Lecture 1-2: Properties of the Solar System
|
|
|
- Lorin Moore
- 7 years ago
- Views:
Transcription
1 Lecture 1-2: Prperties f the Slar System Tpics in this lecture: Planetary rbits Mass distributin Angular mmentum distributin Lecture 1-2: Prperties f the slar system
2 Prperties f the Slar System 1. Planets rbit rughly in the ecliptic plane. 2. Planetary rbits are slightly elliptical, and very nearly circular. 3. Planets and Sun revlve and rbit in a west-t-east directin. The planets bliquity (tilt f rtatin axes t their rbits) are small. Uranus and Venus are exceptins. 4. The planets differ in cmpsitin. Their cmpsitin varies rughly with distance frm the Sun: dense, metal-rich planets are in the inner part and giant, hydrgen-rich planets are in the uter part. 5. Meterites differ in chemical and gelgic prperties frm the planets and the Mn. 6. The rtatin rates f the planets and asterids are similar (5 t 15 hurs). 7. Planet distances frm the Sun bey Bde's law. 8. Planet-satellite systems resemble the slar system. 9. The Ort Clud and Edgewrth-Kuiper Belt f cmets. 10. Planets cntain ~99% f the slar system's AM but Sun cntains >99% f slar system's mass. Lecture 1-2: Prperties f the slar system
3 Orbits f the planets Planets mves arund the Sun in an rbit effected by the Sun s mass, and t a less extent, by ther bdies in the Slar System. Laws gverning planetary mtin was frmulated by Jhannes Kepler and based n Tych Brahe s bservatins. Kepler s Laws: 1. Planets have elliptical rbits with the Sun at ne fcus. 2. As a planet rbits, a line cnnecting the planet t the Sun sweeps ut equal areas in equal times. 3. The square f the rbital perid is prprtinal t the cube f the semimajr axis f the rbit. Lecture 1-2: Prperties f the slar system
4 Orbits f Planets Frm Physical Prcesses in the Slar System by J. Landstreet Lecture 1-2: Prperties f the slar system
5 Planetary Prperties Lecture 1-2: Prperties f the slar system
6 Helisphere (>100 AU frm Sun) Lecture 1-2: Prperties f the slar system
7 Kepler s 1 st Law: Law f Orbits Planets have elliptical rbits with the Sun at ne fcus. Equatin f ellipse: r + r = 2 a a is semimajr axis, b is semiminr axis f ellipse, F and F are fcal pint. Distance f fcus frm ellipse centre is a e, where e is the eccentricity: e = 0 => circle 0 < e < 1 => ellipse e = 1 => parabla e > 1 => hyperbla Lecture 1-2: Prperties f the slar system
8 Kepler s 1 st Law (cnt.) Implies that a planet s distance frm the Sun varies during its rbit. Clsest pint t Sun: perihelin. Farthest pint frm Sun: aphelin. Average f perihelin and aphelin is called the semimajr axis. Lecture 1-2: Prperties f the slar system
9 Elliptical rbits Cnsider a pint at either end f the semiminr axis where r = r. Using the Pythagrean Therem, r 2 = b 2 + (ae) 2 Setting r = a, we may write: a 2 = b 2 + a 2 e 2 => b 2 = a 2 (1 - e 2 ) r Relates semiminr axis t eccentricity and the semimajr axis. Lecture 1-2: Prperties f the slar system
10 Elliptical rbital path Frm figure belw, r 2 =r 2 sin 2 θ + (2ae + rcsθ) 2 Eqn 1 But as r + r = 2a r r = 2a - r, we may write r 2 = 4a 2-4ra + r 2 Eqn 2 Equating the RHS f Eqns 1 and 2: 4a 2-4ra + r 2 = r 2 sin 2 θ + (2ae + rcsθ) 2 = r 2 (sin 2 θ +cs 2 θ) + 4a 2 e 2 + 4aer csθ As sin 2 θ +cs 2 θ = 1 =>4a 2-4ra = 4a 2 e 2 + 4aer csθ Rearranging gives, r(θ) = a(1 e2 ) 1+ ecsθ Eqn 3 Fr 0<e<1, this is the equatin f an ellipse in plar crdinates. Lecture 1-2: Prperties f the slar system
11 Perihelin and aphelin distances If θ = 0, cs θ = 1 and r = a(1 e2 ) 1+ e The planet is at perihelin, the clsest pint t the Sun. = r = a(1 e) a(1 e)(1+ e) (1+ e) θ = 180 θ θ = 0 If θ = 180, cs θ = -1 and r = a(1 e2 ) 1 e = r = a(1+ e) a(1 e)(1+ e) (1 e) The planet at the aphelin, the mst distant pint frm the Sun. Example: The semimajr axis f Mars is AU and the eccentricity is What is the distance f Mars at perihelin? r = a(1-e) = ( ) = AU What is the distance f Mars at aphelin? Lecture 1-2: Prperties f the slar system
12 Kepler s 2 nd Law: Law f areas As a planet rbits, a line cnnecting the planet t the Sun sweeps ut equal areas in equal times. da dt = cnst => Planet mvies faster at perihelin. Lecture 1-2: Prperties f the slar system
13 Kepler s 2 nd Law: Law f areas Angular mmentum f planet: L = r p = m (r v). During Δt, radius vectr sweeps thrugh Δθ = v t Δt / r, where v t is the cmpnent f v perpendicular t r. During this time, the radius vectr has swept ut the triangle, f area A = rv t Δt / 2. As Δt - > 0, da/dt = rv t / 2 = 1 2 r 2 (dθ/dt). Nw, the magnitude f L is given by L = m v t r= m r 2 dθ/dt. F Δθ r ΔA v t v r v => da/dt = L / 2m = cnst i.e. the rate f sweeping ut area is a cnstant. Lecture 1-2: Prperties f the slar system
14 Kepler s 3 rd Law: Law f Perids The square f the rbital perid is prprtinal t the cube f the semimajr axis f the rbit: P 2 ~ a 3 P is the perid measured in years and a is the semimajr axis in AU. Cnsider m 1 and m 2 rbiting at r 1 and r 2. Bth cmplete ne rbit in perid P. Frces due t centripetal acceleratins are: F 1 = m 1 v 1 2 / r 1 = 4 π 2 m 1 r 1 / P 2 F 2 = m 1 v 2 2 / r 2 = 4 π 2 m 2 r 2 / P 2 r 1 r 2 v 2 using v = 2πr / P v 1 m 1 COM a m 2 Lecture 1-2: Prperties f the slar system
15 Kepler s 3 rd Law: Law f Perids As F 1 = F 2 => r 1 / r 2 = m 2 / m 1 (mre massive bdy rbits clser t centre f mass). r 1 r 2 v 2 m 1 Separatin f the bdies is a = r 1 + r 2, and r 1 = m 2 a / (m 1 + m 2 ) v 1 COM a m 2 Cmbining with F 1 and F = F 1 = F 2 = Gm 1 m 2 /a 2 : P 2 = 4 π 2 a 3 / G(m 1 + m 2 ) As M sun (= m 1 ) >> m planet (=m 2 ), cnst = 4 π 2 / GM Sun. Lecture 1-2: Prperties f the slar system
16 Bde s Law Empirical predictin f planet distances frm Sun. Begin with: 0, 3, 6, 12, 24, 48, 96, 192, 384 Planet Distance (AU) Mercury Bde s Law (AU) Nw add 4: 4, 7, 10, 16, 28, 52, 100, 196, 388 Then divide by 10: 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, 38.8 Sequence is clse t mean distances f planets frm the Sun. Venus Earth Mars Ceres Jupiter Bde s Law r Titus-Bde s Law: r n = n Saturn Uranus Lecture 1-2: Prperties f the slar system
17 Bde s Law (cnt.) r n = n n Planet Mercury Venus Earth Mars Ceres Jupiter Saturn Uranus s-m axis r n Lecture 1-2: Prperties f the slar system
18 Bde s Law (cnt.) Law lead Bde t predict existence f anther planet between Mars and Jupiter - asterids belt later fund. Uranus fitted law when discvered. Neptune was discvered in 1846 at the psitin predicted by Adams, t explain the deviatin f Uranus frm its predicted rbit. Plut s rbit when discvered in 1930 did nt fit the relatin. Nt a planet anymre! Planet Distance (AU) r n (AU) Uranus Neptune Plut Lecture 1-2: Prperties f the slar system
19 The Slar System t scale Lecture 1-2: Prperties f the slar system
20 Mass distributin The density f a planet is measured in g cm -3 (cgs units). Cnvenient because the density f water is 1 g cm -3. T determine vlume, need: Mass Density = Vlume 1. Distance frm Earth. 2. Angular extent f the planet. T determine the mass (frm Kepler s 3 rd Law) we need: 1. Mean Sun-planet separatin. 2. Orbital perid. Lecture 1-2: Prperties f the slar system
21 Mass Distributin (cnt.) The vlume is determined frm: V = 4/3 π R 3 where 2R = 2πdθ / 360. θ d 2R Mass determined frm Newtn s frm f Kepler s 3 rd Law: P 2 = 4 π 2 a 3 / G (m + M ) => m = ( 4 π 2 a 3 / G P 2 ) - M ρ = m / V g cm -3 Cmpare t: Crk: 0.2 Wd: 0.5 Water: 1.0 Basalt: 3.3 Lead: 11.0 Gld: 19.0 Lecture 1-2: Prperties f the slar system
22 Prperties f the planets Frm cnsideratin f size and density, can divide the planets int tw categries: 1. Terrestrial Planets Small size, high density and in the inner slar system. Mercury, Venus, Earth, Mars. 2. Jvian Planets Large size, lw density and in uter slar system: Jupiter, Saturn, Uranus, Neptune. Plut Plut is in categry f wn. It has small size and lw density. Lecture 1-2: Prperties f the slar system
23 Cmpressin vs. cmpsitin: The inner planets Frm their densities, inner planets likely t be cmpsed f rck and sme metal in cres. Might expect that planets less massive than the Earth wuld have lesser densities, because they are less cmpressed at the center by gravity. Amngst the terrestrial planets, this is true fr bth Mars and the Mn, which are bth smaller and less dense than the Earth. Venus is rughly the same size and density as Earth. But, Mercury is bth less massive and mre dense than the Earth. => Has Mercury a different cmpsitin than the Earth? Lecture 1-2: Prperties f the slar system
24 Cmpressin vs. cmpsitin: The uter planets What abut the densities f the uter planets? Might expect the uter planets, which are very massive, t be much mre cmpressed than the inner planets, and s mre dense. In fact, these heavier bdies are less dense than the inner, terrestrial planets. The nly cmpsitin which we can use t cnstruct such massive bdies with such lw densities is a mixture f hydrgen and helium, the tw lightest elements. The cmpsitin f the uter planets is hence mre similar t the Sun and stars than t the inner planets. Lecture 1-2: Prperties f the slar system
25 Angular mmentum distributin The Sun has a relatively slw rtatinal perid f ~26-days. => Like mst G-, K- and M-class stars. The rbital AM is: h rb = mvr = 2πmr 2 /P (r = distance) The spin AM f a inhmgeneus nnspherical rtating bdy is mre difficult t evaluate. The mass f the bdy is 4πρ ave R 3 /3, where R is the radius and ρ ave is the mean density. Lecture 1-2: Prperties f the slar system
26 Angular mmentum f the Sun An average density adpted fr Sun and it is assumed that mass is mstly within 0.6R. This is 0.72 fr a perfect sphere, but the Sun is blate. Mean density = 1.41 g cm -3 Mass = 2 x g Perid at equatr = 26.5 days = s Radius = 6.96 x cm The spin AM is therefre: h Sun = mvr = 4πρR3 3 2πr P R Setting R = 0.6R => Detailed mdelling gives ~1.7 x g cm 2 s -1. h Sun = mvr = 4πρ 2π 3 P (0.6R)5 =1.9ρR 5 /P = g cm 2 s 1 Lecture 1-2: Prperties f the slar system
27 Angular mmentum f the planets The rbital AM is: h rbit = 2πmr2 P Earth m = 5.97 x g r = 1 AU = 1.5 x cm P = 1 year Jupiter m = 1898 x g r = 5.2 AU = 5.2 x 1.5 x cm P = years Saturn m = 586 x g r =9.61 AU P = 29.5 years h rbit = 2π( )( ) = g cm 2 s 1 h rbit = g cm 2 s 1 h rbit = g cm 2 s 1 Jupiter therefre carries ~50% f the ttal AM f the Slar System, while the Jvian planets tgether make up ~99.27% f the ttal! Lecture 1-2: Prperties f the slar system
28 Angular mmentum distributin Planet Mass (x10 27 kg) Perid (years) AM (gcm 2 s -1 ) Mercury x10 45 Venus x10 47 Earth x10 47 Mars x % AM Jupiter x10 50 Saturn x10 49 Uranus x10 49 Neptune x10 49 Plut x % AM =>Sun nly has 0.4% f the ttal AM in slar system. Lecture 1-2: Prperties f the slar system
29 Orbital angular mmenta f the planets Nte the verwhelming imprtance f the Jvian planets. The symbl assciated with each planet: Lecture 1-2: Prperties f the slar system
30 Mass and AM distributins Althugh Sun cntains 99.9% f the mass f Slar System, the uter planets have 98% f system s angular mmentum. This is a serius prblem: material accreting nt the Sun cannt have retained all its riginal AM. There are tw parts t the prblem: 1. Hw des material lse AM and fall int the star in the first place? 2. Hw des the star lse AM and slw dwn? Slar-type stars all rtate at abut the same speed at the Sun. Lecture 1-2: Prperties f the slar system
Introduction. The activity
Teacher Ntes Intrductin The shift frm the gecentric t helicentric accunts f ur surrundings is ne f the greatest shifts ever made in human thinking, nt least because it verthrew the authrity f ld bks as
Coordinates. Definition of terms
Crdinates Definitin f terms C Lcal crdinates C Gegraphical C Latitude - angular measurement f a lcatin n Earth frm the equatr C Lngitude - angular measurement f a lcatin n Earth frm the Prime Meridian
Space Exploration Classroom Activity
Space Explratin Classrm Activity The Classrm Activity intrduces students t the cntext f a perfrmance task, s they are nt disadvantaged in demnstrating the skills the task intends t assess. Cntextual elements
Solar Geometry P L A N E O F S U N
1 Slar Gemetry The Earth s daily rtatin abut the axis thrugh its tw celestial ples (Nrth and Suth) is perpendicular t the equatr, but it is nt perpendicular t the plane f the Earth s rbit. In fact, the
Distribution of Globular Clusters and Young Star Groups on the Sky. x x x
PENN STATE ASTRONOMY LABORATORY è 11 THE STRUCTURE OF THE MILKY WAY GALAXY I. Objective In this lab, yu will learn that we live in the Milky Way Galay. Our slar system and all the stars yu can see with
Times Table Activities: Multiplication
Tny Attwd, 2012 Times Table Activities: Multiplicatin Times tables can be taught t many children simply as a cncept that is there with n explanatin as t hw r why it is there. And mst children will find
Chapter 6. Work and Energy
Chapter 6 Wrk and Energy 6. Wrk Dne by a Cnstant Frce Wrk invlves frce and displacement. W = Fs N! m = jule ( J) 6. Wrk Dne by a Cnstant Frce 6. Wrk Dne by a Cnstant Frce Mre general definitin f the wrk
Invisible Collisions
Invisible Cllisins Overview: This activity relates an elastic cllisin t the change in a satellite s r spacecraft s speed and directin resulting frm a planetary fly-by, ften called a gravity assist maneuver.
Born-Oppenheimer Approximation is the assumption that the electronic motion and the nuclear motion in molecules can be separated.
Rtatinal transitins Vibratinal transitins Electrnic transitins Brn-Oppenheimer Apprximatin is the assumptin that the electrnic mtin and the nuclear mtin in mlecules can be separated. This leads t mlecular
Gauss Law. AP Physics C
Gauss Law AP Physics C lectric Flux A Let's start be defining an area n the surface f an bject. The magnitude is A and the directin is directed perpendicular t the area like a frce nrmal. Flux ( r FLOW)
Lecture 13. Gravity in the Solar System
Lecture 13 Gravity in the Solar System Guiding Questions 1. How was the heliocentric model established? What are monumental steps in the history of the heliocentric model? 2. How do Kepler s three laws
Kinetic Molecular Theory of Gases/Ideal Gases. Kinetic Molecular Theory of Gases/Ideal Gases. Kinetic Molecular Theory of Gases/Ideal Gases
CHEMISTRY 000 Tpic #: Intermlecular Frces What Attracts Mlecules t Each ther? Spring 009 Prf. René Beré Kinetic Mlecular Thery f Gases/Ideal Gases In an ideal gas : The distance between gas particles (atms
From Aristotle to Newton
From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. The Geocentric Model Ancient Greek astronomers
astronomy 2008 1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times.
1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times. 5. If the distance between the Earth and the Sun were increased,
Gravitation and Newton s Synthesis
Gravitation and Newton s Synthesis Vocabulary law of unviversal Kepler s laws of planetary perturbations casual laws gravitation motion casuality field graviational field inertial mass gravitational mass
!"#$%&'()%"*#%*+,-./-*+01.2(.*3+456789*!"#$%&"'()'*+,-."/01&2#."'3424,'
"#$()"*#*+,-./-*+01.2(.*3+456789* "#$"()*+,-."/012#."3424, Dr. Peter T. Gallagher Astrphysics Research Grup Trinity Cllege Dublin :2";,
David Drivers Revit One-sheets: Linked Project Positioning and shared coordinates
This paper discusses the fllwing features f Revit Building Shared Crdinates Named lcatins Publish and acquire Vs Saving lcatins Shared Crdinates and wrkset enabled files Revisin 1 (Versin 9.0) David Driver.
Astronomy 1140 Quiz 1 Review
Astronomy 1140 Quiz 1 Review Prof. Pradhan September 15, 2015 What is Science? 1. Explain the difference between astronomy and astrology. (a) Astrology: nonscience using zodiac sign to predict the future/personality
Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13.
Chapter 5. Gravitation Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. 5.1 Newton s Law of Gravitation We have already studied the effects of gravity through the
MATHEMATICS FOR ENGINEERING TRIGONOMETRY TUTORIAL 1 TRIGONOMETRIC RATIOS, TRIGONOMETRIC TECHNIQUES AND GRAPHICAL METHODS
MATHEMATICS FOR ENGINEERING TRIGONOMETRY TUTORIAL 1 TRIGONOMETRIC RATIOS, TRIGONOMETRIC TECHNIQUES AND GRAPHICAL METHODS This is the ne f a series f basic tutrials in mathematics aimed at beginners r anyne
PIROUETT! June 2015 GENERALITIES
GENERALITIES 1.5.4. Penalty by the Difficulty (D) Judge: 0.50 pint if music with vice and wrds is used but the cach des nt specify n D frm which exercise uses music with vice and wrds Official Frm: Use
Unemployment, Gold, Money and Forecasts of Inflation
Carnegie Melln University Research Shwcase @ CMU Tepper Schl f Business 3-1996 Unemplyment, Gld, Mney and Frecasts f Inflatin Allan H. Meltzer Carnegie Melln University, am05@andrew.cmu.edu Fllw this and
Unit 8 Lesson 2 Gravity and the Solar System
Unit 8 Lesson 2 Gravity and the Solar System Gravity What is gravity? Gravity is a force of attraction between objects that is due to their masses and the distances between them. Every object in the universe
Combination of beams. Chapter 12 Treatment Planning Combination of Beams. Opposing pairs of beams. Opposing pairs of beams. Opposing pairs of beams
Chapter 12 Treatment Planning Cmbinatin f Beams Radiatin Dsimetry I Text: H.E Jhns and J.R. Cunningham, The physics f radilgy, 4 th ed. http://www.utled.edu/med/depts/radther Cmbinatin f beams Achieve
Experiment 1: Freezing Point Depression
Experiment 1: Freezing Pint Depressin Purpse: The purpse f this lab is t experimentally determine the freezing pint f tw slutins and cmpare the effect f slute type and cncentratin fr each slutin. Intrductin:
Lecture 19: Planet Formation I. Clues from the Solar System
Lecture 19: Planet Formation I. Clues from the Solar System 1 Outline The Solar System:! Terrestrial planets! Jovian planets! Asteroid belt, Kuiper belt, Oort cloud Condensation and growth of solid bodies
EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1
Instructor: L. M. Khandro EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 1. An arc second is a measure of a. time interval between oscillations of a standard clock b. time
Angular Velocity vs. Linear Velocity
MATH 7 Angular Velocity vs. Linear Velocity Dr. Neal, WKU Given an object with a fixed speed that is moving in a circle with a fixed ius, we can define the angular velocity of the object. That is, we can
Semester Exam Review Answers. 3. Construct a perpendicular at point B, then bisect the right angle that is formed. 45 o
Unit 1, Tpic 1 1. pint, line, and plane 2. angle bisectr cnstructin 3. Cnstruct a perpendicular at pint B, then bisect the right angle that is frmed. B 45 4. Draw a line thrugh pint H, then cpy the angle
Competitive Intelligence Report - Market Snapshot Explanations of Numbers Suggestions and Tips
Cmpetitive Intelligence Reprt - Market Snapsht Explanatins f Numbers Suggestins and Tips The infrmatin cntained in the tw sectins f the Cmpetitive Intelligence Reprt fr each gegraphic regin is f the highest
Writing a Compare/Contrast Essay
Writing a Cmpare/Cntrast Essay As always, the instructr and the assignment sheet prvide the definitive expectatins and requirements fr any essay. Here is sme general infrmatin abut the rganizatin fr this
Conduction in the Cylindrical Geometry
Cnductin in the Cylindrical Gemetry R. Shankar Subramanian Department f Chemical and Bimlecular Engineering Clarksn University Chemical engineers encunter cnductin in the cylindrical gemetry when they
Chapter 13 Properties of Gases Many chemical insights are gained by studying the simplest chemical phase, gases
Chapter 13 Prperties f Gases Many chemical insights are gained by studying the simplest chemical phase, gases 13-1 Gases Slid - fixed vlume and shape Liquid - fixed vlume but shape can change Gas - bth
Student Academic Learning Services Page 1 of 7. Statistics: The Null and Alternate Hypotheses. A Student Academic Learning Services Guide
Student Academic Learning Services Page 1 f 7 Statistics: The Null and Alternate Hyptheses A Student Academic Learning Services Guide www.durhamcllege.ca/sals Student Services Building (SSB), Rm 204 This
A. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great.
Q12.1 The mass of the Moon is 1/81 of the mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth is A. 81 2
The orbit of Halley s Comet
The orbit of Halley s Comet Given this information Orbital period = 76 yrs Aphelion distance = 35.3 AU Observed comet in 1682 and predicted return 1758 Questions: How close does HC approach the Sun? What
Orbital Dynamics with Maple (sll --- v1.0, February 2012)
Orbital Dynamics with Maple (sll --- v1.0, February 2012) Kepler s Laws of Orbital Motion Orbital theory is one of the great triumphs mathematical astronomy. The first understanding of orbits was published
Honors Geometry A. Semester Exam Review Answers 2015-2016
Hnrs Gemetry A 015-016 Unit 1, Tpic 1 1. pint, line, and plane. angle bisectr cnstructin 3. Cnstruct segment BC, then cnstruct the perpendicular bisectr f CC. C B C 4. Draw a line thrugh pint H, then cpy
Lesson 22. 3-Dimensional Solids. Objectives. Classify 3-Dimensional solids Determine the Volume of 3-Dimensional solids. Student Name: Date:
Student Name: Date: Cntact t Persn Name: Phne Number: Lessn -Dimensinal Slids Objectives Classify -Dimensinal slids Determine the Vlume f -Dimensinal slids Authrs: Jasn March,.A. Tim Wilsn,.A. Editr: Graphics:
GED MATH STUDY GUIDE. Last revision July 15, 2011
GED MATH STUDY GUIDE Last revisin July 15, 2011 General Instructins If a student demnstrates that he r she is knwledgeable n a certain lessn r subject, yu can have them d every ther prblem instead f every
Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X?
Solar System 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? A) Earth B) Sun C) Moon D) Polaris 2. Which object orbits Earth in both the Earth-centered
Planetary Orbit Simulator Student Guide
Name: Planetary Orbit Simulator Student Guide Background Material Answer the following questions after reviewing the Kepler's Laws and Planetary Motion and Newton and Planetary Motion background pages.
UNIT V. Earth and Space. Earth and the Solar System
UNIT V Earth and Space Chapter 9 Earth and the Solar System EARTH AND OTHER PLANETS A solar system contains planets, moons, and other objects that orbit around a star or the star system. The solar system
Work, Energy, and Power. AP Physics C
rk, Energ, and Pwer AP Phsics C There are man different TYPES f Energ. Energ is expressed in JOULES (J) 4.19 J 1 calrie Energ can be expressed mre specificall b using the term ORK() rk The Scalar Dt Prduct
1.3. The Mean Temperature Difference
1.3. The Mean Temperature Difference 1.3.1. The Lgarithmic Mean Temperature Difference 1. Basic Assumptins. In the previus sectin, we bserved that the design equatin culd be slved much easier if we culd
How do I evaluate the quality of my wireless connection?
Hw d I evaluate the quality f my wireless cnnectin? Enterprise Cmputing & Service Management A number f factrs can affect the quality f wireless cnnectins at UCB. These include signal strength, pssible
The Main Point. Lecture #34: Solar System Origin II. Chemical Condensation ( Lewis ) Model. How did the solar system form? Reading: Chapter 8.
Lecture #34: Solar System Origin II How did the solar system form? Chemical Condensation ("Lewis") Model. Formation of the Terrestrial Planets. Formation of the Giant Planets. Planetary Evolution. Reading:
USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION
USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION Ian Cooper School of Physics The University of Sydney i.cooper@physics.usyd.edu.au Introduction The numerical calculations performed by scientists and engineers
Time is Money Profiting from Reduced Cycle Time
Time is Mney Prfiting frm Reduced Cycle Time Yur retail custmers are demanding smaller, mre frequent shipments, which increases yur cst-t-serve them. While this makes their inventry mre predictable and
Chapter 25.1: Models of our Solar System
Chapter 25.1: Models of our Solar System Objectives: Compare & Contrast geocentric and heliocentric models of the solar sytem. Describe the orbits of planets explain how gravity and inertia keep the planets
Chapter 3: Cluster Analysis
Chapter 3: Cluster Analysis 3.1 Basic Cncepts f Clustering 3.1.1 Cluster Analysis 3.1. Clustering Categries 3. Partitining Methds 3..1 The principle 3.. K-Means Methd 3..3 K-Medids Methd 3..4 CLARA 3..5
Fixed vs. Variable Interest Rates
Fixed vs. Variable Interest Rates Understanding the Advantages and Disadvantages f Each Rate Type When shpping fr financial prducts, there are a lt f factrs t cnsider. Much has changed in the financial
Chapter 6 Formation of Planetary Systems Our Solar System and Beyond
Chapter 6 Formation of Planetary Systems Our Solar System and Beyond The solar system exhibits clear patterns of composition and motion. Sun Over 99.9% of solar system s mass Made mostly of H/He gas (plasma)
Background Information
Background Information The Second Law of Motion and The Law of Gravitation Student Activities 1. Round and Round They Go! 2. onic Sections - Movement in Newton s Gravitational orce Notes to Teachers Teacher
DIRECT DATA EXPORT (DDE) USER GUIDE
2 ND ANNUAL PSUG-NJ CONFERNCE PSUG-NJ STUDENT MANAGEMENT SYSTEM DIRECT DATA EXPORT (DDE) USER GUIDE VERSION 7.6+ APRIL, 2013 FOR USE WITH POWERSCHOOL PREMIER VERSION 7.6+ Prepared by: 2 TABLE OF CONTENTS
Science Unit: Twinkle, Twinkle Little Star
Science Unit: Lessn 5: Space Twinkle, Twinkle Little Star Schl year: 2006/2007 Develped fr: Develped by: Grade level: Duratin f lessn: Sexsmith Elementary Schl, Vancuver Schl District Luana Avila (scientist),
Lab 6: Kepler's Laws. Introduction. Section 1: First Law
Lab 6: Kepler's Laws Purpose: to learn that orbit shapes are ellipses, gravity and orbital velocity are related, and force of gravity and orbital period are related. Materials: 2 thumbtacks, 1 pencil,
My Academic Requirements and Degree Audit Report (pdf) Field Descriptions
My Academic s and Degree Audit Reprt Field Descriptins My Academic s and Degree Audit Reprt (pdf) Field Descriptins Imprtant Infrmatin Field descriptins f bth the nline My Academic s reprt and the Degree
Unit tests need to be supervised and the final exam invigilated.
Activating the Curse: Pre-Calculus 11 requires students t cmplete a threshld in rder t be cnsidered active in the curse. The threshld cnsists f the first tw assignments; Quadratic Functins 1 and Quadratic
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Why are celestial motions and forces important? They explain the world around
VAPOUR PRESSURE. Ranges of Vapour Pressures for some Important Classes of Organic Compounds at 25 o C
VAPOUR PRESSURE The r pressure (P ) is the pressure f the r f a cmpund in equilibrium with its pure cndensed phase (slid r liquid). Vapur pressures depend strngly n the temperature and vary widely with
Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law
Electrochemical cells
Electrchemical cells In this chapter, we turn ur attentin t electrn transfer reactins. T identify an electrn transfer reactins, we must assign xidatin states review rules in Chapter 3. e.g. Zn(s) Cu(NO
Newton s Law of Universal Gravitation
Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just two different versions of the same thing.
Success in Mathematics
Success in Mathematics Tips n hw t study mathematics, hw t apprach prblem-slving, hw t study fr and take tests, and when and hw t get help. Math Study Skills Be actively invlved in managing the learning
Honours in Psychological Sciences
Hnurs in Psychlgical Sciences (Mst f this is thanks t Stephen Bwden) Mst f it will be in the 4 th year manual when it is finalised (very snish) Curse structure a cmpulsry riginal supervised research prject
Getting Your Fingers In On the Action
Rry Garfrth Getting Yur Fingers In On the Actin Once yu are able t strum with yur fingers, yu can begin fingerpicking! The first task is t learn yur hand psitin and t learn which fingers are used n which
VARIABILITY OF TEC OVER AN EQUATORIAL STATION
XA0101446 VARIABILITY OF TEC OVER A EQUATORIAL STATIO J.O. Adeniyi 1 and S.M. Radicella 2 1 Physics Department, University f Ilrin, Ilrin, igeria 2 The Abdus Salam Internatinal Centre fr Theretical Physics,
Lecture 16: 11.04.05 Single-Component phase diagrams continued; Thermodynamics of solutions
Lecture 16: 11.04.05 Single-Cmpnent phase diagrams cntinued; Thermdynamics f slutins Tday: LAST TIME...2 Single-cmpnent phase diagrams and the Gibbs phase rule...2 Cnstraints n the shape f phase bundaries
Solar System Fundamentals. What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System
Solar System Fundamentals What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System Properties of Planets What is a planet? Defined finally in August 2006!
Equal Pay Audit 2014 Summary
Equal Pay Audit 2014 Summary Abut the dcument The fllwing summary is an abridged versin f Ofcm s equal pay audit 2014. In the full versin f the reprt we set ut ur key findings, cmment n any issues arising
Applied Spatial Statistics: Lecture 6 Multivariate Normal
Applied Spatial Statistics: Lecture 6 Multivariate Nrmal Duglas Nychka, Natinal Center fr Atmspheric Research Supprted by the Natinal Science Fundatin Bulder, Spring 2013 Outline additive mdel Multivariate
Volume of Snow and Water
Vlume f Snw and Water Grade Levels: 5th Length f Lessn Sequence: Tw 30 minute perids Brief Descriptin: Water and snw d nt have the same vlume because snwflakes have air pckets trapped inside. When snw
Disk Redundancy (RAID)
A Primer fr Business Dvana s Primers fr Business series are a set f shrt papers r guides intended fr business decisin makers, wh feel they are being bmbarded with terms and want t understand a cmplex tpic.
Newton s Law of Gravity
Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has
ENME599 1. I. The rotating system tested in this experiment can cause SERIOUS HARM if not properly operated. Therefore:
ENME599 LAB #5: Dynamics f a Single Rtr System!"#$%&"'()#'"(*%+$(",%(-+./*+"/*0(&'"*#2"/&()+&#+-(3*/*("/(",%(-+.('%''/&4((5,%(-+.(*%3/*"(',/#-$(.%(%",%*("03%$(/*( 2-%+*-0(6*""%&(+&$('#.)""%$(&(",%(7/--/6&8(-+.('%''/&4(9:&%(*%3/*"(3%*(8*/#3;4(5,%(2/)3#"%*(2/$%'(',/#-$(.%(
Licensing the Core Client Access License (CAL) Suite and Enterprise CAL Suite
Vlume Licensing brief Licensing the Cre Client Access License (CAL) Suite and Enterprise CAL Suite Table f Cntents This brief applies t all Micrsft Vlume Licensing prgrams. Summary... 1 What s New in This
Lecture 10 Formation of the Solar System January 6c, 2014
1 Lecture 10 Formation of the Solar System January 6c, 2014 2 Orbits of the Planets 3 Clues for the Formation of the SS All planets orbit in roughly the same plane about the Sun. All planets orbit in the
Introduction to the Solar System
Introduction to the Solar System Lesson Objectives Describe some early ideas about our solar system. Name the planets, and describe their motion around the Sun. Explain how the solar system formed. Introduction
Planets and Dwarf Planets by Shauna Hutton
Name: Wow! Technology has improved so well in the last several years that we keep finding more and more objects in our solar system! Because of this, scientists have had to come up with new categories
SUPPLEMENTARY TOPIC 1 STATES OF MATTER.
SUPPLEMENTARY TOPIC 1 STATES OF MATTER. States f matter. Matter is generally regarded as existing in three pssible phases - slid, liquid r gas. Fr example, water can be in the slid frm (ice) r the familiar
What Does Specialty Own Occupation Really Mean?
What Des Specialty Own Occupatin Really Mean? Plicy definitins are cnfusing, nt nly t cnsumers but als t many f the insurance prfessinals wh sell them. Belw we will try t prvide an understandable explanatin
CSE 231 Fall 2015 Computer Project #4
CSE 231 Fall 2015 Cmputer Prject #4 Assignment Overview This assignment fcuses n the design, implementatin and testing f a Pythn prgram that uses character strings fr data decmpressin. It is wrth 45 pints
Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law
Sensori and its Advantages
CAS 765 Fall 15 Mbile Cmputing and Wireless Netwrking Rng Zheng Andrid Sensing Subsystem Qiang Xu 2 What is a Sensr? A cnverter that measures a physical quantity and cverts it int a signal which can be
Class 2 Solar System Characteristics Formation Exosolar Planets
Class 1 Introduction, Background History of Modern Astronomy The Night Sky, Eclipses and the Seasons Kepler's Laws Newtonian Gravity General Relativity Matter and Light Telescopes Class 2 Solar System
Defining Sales Campaign Automation How e-mail, the Killer App, is best applied to marketing
Defining Sales Campaign Autmatin Hw e-mail, the Killer App, is best applied t marketing Summary: Cmpanies tday are steadily adpting strategies and technlgies t reach prspects, custmers, and partners thrugh
Binary Stars. Kepler s Laws of Orbital Motion
Binary Stars Kepler s Laws of Orbital Motion Kepler s Three Laws of orbital motion result from the solution to the equation of motion for bodies moving under the influence of a central 1/r 2 force gravity.
Motor Calculations. Calculating Mechanical Power Requirements Torque - Speed Curves Numerical Calculation Sample Calculation Thermal Calculations
Mtr Calculatins Calculating Mechanical Pwer Requirements Trque - Speed Curves Numerical Calculatin Sample Calculatin Thermal Calculatins Calculating Mechanical Pwer Requirements Physically, pwer is defined
Chris Chiron, Interim Senior Director, Employee & Management Relations Jessica Moore, Senior Director, Classification & Compensation
TO: FROM: HR Officers & Human Resurces Representatives Chris Chirn, Interim Senir Directr, Emplyee & Management Relatins Jessica Mre, Senir Directr, Classificatin & Cmpensatin DATE: May 26, 2015 RE: Annual
O5: Lenses and the refractor telescope
O5: Lenses and the reractr telescpe Intrductin In this experiment, yu will study cnverging lenses and the lens equatin. Yu will make several measurements the cal length lenses and yu will cnstruct a simple
Related Standards and Background Information
Related Standards and Background Information Earth Patterns, Cycles and Changes This strand focuses on student understanding of patterns in nature, natural cycles, and changes that occur both quickly and
3 Fluid flow in porous media
Fluid flw in prus media In Chapter we cnsidered hw t represent a particle size distributin by, where pssible, a single term that is representatie f all the particle sizes. This term may then be used fr
managing your student loan portfolio
managing yur student lan prtfli Table f cntents 2 Step 1. Cnsider Yur Payment Optins 4 Step 2. Ask Yurself: Is Lan Cnslidatin Right Fr Me? 5 Step 3. Determine What Lans Are In Yur Prtfli 7 Step 4. Estimate
The Gibbs Free Energy and Cell Voltage
The Gibbs Free Energy and Cell Vltage When an amunt f charge, Q, mves thrugh a ptential difference, E w = - Q E b/c wrk dne by the system E > 0 fr galvanic (vltaic) cells Recall, G = H TS = E + PV TS Fr
Study Guide: Solar System
Study Guide: Solar System 1. How many planets are there in the solar system? 2. What is the correct order of all the planets in the solar system? 3. Where can a comet be located in the solar system? 4.
Earth s Composition and Structure: A Journey to the Center of the Earth
Earth s Cmpsitin and Structure: A Jurney t the Center f the Earth Earth s Surface Our experience with Earth is limited t its surface. Yet Earth has a cmplicated interir. Earth is characterized by An internally
The Layout of the Solar System
The Layout of the Solar System Planets fall into two main categories Terrestrial (i.e. Earth-like) Jovian (i.e. Jupiter-like or gaseous) [~5000 kg/m 3 ] [~1300 kg/m 3 ] What is density? Average density
SEC FLASH REPORT. June 28, 2011
SEC FLASH REPORT The Securities and Exchange Cmmissin Issues Prpsal t Strengthen Audits and Reprting f Brker-Dealers t Prtect Custmer Assets and Requests Cmments June 28, 2011 On June 15, 2011, the U.S.
Military: Exemptions for Texas Veterans (Hazlewood Exemption) FAQs
Military: Exemptins fr Texas Veterans (Hazlewd Exemptin) FAQs What charges are cvered? What charges are nt cvered? Des the Hazlewd Act cver teacher certificatin fees? Des the Hazlewd Act cver credit by