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Introduction to Astronomy from Darkness to Blazing Glory
Introduction to Astronomy From Darkness to Blazing Glory Published by JAS Educational Publications Copyright Pending 2010 JAS Educational Publications All rights reserved. Including the right of reproduction in whole or in part in any form. Second Edition Author: Jeffrey Wright Scott Photographs and Diagrams: Credit NASA, Jet Propulsion Laboratory, USGS, NOAA, Aames Research Center JAS Educational Publications 2601 Oakdale Road, H2 P.O. Box 197 Modesto California 95355 1-888-586-6252 Website: http://.Introastro.com Printing by Minuteman Press, Berkley, California ISBN 978-0-9827200-0-4 1 Introduction to Astronomy From Darkness to Blazing Glory The moon Titan is in the forefront with the moon Tethys behind it. These are two of many of Saturn’s moons Credit: Cassini Imaging Team, ISS, JPL, ESA, NASA 2 Introduction to Astronomy Contents in Brief Chapter 1: Astronomy Basics: Pages 1 – 6 Workbook Pages 1 - 2 Chapter 2: Time: Pages 7 - 10 Workbook Pages 3 - 4 Chapter 3: Solar System Overview: Pages 11 - 14 Workbook Pages 5 - 8 Chapter 4: Our Sun: Pages 15 - 20 Workbook Pages 9 - 16 Chapter 5: The Terrestrial Planets: Page 21 - 39 Workbook Pages 17 - 36 Mercury: Pages 22 - 23 Venus: Pages 24 - 25 Earth: Pages 25 - 34 Mars: Pages 34 - 39 Chapter 6: Outer, Dwarf and Exoplanets Pages: 41-54 Workbook Pages 37 - 48 Jupiter: Pages 41 - 42 Saturn: Pages 42 - 44 Uranus: Pages 44 - 45 Neptune: Pages 45 - 46 Dwarf Planets, Plutoids and Exoplanets: Pages 47 -54 3 Chapter 7: The Moons: Pages: 55 - 66 Workbook Pages 49 - 56 Chapter 8: Rocks and Ice: -
Energy Literacy Essential Principles and Fundamental Concepts for Energy Education
Energy Literacy Essential Principles and Fundamental Concepts for Energy Education A Framework for Energy Education for Learners of All Ages About This Guide Energy Literacy: Essential Principles and Intended use of this document as a guide includes, Fundamental Concepts for Energy Education but is not limited to, formal and informal energy presents energy concepts that, if understood and education, standards development, curriculum applied, will help individuals and communities design, assessment development, make informed energy decisions. and educator trainings. Energy is an inherently interdisciplinary topic. Development of this guide began at a workshop Concepts fundamental to understanding energy sponsored by the Department of Energy (DOE) arise in nearly all, if not all, academic disciplines. and the American Association for the Advancement This guide is intended to be used across of Science (AAAS) in the fall of 2010. Multiple disciplines. Both an integrated and systems-based federal agencies, non-governmental organizations, approach to understanding energy are strongly and numerous individuals contributed to the encouraged. development through an extensive review and comment process. Discussion and information Energy Literacy: Essential Principles and gathered at AAAS, WestEd, and DOE-sponsored Fundamental Concepts for Energy Education Energy Literacy workshops in the spring of 2011 identifies seven Essential Principles and a set of contributed substantially to the refinement of Fundamental Concepts to support each principle. the guide. This guide does not seek to identify all areas of energy understanding, but rather to focus on those To download this guide and related documents, that are essential for all citizens. The Fundamental visit www.globalchange.gov. Concepts have been drawn, in part, from existing education standards and benchmarks. -
STARS in HYDROSTATIC EQUILIBRIUM Gravitational Energy
STARS IN HYDROSTATIC EQUILIBRIUM Gravitational energy and hydrostatic equilibrium We shall consider stars in a hydrostatic equilibrium, but not necessarily in a thermal equilibrium. Let us define some terms: U = kinetic, or in general internal energy density [ erg cm −3], (eql.1a) U u ≡ erg g −1 , (eql.1b) ρ R M 2 Eth ≡ U4πr dr = u dMr = thermal energy of a star, [erg], (eql.1c) Z Z 0 0 M GM dM Ω= − r r = gravitational energy of a star, [erg], (eql.1d) Z r 0 Etot = Eth +Ω = total energy of a star , [erg] . (eql.1e) We shall use the equation of hydrostatic equilibrium dP GM = − r ρ, (eql.2) dr r and the relation between the mass and radius dM r =4πr2ρ, (eql.3) dr to find a relations between thermal and gravitational energy of a star. As we shall be changing variables many times we shall adopt a convention of using ”c” as a symbol of a stellar center and the lower limit of an integral, and ”s” as a symbol of a stellar surface and the upper limit of an integral. We shall be transforming an integral formula (eql.1d) so, as to relate it to (eql.1c) : s s s GM dM GM GM ρ Ω= − r r = − r 4πr2ρdr = − r 4πr3dr = (eql.4) Z r Z r Z r2 c c c s s s dP s 4πr3dr = 4πr3dP =4πr3P − 12πr2P dr = Z dr Z c Z c c c s −3 P 4πr2dr =Ω. Z c Our final result: gravitational energy of a star in a hydrostatic equilibrium is equal to three times the integral of pressure within the star over its entire volume. -
Energy Conservation in a Spring
Part II: Energy Conservation in a Spring Activity 4 Title: Forces and Energy in a Spring Summary: Students will use the “Masses and Springs” simulation from PhET to investigate the relationship between gravitational potential energy, spring potential energy, and mass. Standard: PS2 (Ext) - 5 Students demonstrate an understanding of energy by… 5aa Identifying, measuring, calculating and analyzing qualitative and quantitative relationships associated with energy transfer or energy transformation. Specific Learning Goals: 1. Understand how to calculate the force constant of a spring using the formula F = -k ∆x 2. Understand that even though energy is transformed during the oscillation of a spring among gravitational potential energy, elastic potential energy, and kinetic energy, the total energy in the system remains constant. 3. Understand how to calculate the gravitational potential energy for a mass which is lifted to a height above a table. 4. Understand how to calculate the elastic potential energy for a spring which has been displaced by a certain distance. Prior Knowledge: 1. The restoring force that a spring exerts on a mass is proportional to the displacement of the spring and the spring constant and is in a direction opposite the displacement: F = -k ∆x 2. Gravitational potential energy is calculated by the formula: PEg = mgΔh 2 3. Elastic potential energy is calculated by the formula: PEs = ½ k ∆x 4. In a mass and spring system at equilibrium, the restoring force is equal to the gravitational force on the suspended mass (Fg = mg) Schedule: 40-50 minutes Materials: “Masses and Springs 2.02 PhET” Engage: Three different masses are suspended from a spring. -
Potential Energy
Potential Energy • So far: Considered all forces equal, calculate work done by net force only => Change in kinetic energy. – Analogy: Pure Cash Economy • But: Some forces seem to be able to “store” the work for you (when they do negative work) and “give back” the same amount (when they do positive work). – Analogy: Bank Account. You pay money in (ending up with less cash) - the money is stored for you - you can withdraw it again (get cash back) • These forces are called “conservative” (they conserve your work/money for you) Potential Energy - Example • Car moving up ramp: Weight does negative work ΔW(grav) = -mgΔh • Depends only on initial and final position • Can be retrieved as positive work on the way back down • Two ways to describe it: 1) No net work done on car on way up F Pull 2) Pulling force does positive F Normal y work that is stored as gravitational x potential energy ΔU = -ΔW(grav) α F Weight Total Mechanical Energy • Dimension: Same as Work Unit: Nm = J (Joule) Symbol: E = K.E. + U 1) Specify all external *) forces acting on a system 2) Multiply displacement in the direction of the net external force with that force: ΔWext = F Δs cosφ 3) Set equal to change in total energy: m 2 m 2 ΔE = /2vf - /2vi + ΔU = ΔWext ΔU = -Wint *) We consider all non-conservative forces as external, plus all forces that we don’t want to include in the system. Example: Gravitational Potential Energy *) • I. Motion in vertical (y-) direction only: "U = #Wgrav = mg"y • External force: Lift mass m from height y i to height y f (without increasing velocity) => Work gets stored as gravitational potential energy ΔU = mg (yf -yi)= mg Δy ! • Free fall (no external force): Total energy conserved, change in kinetic energy compensated by change in m 2 potential energy ΔK.E. -
How Long Would the Sun Shine? Fuel = Gravitational Energy? Fuel
How long would the Sun shine? Fuel = Gravitational Energy? • The mass of the Sun is M = 2 x 1030 kg. • The Sun needs fuel to shine. – The amount of the fuel should be related to the amount of – The Sun shines by consuming the fuel -- it generates energy mass. from the fuel. • Gravity can generate energy. • The lifetime of the Sun is determined by – A falling body acquires velocity from gravity. – How fast the Sun consumes the fuel, and – Gravitational energy = (3/5)GM2/R – How much fuel the Sun contains. – The radius of the Sun: R = 700 million m • How fast does the Sun consume the fuel? – Gravitational energy of the Sun = 2.3 x 1041 Joules. – Energy radiated per second is called the “luminosity”, which • How long could the Sun shine on gravitational energy? is in units of watts. – Lifetime = (Amount of Fuel)/(How Fast the Fuel is – The solar luminosity is about 3.8 x 1026 Watts. Consumed) 41 26 • Watts = Joules per second – Lifetime = (2.3 x 10 Joules)/(3.8 x 10 Joules per second) = 0.6 x 1015 seconds. • Compare it with a light bulb! – Therefore, the Sun lasts for 20 million years (Helmholtz in • What is the fuel?? 1854; Kelvin in 1887), if gravity is the fuel. Fuel = Nuclear Energy Burning Hydrogen: p-p chain • Einstein’s Energy Formula: E=Mc2 1 1 2 + – The mass itself can be the source of energy. • H + H -> H + e + !e 2 1 3 • If the Sun could convert all of its mass into energy by • H + H -> He + " E=Mc2… • 3He + 3He -> 4He + 1H + 1H – Mass energy = 1.8 x 1047 Joules. -
1. Two Objects Attract Each Other Gravitationally. If the Distance Between Their Centers Is Cut in Half, the Gravitational Force A) Is Cut to One Fourth
MULTIPLE CHOICE REVIEW – GRAVITATION (Dynamics Part 3) 1. Two objects attract each other gravitationally. If the distance between their centers is cut in half, the gravitational force A) is cut to one fourth. B) is cut in half. C) doubles. D) quadruples 2. Two objects, with masses m1 and m2, are originally a distance r apart. The magnitude of the gravitational force between them is F. The masses are changed to 2m1 and 2m2, and the distance is changed to 4r. What is the magnitude of the new gravitational force? A) F/16 B) F/4 C) 16F D) 4F 3. As a rocket moves away from the Earth's surface, the rocket's weight A) increases. B) decreases. C) remains the same. D) depends on how fast it is moving. 4. A hypothetical planet has a mass of half that of the Earth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the Earth? A) g B) g/2 C) g/4 D) g/8 5. Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B? A) 0.707r B) r C) 1.41r D) 4r 6. A planet is discovered to orbit around a star in the galaxy Andromeda, with the same orbital diameter as the Earth around our Sun. If that star has 4 times the mass of our Sun, what will the period of revolution of that new planet be, compared to the Earth's orbital period? A) one-fourth as much B) one-half as much C) twice as much D) four times as much 7. -
Gravitational Potential Energy
An easy way for numerical calculations • How long does it take for the Sun to go around the galaxy? • The Sun is travelling at v=220 km/s in a mostly circular orbit, of radius r=8 kpc REVISION Use another system of Units: u Assume G=1 Somak Raychaudhury u Unit of distance = 1kpc www.sr.bham.ac.uk/~somak/Y3FEG/ u Unit of velocity= 1 km/s u Then Unit of time becomes 109 yr •Course resources 5 • Website u And Unit of Mass becomes 2.3 × 10 M¤ • Books: nd • Sparke and Gallagher, 2 Edition So the time taken is 2πr/v = 2π × 8 /220 time units • Carroll and Ostlie, 2nd Edition Gravitational potential energy 1 Measuring the mass of a galaxy cluster The Virial theorem 2 T + V = 0 Virial theorem Newton’s shell theorems 2 Potential-density pairs Potential-density pairs Effective potential Bertrand’s theorem 3 Spiral arms To establish the existence of SMBHs are caused by density waves • Stellar kinematics in the core of the galaxy that sweep • Optical spectra: the width of the spectral line from around the broad emission lines Galaxy. • X-ray spectra: The iron Kα line is seen is clearly seen in some AGN spectra • The bolometric luminosities of the central regions of The Winding some galaxies is much larger than the Eddington Paradox (dilemma) luminosity is that if galaxies • Variability in X-rays: Causality demands that the rotated like this, the spiral structure scale of variability corresponds to an upper limit to would be quickly the light-travel time erased. -
Gravitational Potential and Energy of Homogeneous Rectangular
View metadata, citationGravitational and similar papers potential at core.ac.uk and energy of homogeneous rectangular parallelepipedbrought to you by CORE provided by CERN Document Server Zakir F. Seidov, P.I. Skvirsky Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel Gravitational potential and gravitational energy are presented in analytical form for homogeneous right parallelepiped. PACS numbers: 01.55.+b, 45.20.Dd, 96.35.Fs Keywords: Newtonian mechanics; mass, size, gravitational fields I. INTRODUCTION: BASIC FORMULAE As it is well known, Newtonian gravitational potential, of homogeneous body with constant density ρ,atpoint (X,Y,Z) is defined as triple integral over the body's volume: ZZZ U(X; Y; Z)=Gρ u(X; Y; Z; x; y; z) dxdydz (1) with −1=2 u(X; Y; Z; x; y; z)=[(x − X)2 +(y − Y )2 +(z − Z)2] ;(2) here G stands for Newtonian constant of gravitation. In spite of almost 400-year-long attempts since Isaac Newton' times, the integral (1) is known in closed form (not in the series!) in quite a few cases [1]: a) a piece of straight line, b) a sphere, c) an ellipsoid; note that both cases a) and b) may be considered as particular cases of c). As to serial solution, the integral (1) is expressed in terms of the various kinds of series for external points outside the minimal sphere containing the whole body (non-necessary homogeneous), as well as for inner points close to the origin of co-ordinates. However in this note we do not touch the problem of serial solution and are only interested in exact analytical solution of (1). -
Mechanical Energy
Chapter 2 Mechanical Energy Mechanics is the branch of physics that deals with the motion of objects and the forces that affect that motion. Mechanical energy is similarly any form of energy that’s directly associated with motion or with a force. Kinetic energy is one form of mechanical energy. In this course we’ll also deal with two other types of mechanical energy: gravitational energy,associated with the force of gravity,and elastic energy, associated with the force exerted by a spring or some other object that is stretched or compressed. In this chapter I’ll introduce the formulas for all three types of mechanical energy,starting with gravitational energy. Gravitational Energy An object’s gravitational energy depends on how high it is,and also on its weight. Specifically,the gravitational energy is the product of weight times height: Gravitational energy = (weight) × (height). (2.1) For example,if you lift a brick two feet off the ground,you’ve given it twice as much gravitational energy as if you lift it only one foot,because of the greater height. On the other hand,a brick has more gravitational energy than a marble lifted to the same height,because of the brick’s greater weight. Weight,in the scientific sense of the word,is a measure of the force that gravity exerts on an object,pulling it downward. Equivalently,the weight of an object is the amount of force that you must exert to hold the object up,balancing the downward force of gravity. Weight is not the same thing as mass,which is a measure of the amount of “stuff” in an object. -
Tidal Tomography to Probe the Moon's Mantle Structure Using
Tidal Tomography to Probe the Moon’s Mantle Structure Using Lunar Surface Gravimetry Kieran A. Carroll1, Harriet Lau2, 1: Gedex Systems Inc., [email protected] 2: Department of Earth and Planetary Sciences, Harvard University, [email protected] Lunar Tides Gravimetry of the Lunar Interior VEGA Instrument through the Moon's PulSE • Gedex has developed a low cost compact space gravimeter instrument , VEGA (Vector (GLIMPSE) Investigation Gravimeter/Accelerometer) Moon • Currently this is the only available gravimeter that is suitable for use in space Earth GLIMPSE Investigation: • Proposed under NASA’s Lunar Surface Instrument and Technology Payloads • ca. 1972 MIT developed a space gravimeter (LSITP) program. instrument for use on the Moon, for Apollo 17. That instrument is long-ago out of • To fly a VEGA instrument to the Moon on a commercial lunar lander, via NASA’s production and obsolete. Commercial Lunar Payload Services (CLPS) program. VEGA under test in thermal- GLIMPSE Objectives: VEGA Space Gravimeter Information vacuum chamber at Gedex • Prove the principle of measuring time-varying lunar surface gravity to probe the lunar • Measures absolute gravity vector, with no • Just as the Moon and the Sun exert tidal forces on the Earth, the Earth exerts tidal deep interior using the Tidal Tomography technique. bias forces on the Moon. • Determine constraints on parameters defining the Lunar mantle structure using time- • Accuracy on the Moon: • Tidal stresses in the Moon are proportional to the gravity gradient tensor field at the varying gravity measurements at a location on the surface of the Moon, over the • Magnitude: Effective noise of 8 micro- Moon’s centre, multiplies by the distance from the Moon’s centre. -
How Stars Work: • Basic Principles of Stellar Structure • Energy Production • the H-R Diagram
Ay 122 - Fall 2004 - Lecture 7 How Stars Work: • Basic Principles of Stellar Structure • Energy Production • The H-R Diagram (Many slides today c/o P. Armitage) The Basic Principles: • Hydrostatic equilibrium: thermal pressure vs. gravity – Basics of stellar structure • Energy conservation: dEprod / dt = L – Possible energy sources and characteristic timescales – Thermonuclear reactions • Energy transfer: from core to surface – Radiative or convective – The role of opacity The H-R Diagram: a basic framework for stellar physics and evolution – The Main Sequence and other branches – Scaling laws for stars Hydrostatic Equilibrium: Stars as Self-Regulating Systems • Energy is generated in the star's hot core, then carried outward to the cooler surface. • Inside a star, the inward force of gravity is balanced by the outward force of pressure. • The star is stabilized (i.e., nuclear reactions are kept under control) by a pressure-temperature thermostat. Self-Regulation in Stars Suppose the fusion rate increases slightly. Then, • Temperature increases. (2) Pressure increases. (3) Core expands. (4) Density and temperature decrease. (5) Fusion rate decreases. So there's a feedback mechanism which prevents the fusion rate from skyrocketing upward. We can reverse this argument as well … Now suppose that there was no source of energy in stars (e.g., no nuclear reactions) Core Collapse in a Self-Gravitating System • Suppose that there was no energy generation in the core. The pressure would still be high, so the core would be hotter than the envelope. • Energy would escape (via radiation, convection…) and so the core would shrink a bit under the gravity • That would make it even hotter, and then even more energy would escape; and so on, in a feedback loop Ë Core collapse! Unless an energy source is present to compensate for the escaping energy.