earth's “sister” - similar size, orbital distance Covered with very thick cloud layer Atmospheric pressure 100 times that on Earth Temperature is 700 K Mainly CO2 atmosphere – strong Greenhouse Effect Greenhouse Effect Some gases, especially CO2 and water vapor, block some infrared radiation, preventing the planet from cooling. Earth would freeze without this! While Earth is 35 K warmer because of it, a The Giant Planets Called giant planets because of their mass —from 15 Earth masses (Uranus/Neptune) to 300 (Jupiter)—and also, their physical size. We can’t see solid surfaces, just see the Terminology “Gas” is used to refer to hydrogen and helium. Jupiter and Saturn are Gas Giants because they are composed mainly of these “gasses” though these “gasses” are not always found in a gaseous state. “Ice” is used to refer to heavier elements like oxygen, carbon, and nitrogen. Uranus and Neptune are Ice Giants because though they are composed of mostly “gasses”, they contain fractionally much more “ice” than Jupiter or Saturn. “Rocks” are what even heavier elements are referred to in this context: magnesium, silicon, iron, etc. IN ASTRONOMY, everything heavier than hydrogen and helium is called a “metal” — > not in other fields, and strictly speaking this is not true in reality Belts and Zones Convection, chemistry, and rotation drive Jupiters banded appearance of belts & zones, where convection is a process of heat transfer from hotter to colder regions in a fluid Rotation of the Giants Uranus in infrared. The south pole visible here is pointing almost directly towards the Sun. With an orbital period of 84 years, the southern hemisphere is in the midst of an extreme 21 year summer here. New Definition of a Planet #3 is new! Has to clear its neighborhood! Dwarf Planets: Pluto and More Much smaller than major planets Icy, comet-like composition Pluto’s main moon (Charon) is of similar size. Pluto’s average surface temperature: 44 K THE ECLIPTIC PLANE Formation of the Solar System How Did We Arrive at a Theory of Solar System Formation? The nebular theory states that our solar system formed from the gravitational collapse of a giant interstellar gas cloud—the solar nebula. – (Nebula is the Latin word for cloud.) Kant and Laplace proposed the nebular hypothesis over two centuries ago. 1. Long long ago, our solar system began as a giant cloud of dusty gas – a Nebula Orion Nebula The Solar Nebula Model Rotation speed of the cloud from which our solar system formed must have increased as the cloud contracted. Rotation of a contracting cloud speeds up for the same reason a skater speeds up as they pull in their arms. 2. Over time, gravity will contract this nebula (gas/dust Why cloud), does it spin faster? forming Conservation of Angular momentum an accretion disk http://www.youtube.com/w atch? v=AQLtcEAG9v0 Why does the disk flatten? —> Collisions Flattening Collisions between gas particles in the cloud caused it to flatten into a disk by gradually reducing random motions. Collisions between the particles also reduce up and down motions. Spinning cloud flattens as Disks AroundOther Stars (1 of 2) Observations of disks around other stars support the nebular hypothesis. Disks AroundOther Stars (2 of 2) The gaps in this protoplanetary disk, as imaged by ALMA, are likely due to forming planets. Formation of a Protostar Protostar: large hot ball of gas (not a star yet) at the center of the accretion disk Protoplanetary disk: Leftover gas and dust where the rest of the Solar System forms 4. Accretion – formation of larger dust grains and “planetesimals” Mutual gravity pulled the grains together and they stuck together because of electrostatic forces. Over time, the grains grew larger and larger = planetesimals (about 1km in size). 5. From Planetesimals to Planets Once they are planetesimals, they will pull more particles onto them by gravity, leading to planets. Planet: a body that orbits a star, has a mass less than 13 times that of Jupiter, has “cleared its orbit,” and is spherical. Today’s remaining planetesimals: Formation of Planets Terrestrial: Small particles of rock and metal are present inside the frost line. These particles accrete to form the rocky terrestrial planets. Jovian planets: Condensation of gases. Both ice and rock form small solid particles outside the frost line. Larger planet cores form. The gravity of the Jovian planet cores draws in cold hydrogen and helium gases and causes them to condense. It’s easier to draw in The Solar Nebula Model: Temperature Differences Asteroids and Comets Leftovers from the accretion process Rocky asteroids inside frost line Icy comets outside frost line Captured Moons Unusual moons of some planets may be captured planetesimals. Odd Rotation Giant impacts might also explain the different rotation axes of some planets. How Do We Know the Ageof the Solar System? Radiometric dating tells us that oldest moon rocks are 4.4 billion years old. Oldest meteorites are 4.55 billion years old. Planets probably formed 4.5 billion years ago. Some isotopes decay into other nuclei. A half-life is the time for half the nuclei in a substance to decay. Electron capture/inverse beta decay Core: Highest density; nickel and iron Earth’s Interior Mantle: Moderate density; silicon, oxygen, etc. Crust: Lowest density; granite, basalt, etc. A planet's outer layer of cool, rigid rock is called the lithosphere. It “floats” on the warmer, softer rock that lies beneath. Differentiation — applies to all of the planets Gravity pulls high-density material to center. Lower-density material rises to surface. Material ends up separated by Heating of Planetary Interiors Accretion and differentiation deposited heat when planets first formed Radioactive decay is the most important ACTIVE heat source today for rocky planets Convection transports heat as hot material rises and Cooling of Planetary Interiors cool material falls [takes place in mantle] Conduction transfers heat from hot material to cool material [takes place in lithosphere] Radiation sends energy into space. [takes place at surface, black body radiation] Planetary Size Controls Geological Activity Smaller worlds cool off faster and harden earlier. The Moon and Mercury are now geologically “dead.” Heat content depends on volume. Loss of heat through radiation depends on surface area. Time to cool depends on surface area divided by volume: Larger objects have a smaller ratio and cool more slowly. Internal Heat Allows for Magnetic Fields A planet can have a magnetic field if charged particles are moving inside. Three requirements: – Molten, electrically conducting interior – Convection – Moderately rapid rotation Processes That Shape Surfaces Impact cratering – Impacts by asteroids or comets Volcanism – Eruption of molten rock onto surface Tectonics – Disruption of a planet’s surface by internal stresses Erosion – Surface changes made by wind, water, or ice Volcanism also releases gases from Outgassing Earth’s interior into the atmosphere. Virtually all the gas that made the atmospheres of Venus, Earth, and Mars—and the water vapor that rained down to form Earth’s oceans—originally was released from the planetary interiors by Cratering of Moon (1 of 2) Some areas of Moon are more heavily cratered than others. Younger regions were flooded by lava after most cratering. Why do the terrestrial planets have different geological histories?… The Role of Planetary Size Smaller worlds cool off faster and harden earlier. Larger worlds remain warm inside, promoting volcanism and tectonics. Larger worlds also have more erosion because their gravity retains an atmosphere. Role of Distance from Sun Planets close to the Sun are too hot for rain, snow, ice and so have less erosion. Hot planets have more difficulty retaining an atmosphere. Planets far from the Sun are too cold for rain, limiting erosion. Role of Rotation Planets with slower rotation have less weather, less erosion, and a weak magnetic field. Planets with faster rotation have more weather, more erosion, and a stronger magnetic field. What Is an Atmosphere? An atmosphere is a layer of gas that surrounds a planet. Atmospheric Pressure (2 of 2) Pressure and density decrease with altitude because the weight of overlying layers is less. Earth’s pressure at sea level is: – 1.03 kg per sq ilo ram uare centimeter. Where Does an Atmosphere End? (1 of 2) There is no clear upper boundary. Most of Earth’s gas is less than 10 kilometers from the surface, but a small fraction extends to more than 100 kilometers. Altitudes more than 100 kilometers are Planetary Temperature A planet’s surface temperature is determined by the balance between energy from sunlight it absorbs and energy ofoutgoing thermal radiation. Temperature and Distance A planet’s distance from the Sun determines the total amount of incoming sunlight. The amount of energy received from the Sun decreases with distance from the Sun. *The energy received per unit area, per unit time at a planet falls off with the inverse Flux = Luminosity square of its distance to the 4πR2 Sun. Luminosity is the intrinsic Temperature and Rotation A planet’s rotation rate affects the temperature differences between day and night. Slower rotation can create larger temperature differences. It does not affect the average temperature of the planet. Temperature and Reflectivity A planet’s reflectivity (or albedo) is the fraction of incoming sunlight it reflects. Planets with low albedo absorb more sunlight, leading to hotter temperatures. Light’s Effects on Earth’s Atmosphere (1Ionization: of 2) Removal ofan electron: X-rays and U V light can ionize and dissociate molecules. Dissociation: Destruction of a molecule Scattering: Change in photon’s direction. Molecules in the atmosphere tend to scatter blue light Absorption: Photon’s energy is absorbed. Molecules in the atmosphere tend to absorb infrared. Earth’s Atmospheric Structure (2 of4) Stratosphere: Layer above the troposphere Temperature rises with altitude in lower part, drops with altitude in upper part. Warmed by absorption of ultraviolet sunlight Earth’s Atmospheric Structure (3 of4) Thermosphere: Layer at about 100 kilometers altitude Temperature rises with altitude. X-rays and ultraviolet light from the Sun heat and ionize gases. Most X-ray absorption happens in upper layer of thermosphere called “ionosphere”, for completely ionized gas which is opaque to Earth’s Atmospheric Structure (4 of4) Exosphere: Highest layer in which atmosphere gradually fades into space. Temperature rises with altitude; atoms can escape into space. Warmed by x-rays and UV light Sources of Gas 1. Outgassing 2. Vaporization 3. Surface ejection Losses of Gas 1. Condensation (Reverse of vaporization) 2. Chemical Reactions — e.g., rusting 3. Solar wind stripping 4. Thermal Escape Thermal Escape from an Atmosphere Lightweight gases escape more easily and thermal escape is greaterthe lower the mass of the planet Sizes of Jovian Planets (1 of 2) Adding mass to a jovian planet compresses the underlying gas layers. Inside Jupiter (1 of 3) High pressures inside Jupiter cause phase of hydrogen to change with depth. The high temperatures and pressures inside Jupiter liquefy Hydrogen and allow for it to act like a metal deep inside of Jupiter Hydrogen acts like a metal at great depths because its electrons move freely. Inside Jupiter (2 of 3) Gravitational field measurements from the Juno mission indicate that the core of Jupiter is diffuse. Juno is a space probe in orbit around Jupiter and was launched in August 2011, arriving in 2016 (1.7 billion-mile journey) Hydrogen compounds, rock, and metal gradually become more common in the Jupiter’s Internal Heat Jupiter radiates twice as much energy as it receives from the Sun. Energy probably comes from slow contraction of interior Other Magnetospheres All jovian planets have substantial magnetospheres, but Jupiter’s is the largest by far. The fields of Uranus and Neptune are not roughly aligned with their axes of rotation, unlike the other Magnetic Fields All of the Giant Planets have strong intrinsic magnetic fields generated by electric currents driven by rapid 0.31 G 4.28 G 0.22 G 0.23 G 0.13 G rotation. Magnetic Fields It is actually by watching the magnetic fields rotate that we infer the rotation rate of the Giant Planets. The magnetic fields are anchored deep in the 0.31 G 4.28 G 0.22 G 0.23 G the motion of the 0.13 G planet and don’t trace clouds that we can see near the surface. Moons are made of rock, ice, or mixtures of both – no “gas Moo moons” ns Larger Most planets have moons of the larger more moons formed with their planets like miniature Solar Systems Some moons are objects that formed away from a planet, but were later gravitationally captured Almost all are tidally locked like our Moon – the same side always faces the planet Moon Surfaces Moons can be geologically active Craters (or a lack of) and bright/dark areas (from past lava flows) reveal geological activity. Some surfaces are old and fully cratered while some are young and smooth – these were recently resurfaced by geological activity A B side side Sizes of Moons Small moons (< 300 k m ) – No geological ilo eter activity Medium-sized moons (300–1500 k m ) – Geological activity in past ilo eter Large moons (> 1500 k m ) ilo eter – Ongoing geological activity Medium andLarge Moons Enough self-gravity to be spherical Have substantial amounts of ice Formedin orbit around jovian planets Circular orbits in same direction as planet Small Moons These are far more numerous than the medium and large moons. They do not have enough gravity to be spherical: Most are “potato-shaped.” Pan orbits within Saturn’s rings and has accumulated a ridge of ring dust on its equator. They are captured asteroids or Rings All of the Giant Planets have ring systems, though none quite like Saturn Ring particles obey Kepler’s Laws – they orbit! There are bright and dark rings, “gaps,” and divisions. They are made up of numerous, Saturn’s tiny individual particles. Rings Saturn’s rings are 70,000 km wide but only about 10-20 meters thick… like the thickness of a sheet of paper if the sheet of paper were a kilometer wide They orbit around Saturn’s equator. Gaps are not completely empty. Brightness/darkness reflects the amount of material in each ring. The Cassini spacecraft revealed many concentric rings. Ring formation - Roche Limit If a moon gets too close to a planet, it will disintegrate because of tidal forces from the planet’s gravity. The point at which it will disintegrate is called the Roche Asteroids Are Thought to Be (1 of 2) a. the remains of a planet between Mars and Jupiter that broke up. b. escaped small moons. c. leftover planetesimals from the inner solar system. d. leftover planetesimals from the outer solar system. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Asteroids Are Thought to Be (2 of 2) a. the remains of a planet between Mars and Jupiter that broke up. b. escaped small moons. c. leftover planetesimals from the inner solar system. d. leftover planetesimals from the outer solar system. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Most Asteroids Orbit the Sun in the Asteroid Belt, Which Is Located (1 of 2) a. between the orbits of Mars and Jupiter. b. between the orbits of Neptune and Pluto. c. beyond the orbit of Neptune. d. None of the above is correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Most Asteroids Orbit the Sun in the Asteroid Belt, Which Is Located (2 of 2) a. between the orbits of Mars and Jupiter. b. between the orbits of Neptune and Pluto. c. beyond the orbit of Neptune. d. None of the above is correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Do We Think the Composition of the Solar Nebula Was? (1 of 2) a. About half hydrogen and helium, half heavier elements (iron, carbon, silicon, etc.) b. About 98% hydrogen and helium, and 2% heavier elements c. About 2% hydrogen and helium, and 98% heavier elements Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Do We Think the Composition of the Solar Nebula Was? (2 of 2) a. About half hydrogen and helium, half heavier elements (iron, carbon, silicon, etc.) b. About 98% hydrogen and helium, and 2% heavier elements c. About 2% hydrogen and helium, and 98% heavier elements Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Doesan Object’s Rate of Cooling Vary With Size? (1 of 2) a. A larger object cools more slowly than a smaller object. b. A smaller object cools more slowly than a larger object. c. Size has no effect on an object’s rate of cooling. Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Doesan Object’s Rate of Cooling Vary With Size? (2 of 2) a. A larger object cools more slowly than a smaller object. b. A smaller object cools more slowly than a larger object. c. Size has no effect on an object’s rate of cooling. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is the Source of Earth’s Magnetic Field? (1 of 2) a. Magnetic rocks b. Magnetized iron in Earth’s crust c. Magnetized iron in Earth’s core d. Molten metal circulating inside Earth Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Is the Source of Earth’s Magnetic Field? (2 of 2) a. Magnetic rocks b. Magnetized iron in Earth’s crust c. Magnetized iron in Earth’s core d. Molten metal circulating inside Earth Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Are Smaller Terrestrial Bodies Such as Mercury or the Moon “Geologically Dead”? (1 of 2) a. They cooled off faster than Earth did. b. They don’t have erosion. c. They were hit by fewer meteorites than Earth. d. They are made of different materials than Earth. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Are Smaller Terrestrial Bodies Such as Mercury or the Moon “Geologically Dead”? (2 of 2) a. They cooled off faster than Earth did. b. They don’t have erosion. c. They were hit by fewer meteorites than Earth. d. They are made of different materials than Earth. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Which of the Following Is an Example of Convection? (1 of 2) a. Heat radiates from a planet into space. b. Heat travels from atom to atom, from inside a planet to the outside. c. Hot material inside a planet rises, and cool material sinks toward the center. d. Metal conducts energy throughout Earth’s core. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Which of the Following Is an Example of Convection? (2 of 2) a. Heat radiates from a planet into space. b. Heat travels from atom to atom, from inside a planet to the outside. c. Hot material inside a planet rises, and cool material sinks toward the center. d. Metal conducts energy throughout Earth’s core. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Is Atmospheric Pressure Less on Top of a Mountain Than at Sea Level? (1 of in a. It is cooler 2) the mountains. b. Denser air sinks to sea level; the air on mountains is lighter. c. The pressure at every height in the atmosphere is due to the weight of the air above it. d. None of the above is correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Why Is Atmospheric Pressure Less on Top of a Mountain Than at Sea Level? (2 of in a. It is cooler 2) the mountains. b. Denser air sinks to sea level; the air on mountains is lighter. c. The pressure at every height in the atmosphere is due to the weight of the air above it. d. None of the above is correct. Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Was the Source of the Atmospheres WeSee Today? (1 of 2) a. Gas accreted from the solar nebula b. Comets c. Gas released from interior rocks (outgassing) d. Evaporation from ice Copyright © 2024 Pearson Education, Inc. All Rights Reserved What Was the Source of the Atmospheres WeSee Today? (2 of 2) a. Gas accreted from the solar nebula b. Comets c. Gas released from interior rocks (outgassing) d. Evaporation from ice Copyright © 2024 Pearson Education, Inc. All Rights Reserved Jupiter Does Not Have a Large Metal Core Like Earth. How Can It Havea Magnetic Field? (1 of 2) a. The magnetic field is left over from when Jupiter accreted. b. Its magnetic field comes from the Sun. c. It has metallic hydrogen inside, which circulates and makes a magnetic field. d. It has a large metal core. Copyright © 2024 Pearson Education, Inc. All Rights Reserved Jupiter Does Not Have a Large Metal Core Like Earth. How Can It Havea Magnetic Field? (2 of 2) a. The magnetic field is left over from when Jupiter accreted. b. Its magnetic field comes from the Sun. c. It has metallic hydrogen inside, which circulates and makes a magnetic field. d. It has a large metal core. Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Do Astronomers Think Jupiter Generates Internal Heat? (1 of 2) a. Fusion b. Chemical reactions c. Friction due to its fast rotation d. Shrinking and releasing gravitational potential energy e. Tidal heating Copyright © 2024 Pearson Education, Inc. All Rights Reserved How Do Astronomers Think Jupiter Generates Internal Heat? (2 of 2) a. Fusion b. Chemical reactions c. Friction due to its fast rotation d. Shrinking and releasing gravitational potential energy e. Tidal heating Copyright © 2024 Pearson Education, Inc. All Rights Reserved An Intro to TheSolar System: Asteroids, comets, and the outer Solar System See cool interactive infographic at NASA website: https://solarsystem.nasa.gov/solar- system/our-solar-system/overview/ Asteroids and Comets Asteroids and comets arerelics of the early Solar System formation – the bits that were not swept into planets. Asteroids: rocky, most in betweenMars and Jupiter. Comets: icy, very large elliptical orbits, have tails Asteroid Facts Asteroids are rocky leftovers of early planet formation. They are small, have irregular shapes, and are heavily cratered They are composed of rock and metal Orbits confined to between Mars and Jupiter with orbital periods between ~3 and 6 years Typical distances between There are 150,000 in catalogs, and probably over a million with diameter > 0.5 kilometer. Average separation between asteroids is ~ 106 km Small asteroids are more common than large asteroids. Orbits of Most are in the Asteroids asteroid belt between Mars and Jupiter — did not accrete into a planet. Jupiter’s gravity, through influence of orbital resonances, stirred up asteroid orbits and prevented their accretion into a planet. How do we deflect an potential impact? 1.Destruction – blow it up, but then the pieces will still hit Earth, but could be our best shot in short notice 2.Delay – gently push it away with little explosions or rocket The Kuiper Belt KB extends from ~30-50 AU It is ~20 times wider and contains 20-200 times more mass than the asteroid belt May contain upwards of 100,000 objects with diameters exceeding 100 km Most KB objects are in stable orbits, but an overlapping population known The Kuiper Belt as the scattered disk is the likely source of short-period comets Short-period comets have orbital periods shorter than 200 years Scattered disk objects are highly inclined to the ecliptic plane and Halley’s Comet highly elliptical.Eris is the largest — orbital period of 76 years scattered disk object (and is a dwarf planet) KB objects and thus comets are composed of “ices” like frozen ammonia, methane, and water Eri Neptune’s gravity kept Kuiper Belt objects from Plutinos forming a planet, much like Jupiter is responsible for the asteroid belt Trans-Neptunian objects that orbit in a 2:3 orbital resonance with Neptune, for every 2 orbits a Plutino makes, Neptune orbits 3 times (Pluto is the largest member) Make up inner part of Kupier Belt and 1/4 of known Kuiper Belt objects Comets: dirty snowballs Icy planetesimals found beyond the planets — leftover from the early time of planet formation ~ 4.5 billion years ago Located either in the Kuiper Belt (~30-50 AU) — orderly orbits from 30 to 100 A U in disk of solar system — short period comets (

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