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A100H–Exploring the Universe: Energy, Gravity, and Light Martin D. Weinberg UMass Astronomy [email protected] Februrary 04, 2016 Read: Chap 5 02/04/16 – slide 1 Announcements ⊲ Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Read: Chap 5 Open observing at the Orchard Hill Observatory ⊲ ⊲ ⊲ Open on Thursdays when weather is good See http://www.astro.umass.edu/~orchardhill for details E-mail to [email protected] to be put on mailing list 02/04/16 – slide 2 Announcements ⊲ Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Read: Chap 5 Open observing at the Orchard Hill Observatory Check the web site: http://courses.umass.edu/astron100h-mdw ⊲ ⊲ ⊲ ⊲ Syllabus (when are the exams?) Requirements (what is the grading policy?) Lectures (can I look at the slides from class?) Contacts (how to find us or get help) 02/04/16 – slide 2 Announcements ⊲ Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Read: Chap 5 Open observing at the Orchard Hill Observatory Check the web site: http://courses.umass.edu/astron100h-mdw Today: finish Energy, Gravity & Orbits ⊲ ⊲ Where do objects get their energy? How Newton’s Law of Gravity extends Kepler’s Laws? 02/04/16 – slide 2 Announcements ⊲ Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Open observing at the Orchard Hill Observatory Check the web site: http://courses.umass.edu/astron100h-mdw Today: finish Energy, Gravity & Orbits ⊲ ⊲ Today: Light and Electromagnetism (LIGHT, Chap. 5) ⊲ ⊲ Read: Chap 5 Where do objects get their energy? How Newton’s Law of Gravity extends Kepler’s Laws? What is light? What are its properties? How do light and matter interact? 02/04/16 – slide 2 Announcements ⊲ Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Open observing at the Orchard Hill Observatory Check the web site: http://courses.umass.edu/astron100h-mdw Today: finish Energy, Gravity & Orbits ⊲ ⊲ Where do objects get their energy? How Newton’s Law of Gravity extends Kepler’s Laws? Today: Light and Electromagnetism (LIGHT, Chap. 5) ⊲ ⊲ What is light? What are its properties? How do light and matter interact? Questions? Read: Chap 5 02/04/16 – slide 2 Energy! Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 Where do objects get their energy? Energy makes matter move Amount of energy = Work that can be done Energy is conserved, but it can: ⊲ ⊲ Transfer from one object to another Change in form 02/04/16 – slide 3 Types of energy Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Kinetic (motion) Radiative (light) Stored or potential Energy can change type, but cannot be destroyed! Read: Chap 5 02/04/16 – slide 4 Kinetic energy Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ ✓ ✏ ✒ ✑ The kinetic energy of an object is the energy that it possesses due to its motion. Work needed to accelerate a body from rest to velocity v The body with mass m maintains this kinetic energy unless its speed changes The same amount of work is done by the body in decelerating from its current speed to a state of rest In physics: 1 KE = mv 2 2 The standard unit of kinetic energy is the joule. Read: Chap 5 02/04/16 – slide 5 Thermal energy Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 The collective kinetic energy of many particles (for example, in a rock, in air, in water) Temperature is the average kinetic energy of the many particles in a substance Thermal energy is total amount of kinetic energy in a substance 02/04/16 – slide 6 Temperature scales Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 02/04/16 – slide 7 Thermal energy Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on temperature AND density Example: 02/04/16 – slide 8 Entropy Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ A physical definition . . . ✓ ✏ ✒ ✑ The measure of a system’s thermal energy that is unavailable for doing useful work Because work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorder, or randomness, of a system. The concept of entropy provides deep insight into the direction of spontaneous change for many everyday phenomena. Its introduction by the German physicist Rudolf Clausius in 1850 is a highlight of 19th-century physics. Read: Chap 5 02/04/16 – slide 9 Gravitational Potential Energy On can store energy in a gravitational “field” On Earth, depends on: ⊲ ⊲ ⊲ objects mass (m) strength of gravity (g) distance object could potentially fall Read: Chap 5 02/04/16 – slide 10 Gravitational Potential Energy Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts. =⇒ A contracting cloud converts gravitational potential energy to thermal energy. ⊲ Read: Chap 5 02/04/16 – slide 11 Mass-Energy Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Mass itself is a form of potential energy E = mc 2 ⊲ Read: Chap 5 A small amount of mass can release a great deal of energy Concentrated energy can spontaneously turn into particles (for example, in particle accelerators) 02/04/16 – slide 12 Energy conservation Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Summary Energy can be neither created nor destroyed It can change form or be exchanged between objects The total energy content of the Universe was determined in the Big Bang and remains the same today∗ ⊲ Read: Chap 5 02/04/16 – slide 13 Newton’s Law of Gravity Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 02/04/16 – slide 14 Newton’s Law of Gravity Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Every body in the Universe attracts every other body with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: Fgravity M1 M2 =G d2 ⊲ Read: Chap 5 G is the same here as it is in a distant galaxy. It is a physical constant of the Universe. 02/04/16 – slide 15 Newton’s Law of Gravity Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 Gravity is an attractive force, and in accordance with Newton’s Third Law, the two masses feel equal and opposite forces Gravity is relatively weak because of the small value of the gravitation constant G; in metric units: G = 6.7 × 10−11 N · m2 /kg2 Large masses are required to provide an appreciable force, e.g. the mass of the Earth is 6.0 × 1024 kg 02/04/16 – slide 16 Newton’s Law of Gravity Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 On the surface of a planet: Fgravity Fgravity GM2 = M1 × 2 d = M1 × aEarth’s surface ✓ ✏ ✒ ✑ Acceleration caused by the Earth on any object placed on its surface is the same: its value is 9.8 m/sec/sec. Acceleration on the surface determines weight of object 02/04/16 – slide 17 Newton’s Law of Gravity Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ On the surface of a planet: Fgravity Fgravity GM2 = M1 × 2 d = M1 × aEarth’s surface ✓ ✏ ✒ ✑ Acceleration caused by the Earth on any object placed on its surface is the same: its value is 9.8 m/sec/sec. Acceleration on the surface determines weight of object On another planet Mplanet d2Earth aplanet = × 2 aEarth MEarth dplanet Read: Chap 5 02/04/16 – slide 17 Newton’s Law of Gravity Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ On the surface of a planet: Fgravity Fgravity GM2 = M1 × 2 d = M1 × aEarth’s surface ✓ ✏ ✒ ✑ Acceleration caused by the Earth on any object placed on its surface is the same: its value is 9.8 m/sec/sec. Acceleration on the surface determines weight of object On Mars d2 MMars aMars = × Earth = 2 aEarth MEarth dMars Read: Chap 5 0.11 1 × 1 0.53 2 = 0.39 02/04/16 – slide 17 Gravity and Orbits Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Velocity Acceleration Planet Gravity combined with Laws of Motion explains: ⊲ ⊲ ⊲ Read: Chap 5 Orbits Kepler’s Three Laws Resulting trajectory 02/04/16 – slide 18 Gravity and Orbits Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 Newton discovered that orbiting bodies may follow any one of a family of curves called conic sections The ellipse is only one possibility 02/04/16 – slide 19 Gravity and Orbits Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Newton discovered that orbiting bodies may follow any one of a family of curves called conic sections The ellipse is only one possibility Orbits may be bound (circle, ellipse) or unbound (parabola, hyperbola) Read: Chap 5 02/04/16 – slide 19 Escape velocity Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit) Escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr) 02/04/16 – slide 20 Center of Mass Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Because of momentum conservation, orbiting objects orbit around their center of mass ⊲ Read: Chap 5 02/04/16 – slide 21 Center of Mass Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Because of momentum conservation, orbiting objects orbit around their center of mass ⊲ Read: Chap 5 02/04/16 – slide 21 Gravity and Orbits Summary Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides Planets obey the same laws as objects on Earth ⊲ Read: Chap 5 02/04/16 – slide 22 Gravity and Orbits Summary Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Read: Chap 5 Planets obey the same laws as objects on Earth Kepler’s laws: explained by force of gravity ⊲ ⊲ ⊲ Planets orbit around the center of mass of the Solar System Since most of the mass is the Sun, Sun is very close to center of mass Third law depends on the sum of the two masses: 2 4π 2 P = a3 G(M1 + M2 ) 02/04/16 – slide 22 Gravity and Orbits Summary Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Planets obey the same laws as objects on Earth Kepler’s laws: explained by force of gravity ⊲ ⊲ ⊲ Planets orbit around the center of mass of the Solar System Since most of the mass is the Sun, Sun is very close to center of mass Third law depends on the sum of the two masses: 2 4π 2 P = a3 G(M1 + M2 ) New types of unbound orbits — hyperbolas and parabolas — in addition to ellipses Read: Chap 5 02/04/16 – slide 22 Orbits revisited Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides How do gravity and energy together allow us to understand orbits? Total orbital energy (gravitational + kinetic) stays constant if there is no external force Orbits cannot change spontaneously. ⊲ Read: Chap 5 02/04/16 – slide 23 Changing an orbit Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides What can make an object gain or lose orbital energy? Friction or atmospheric drag A gravitational encounter. ⊲ Read: Chap 5 02/04/16 – slide 24 Tides How does gravity cause tides? Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Moon’s gravity pulls harder on near side of Earth than on far side Difference in Moons gravitational pull stretches Earth Read: Chap 5 02/04/16 – slide 25 Tides and Phases Size of tides depends on phase of Moon Read: Chap 5 02/04/16 – slide 26 Tidal Friction Announcements Energy! Types of energy Kinetic energy Thermal energy Temperature scales Entropy Potential Energy Mass-Energy Energy conservation Law of Gravity Law of Gravity Gravity and Orbits Escape velocity Center of Mass Orbits revisited Changing an orbit Tides ⊲ Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth). Moon once orbited faster; tidal friction caused it to “lock” in synchronous rotation. 38 mm/yr, 2.3 ms/hy Read: Chap 5 02/04/16 – slide 27
