VOL. 3, NO. 3, March 2013 ISSN ARPN Journal of Science and Technology All rights reserved.
|
|
- Alyson Arnold
- 5 years ago
- Views:
Transcription
1 A New Theory for Celestial Orbits Necat Taşdelen Dipl.Mech.Engineer, Istanbul-Turkey ABSTRACT Since Kepler s time (1609) we are educated to believe: Orbits of the planets are elliptical, with the Sun at one focus of this trajectory; that the ray Planet-Sun sweeps out equal area in equal interval of time; that a period law is valid. I claim the contrary. Clearly, it is difficult to agree with novelties, when the community is trained on wrong direction since 400 years. But, mathematics can clarify our understanding. According Newton s laws the orbits of celestial bodies are spiraled. After presenting the mathematical foundations I argue that our educational system about Keplerian math should be corrected. Keywords: Kepler laws, elliptic orbits, Newton laws, spiraled orbits, Celestial orbits 1. INTRODUCTION Fig.1 explains the vector components in physics Fig 1: Velocities, forces, works are all directional values: vectors. 2. CONSIDER NEWTON S (F*dt=m*dv) expression; (1) dwr=dfr*lr+fr*dlr dwp=dfp*lp+fp*dlp and we write Where F is a vector and its components are Fradial=Fr and Fperpendicular=Fp and, Work=F*Lwhere (L) is the displacement length;when differentiated (2) dwp=d(m*dvp/dt)*lp+(m*dvp/dt)*dlp In physics the work in the perpendicular direction to the attraction field equal zero. Fig.2 241
2 Fig 2: No work is done in the direction perpendicular to the attraction field direction So, dwp=0 and for this,we have to write dvp/dt=0 (3) 1/2*m*Vt1^2+m*a1*r1+m*Ct1=1/2*m*Vt2^2+m*a2*r 2+m*Ct2=Ct0 (7) (Vt) is a vector and Vt^2=Vradial^2+Vperpendicular^2. which means, when integrating That is: Vp=Ct (4) Kepler s law about the equality of swept out area in equal interval of time is not correct. Kepler says: (r* Vp =Ct) (area law which is pronounced as r and Vp variables) Newton laws say: (Vp = Ct) (no area law) What a claim! This is the basic of the following lines. 3. ON OTHER HAND, (TRAJECTORIES SHAPE) We know: Energy total= E.kinetic+E.potential =Constant (conserved) and we write 1/2*m*Vt^2+m*a*r+1/2*I*w^2= m*r*dvr/dt=ct0 (5) Also, knowing 1/2*I1*w1^2 =m*ct1=1/2*i2*w2^2=m*ct2 (6) as innate (no intervention since the existence) We write, Eliminating m*ct1=m*ct2 on both sides of the equality We write for any position of the planet in its solar system 1/2*m*Vr1^2+1/2*m*Vp1^2+m*a1*r1=1/2*m*Vr2^2+ 1/2*m*Vp2^2+m*a2*r2 (8) As from (4) 1/2*Vp1^2=1/2*Vp2^2 =Ct3, the expression (5) is written as (1/2*m*Vr^2+ m*ct3)+ m*a*r + m*ct1=m*r*dvr/dt=ct0 (9) Dividing both sides by (1/2*m), we have consecutively Vr^2+2*Ct3+2*a*r+2*Ct1=2*r*dVr/dt (Vt^2-Vp^2)+2*Ct3+2*a*r+2*Ct1=2*r*dVr/dt Vr^2+2*a*r+2*Ct1=2*r*dVr/dt (10) The differential form of (10) is r ^2+2*a*r+K=2*r*r (11) where (K=2*Ct1= I*w^2/m). The solution of (11) is r=-a*t^2+a*t*t+z(t) (12) 242
3 where T=Total life-time of the celestial body and the final equations are: Distances equation r=-a*t^2+a*t*t+z(t) (13) Radial velocity =Vr r =dr/dt=-2*a*t+a*t+z (14) Radial acceleration=dvr/dt) r =d(dr/dt)/dt=-2*a +Z (15) Perpendicular Velocity Vp=Constant (4) Perpendicular acceleration dvp/dt=0 (3) Equation (13) does not show any sign of ellipse, but a parabola on Cartesian, a spiraled shape projection on Polar. And that means the shapes of the orbits are not elliptical. The equation (12) is the equation of the planetary motion mathematically. Kepler says: planetary orbits are elliptical Newton laws say: planetary orbits are spiraled; Big difference 4. WHAT IS Z (T)? Consider the equation (11) r ^2+2*a*r+K=2*r*r where (K=2*Ct1= I*w^2/m). r=-a*t^2+a*t*t+z where, when t=0, r=zo constant The solution of (11) is (12). When displayed, and simplified a^2*t^2-2*a^2*t^2+2*a^2*t*t+2*a*z+k=-4*a*z written When (t=0 ) we write also: a^2*t^2+2*a*z+k=-4*a*zo K+a^2*T^2=-6*a*Zo Zo=-(K+a^2*T^2)/(6*a) replacing (Zo) in (13) r=-a*t^2+a*t*t-(k+a^2*t^2)/(6*a) a^2*t^2-2*a*(k+a^2*t^2)/(6*a)=4*a*(k+a^2*t^2)/(6*a) 3*a^2*T^2-6*a(..)/(6*a)=2*6*a(..)/(6*a) 3*a^2*T^2=3*( ) a^2*t^2=k+a^2*t^2 then, K=0 which means: when t=0, w=0, (K=I*w^2/m=0) Zo=-a*T^2/6 is found. We write the final distance equation (13) as: r=-a*t^2+a*t*t-a*t^2/6 (16) Equation (16) shows a multilayer spirals with variable amplitude. When (t=0) the distance is negative, indicating that the planets are born from the Sun: a maturation time inside the Sun, then (r=0) within a special time, then (w) is obtained. Orbiting life-time starts with the maturation. (Kind of pregnancy) Fig.2 shows Earth orbit on Cartesian (left) and its projection on polar (right),shortened to T=3 cycles. is Fig 3: Earth real orbit: birth to death; cycles reduced to 3 cycles for easy understanding of spiral shape. 243
4 5. COMMENTING THE MATHEMATICAL RESULTS FOR PHYSICS - Planets do not orbit the Sun on an elliptical trajectory. - The Sun is not at a focus of such elliptic orbit, but at the barycenter of the spirals.(heliocentric) - There is only one extreme (r) on these orbits; no aphelion, no perihelion. They do not exist. - As the Sun is travelling on its trajectory around the Milky Way, the spirals of the planets are placed on a volume envelope in the form of a parabolic along the Sun s trajectory. - The planet is born from the active Sun billions year ago by a small-bang.(t=0 ; r=zo ) - The moons are born from the active Sun-Planet also billions year ago by small-bangs. - Planet and its moons are in equilibrium inside their family system and acts as single mass. - Period law is not valid for Kepler s orbits, or for spiraled orbits. - Newton says: period law is valid for circular orbits with uniform peripheral velocity, - Kepler says: period law is valid also for elliptical orbit and accelerated motion on the orbit - Spiral theory says: as (r) and time are variables, there is not a constant period for the planets. Period definition is not valid but real time (t) should be considered for the comparison of (r). This is (r1/r2)=(vp1/vp2)^2. 6. CRACKING THE COMMENTS According Kepler, the planets were at their actual position since the beginning and will stay on these elliptical orbits for eternity, on a mathematically blocked, rigid mathematical ellipse.spiraled theory says: the planets are born from the active Sun with a small bang, their distance to the Sun is changing every second, their rotation around the Sun is obligatory a spiral and this rotation time is changing for each cycle. There is no period, but real time for one rotation. Period is a repeating time for repeating motion. There are not repeating celestial motions. As there is only one extreme (r) for the total life-time of the planet, Aphelion and Perihelion definitions are not valid. There is not a constant distances repetition for each cycle of the planet around the Sun. All distances start from zero, go to a maximum and then return back to zero. Like for a parabola on Cartesian, with Vx=Ct and VyMax=(2*a*rMax)^(1/2). Table I, shows the relative time, real time, special dates, formulary distance, corresponding distance, period variations, days in a cycle, for the planet Earth, according the data of era Table I 244
5 7. WHY DO THE PLANETS ORBIT THE SUN? When we say Fattraction=Fcentripetal, we mean equilibrium: G*m1*m2/d^2=m1*Vt1^2/r1=m2*Vt2^2/r2 Vt1 and Vt2 must exist for the equilibrium. This must make the planets orbit while attracting each other. Attraction is not linear due to Vt, but spiraled obligatory. Planet and their moons are considered as a family represented by (m1).fig 5 Fig 5: Obligatory orbits, where r*vp^2=ct for a given era is valid instead of period law. 8. EASY CONFIRMATION: (TRY IT TO BELIEVE) Have the data of the planets for era You find for all the planets, even for Halley and Pluto VpEarth^2*rEarth=(29,786 km/sec)^2*( km)= ,26 km^3/sec^2 VpMars^2*rMars=(24,131km/sec)^2*( km)= ,26 km^3/sec^2 Newton s period law never existed for celestial orbits, while it is correct for mechanical conditions. Kepler discovered the period laws in 1618 and used it for non-circular and accelerated motion. While, 50 years after Kepler, Newton proved that period law is valid only and only for circular movement with constant peripheral velocity. This is a discrepancy, which should be corrected today. In his book PRINCIPIA Newton researched to prove Kepler s discoveries. He did not confirm Kepler. But he found that celestial orbits should be spiraled. Unfortunately he refused spiraled orbit, due to his period law, thinking that on such orbits celestial bodies will go on ad infinitum.[1] As the bodies are at our reach for all evaluation, their orbit should not be spiraled, or hyperbolic or parabolic, he said. 245
6 But planets do not go on ad infinitum. They are located in finitum.[1] r= -4*t^2+4*t*T-4*T^2/6 is the sign of finite location. And (F attraction=f centripetal) means spirals. Due to the existence of Vp, the bodies do not attract each other like magnets on linear trajectories but on spiraled trajectories. No ellipse, anywhere. Fig.6 explains how spirals are formed around the Sun. Bodies are ejected from the Sun; even today But today's Sun is too weak for an expulsion of large bodies. Fig 6: Spirals around the Sun: with Parabolic steps in expansion and in contraction. There is only one extreme. Fig.7 is about a 3D view of the orbits from a galaxy. Spirals are enveloped by a Parabolic volume. Fig 7: Orbits seen from a galaxy outside of the Milky-way 246
7 9. CONCLUSİON Even these considerations necessitate the correction of our educational system. Clearly, it is difficult to agree with novelties, when the community is trained on wrong direction since 400 years. REFERENCES [1] Newton s PRINCIPIA, by A.MOTTE.page290 Author Profile NecatTaşdelen is Diplomedmech. Engineer; retired. In 1959 discovered the formula (a^s+b^s=l^s), a Thales theorem result, for the estimation of elliptical curves perimeter and similar. For an ellipse, the accuracy of the evaluations was error %=0, for the whole range: [1<(b/a)<infinity].The most accurate of that time; even today. 247
Are Kepler s elliptical orbits right?
P a g e 70 Vol.10 Issue 5(Ver 1.0)September 2010 Global Journal of Science Frontier Research Are Kepler s elliptical orbits right? Necat Taşdelen Abstract: Canonically, it is difficult to change the perception
More informationAre Kepler s Elliptical Orbits Right?
P a g e 70 Vol.10 Issue 5(Ver 1.0)September 2010 Are Kepler s Elliptical Orbits Right? Necat Tasdelen GJSFR Classification A (FOR) 020108,020109,020104 Abstract-Canonically, it is difficult to change the
More informationUnit 3 Lesson 2 Gravity and the Solar System. Copyright Houghton Mifflin Harcourt Publishing Company
Florida Benchmarks SC.8.N.1.4 Explain how hypotheses are valuable if they lead to further investigations, even if they turn out not to be supported by the data. SC.8.N.1.5 Analyze the methods used to develop
More informationWhat is the solar system?
Notes Astronomy What is the solar system? 11.1 Structure of the Solar System Our solar system includes planets and dwarf planets, their moons, a star called the Sun, asteroids and comets. Planets, dwarf
More informationO1 History of Mathematics Lecture V Newton s Principia. Monday 24th October 2016 (Week 3)
O1 History of Mathematics Lecture V Newton s Principia Monday 24th October 2016 (Week 3) Summary Isaac Newton (1642 1727) Kepler s laws, Descartes theory, Hooke s conjecture The Principia Editions and
More informationLESSON 1. Solar System
Astronomy Notes LESSON 1 Solar System 11.1 Structure of the Solar System axis of rotation period of rotation period of revolution ellipse astronomical unit What is the solar system? 11.1 Structure of the
More informationVISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLINE EXCEL SIMULATION MOTION OF SATELLITES DOWNLOAD the MS EXCEL program PA50satellite.xlsx and view the worksheet Display as shown in the figure below. One of the most important questions
More informationName Period Date Earth and Space Science. Solar System Review
Name Period Date Earth and Space Science Solar System Review 1. is the spinning a planetary object on its axis. 2. is the backward motion of planets. 3. The is a unit less number between 0 and 1 that describes
More informationIsaac Newton & Gravity
Isaac Newton & Gravity Isaac Newton was born in England in 1642 the year that Galileo died. Newton would extend Galileo s study on the motion of bodies, correctly deduce the form of the gravitational force,
More informationEarth in the Universe Unit Notes
Earth in the Universe Unit Notes The Universe - everything everywhere, 15-20 billion years old Inside the universe there are billions of Galaxies Inside each Galaxy there are billions of Solar Systems
More informationPHYSICS. Chapter 13 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 13 Lecture RANDALL D. KNIGHT Chapter 13 Newton s Theory of Gravity IN THIS CHAPTER, you will learn to understand the motion of satellites
More informationCosmic Landscape Introduction Study Notes
Cosmic Landscape Introduction Study Notes About how much bigger in radius is the Sun than the Earth? The ratio of the Sun's radius to the Earth's radius is 1,392,000/12756 = 109.1 How big is an astronomical
More informationKEPLER S LAWS OF PLANETARY MOTION
KEPLER S LAWS OF PLANETARY MOTION In the early 1600s, Johannes Kepler culminated his analysis of the extensive data taken by Tycho Brahe and published his three laws of planetary motion, which we know
More informationEEn Explain the Earth s motion through space, including precession, nutation, the barycenter, and its path about the galaxy.
EARTH IN SPACE EEn.1.1.1 Explain the Earth s motion through space, including precession, nutation, the barycenter, and its path about the galaxy. I Can Explain the origin of the Earth s motion based on
More informationASTRO 1050 LAB #3: Planetary Orbits and Kepler s Laws
ASTRO 1050 LAB #3: Planetary Orbits and Kepler s Laws ABSTRACT Johannes Kepler (1571-1630), a German mathematician and astronomer, was a man on a quest to discover order and harmony in the solar system.
More information1. The symbols below represent the Milky Way galaxy, the solar system, the Sun, and the universe.
Name Date 1. The symbols below represent the Milky Way galaxy, the solar system, the Sun, and the universe. 4. The diagram below illustrates three stages of a current theory of the formation of the universe.
More informationChapter 13. Gravitation
Chapter 13 Gravitation e = c/a A note about eccentricity For a circle c = 0 à e = 0 a Orbit Examples Mercury has the highest eccentricity of any planet (a) e Mercury = 0.21 Halley s comet has an orbit
More informationPhysics 12. Unit 5 Circular Motion and Gravitation Part 2
Physics 12 Unit 5 Circular Motion and Gravitation Part 2 1. Newton s law of gravitation We have seen in Physics 11 that the force acting on an object due to gravity is given by a well known formula: F
More informationPhys 214. Planets and Life
Phys 214. Planets and Life Dr. Cristina Buzea Department of Physics Room 259 E-mail: cristi@physics.queensu.ca (Please use PHYS214 in e-mail subject) Lecture 13. Midterm review February 4th, 2008 1. Astronomy
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 13. Newton s Theory of Gravity The beautiful rings of Saturn consist of countless centimeter-sized ice crystals, all orbiting the planet under the influence of gravity. Chapter Goal: To use Newton
More informationCH 8. Universal Gravitation Planetary and Satellite Motion
CH 8 Universal Gravitation Planetary and Satellite Motion Sir Isaac Newton UNIVERSAL GRAVITATION Newton: Universal Gravitation Newton concluded that earthly objects and heavenly objects obey the same physical
More informationF = ma. G mm r 2. S center
In the early 17 th century, Kepler discovered the following three laws of planetary motion: 1. The planets orbit around the sun in an ellipse with the sun at one focus. 2. As the planets orbit around the
More informationKepler's Laws and Newton's Laws
Kepler's Laws and Newton's Laws Kepler's Laws Johannes Kepler (1571-1630) developed a quantitative description of the motions of the planets in the solar system. The description that he produced is expressed
More informationChapter 13: universal gravitation
Chapter 13: universal gravitation Newton s Law of Gravitation Weight Gravitational Potential Energy The Motion of Satellites Kepler s Laws and the Motion of Planets Spherical Mass Distributions Apparent
More informationChapter 14 Satellite Motion
1 Academic Physics Mechanics Chapter 14 Satellite Motion The Mechanical Universe Kepler's Three Laws (Episode 21) The Kepler Problem (Episode 22) Energy and Eccentricity (Episode 23) Navigating in Space
More informationPhysics Unit 7: Circular Motion, Universal Gravitation, and Satellite Orbits. Planetary Motion
Physics Unit 7: Circular Motion, Universal Gravitation, and Satellite Orbits Planetary Motion Geocentric Models --Many people prior to the 1500 s viewed the! Earth and the solar system using a! geocentric
More informationAstronomy 1010 Planetary Astronomy Sample Questions for Exam 1
Astronomy 1010 Planetary Astronomy Sample Questions for Exam 1 Chapter 1 1. A scientific hypothesis is a) a wild, baseless guess about how something works. b) a collection of ideas that seems to explain
More informationJohannes Kepler ( ) German Mathematician and Astronomer Passionately convinced of the rightness of the Copernican view. Set out to prove it!
Johannes Kepler (1571-1630) German Mathematician and Astronomer Passionately convinced of the rightness of the Copernican view. Set out to prove it! Kepler s Life Work Kepler sought a unifying principle
More informationAstronomy Notes Chapter 02.notebook April 11, 2014 Pythagoras Aristotle geocentric retrograde motion epicycles deferents Aristarchus, heliocentric
Around 2500 years ago, Pythagoras began to use math to describe the world around him. Around 200 years later, Aristotle stated that the Universe is understandable and is governed by regular laws. Most
More informationAPS 1030 Astronomy Lab 79 Kepler's Laws KEPLER'S LAWS
APS 1030 Astronomy Lab 79 Kepler's Laws KEPLER'S LAWS SYNOPSIS: Johannes Kepler formulated three laws that described how the planets orbit around the Sun. His work paved the way for Isaac Newton, who derived
More informationVISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLINE PRACTICAL ACTIVITY HOW DO THE PANETS MOVE? One of the most important questions historically in Physics was how the planets move. Many historians consider the field of Physics to date
More informationTest Bank for Life in the Universe, Third Edition Chapter 2: The Science of Life in the Universe
1. The possibility of extraterrestrial life was first considered A) after the invention of the telescope B) only during the past few decades C) many thousands of years ago during ancient times D) at the
More informationObservational Astronomy - Lecture 4 Orbits, Motions, Kepler s and Newton s Laws
Observational Astronomy - Lecture 4 Orbits, Motions, Kepler s and Newton s Laws Craig Lage New York University - Department of Physics craig.lage@nyu.edu February 24, 2014 1 / 21 Tycho Brahe s Equatorial
More informationCosmic Microwave Background Radiation
Base your answers to questions 1 and 2 on the passage below and on your knowledge of Earth Science. Cosmic Microwave Background Radiation In the 1920s, Edwin Hubble's discovery of a pattern in the red
More informationASTRONOMY CURRICULUM Unit 1: Introduction to Astronomy
Chariho Regional School District - Science Curriculum September, 2016 ASTRONOMY CURRICULUM Unit 1: Introduction to Astronomy OVERVIEW Summary Students will be introduced to the overarching concept of astronomy.
More informationGravitation and the Waltz of the Planets
Gravitation and the Waltz of the Planets Chapter Four Guiding Questions 1. How did ancient astronomers explain the motions of the planets? 2. Why did Copernicus think that the Earth and the other planets
More informationGravitation and the Waltz of the Planets. Chapter Four
Gravitation and the Waltz of the Planets Chapter Four Guiding Questions 1. How did ancient astronomers explain the motions of the planets? 2. Why did Copernicus think that the Earth and the other planets
More informationAST111, Lecture 1b. Measurements of bodies in the solar system (overview continued) Orbital elements
AST111, Lecture 1b Measurements of bodies in the solar system (overview continued) Orbital elements Planetary properties (continued): Measuring Mass The orbital period of a moon about a planet depends
More informationThe first term involves the cross product of two parallel vectors and so it vanishes. We then get
Physics 3550 Angular Momentum. Relevant Sections in Text: 3.4, 3.5 Angular Momentum You have certainly encountered angular momentum in a previous class. The importance of angular momentum lies principally
More informationProjectile Motion. Conceptual Physics 11 th Edition. Projectile Motion. Projectile Motion. Projectile Motion. This lecture will help you understand:
Conceptual Physics 11 th Edition Projectile motion is a combination of a horizontal component, and Chapter 10: PROJECTILE AND SATELLITE MOTION a vertical component. This lecture will help you understand:
More informationThe Law of Ellipses (Kepler s First Law): all planets orbit the sun in a
Team Number Team Members Present Learning Objectives 1. Practice the Engineering Process a series of steps to follow to design a solution to a problem. 2. Practice the Five Dimensions of Being a Good Team
More informationGravitation and the Motion of the Planets
Gravitation and the Motion of the Planets 1 Guiding Questions 1. How did ancient astronomers explain the motions of the planets? 2. Why did Copernicus think that the Earth and the other planets go around
More informationConceptual Physics 11 th Edition
Conceptual Physics 11 th Edition Chapter 10: PROJECTILE AND SATELLITE MOTION This lecture will help you understand: Projectile Motion Fast-Moving Projectiles Satellites Circular Satellite Orbits Elliptical
More informationLecture 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
More informationAnnouncements. Topics To Be Covered in this Lecture
Announcements! Tonight s observing session is cancelled (due to clouds)! the next one will be one week from now, weather permitting! The 2 nd LearningCurve activity was due earlier today! Assignment 2
More informationLecture Outline. Chapter 13 Gravity Pearson Education, Inc. Slide 13-1
Lecture Outline Chapter 13 Gravity Slide 13-1 The plan Lab this week: exam problems will put problems on mastering for chapters without HW; will also go over exam 2 Final coverage: now posted; some sections/chapters
More informationSol o ar a r S yste t m e F o F r o m r at a i t on o The Ne N b e u b l u a a Hypothesis
Solar System Solar system- the sun and all objects that orbit the sun due to its gravity Solar System Formation The Nebula Hypothesis Parts of the Solar System Planet- a celestial body that is in orbit
More informationLecture 9(+10) Physics 106 Spring 2006
3/22/2006 Andrei Sirenko, NJIT 3 3/22/2006 Andrei Sirenko, NJIT 4 Lecture 9(+10) Physics 106 Spring 2006 Gravitation HW&R http://web.njit.edu/~sirenko/ Gravitation On Earth: the Earth gravitation dominates
More informationThe Universe. 3. Base your answer to the following question on The diagram below represents the bright-line spectrum for an element.
A) B) The Universe 1. According to the Big Bang theory, which graph hest represents the relationship between time and the size of the universe from the beginning of the universe to the present? C) D) 2.
More informationOutline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy. Hello!
PHY131H1F - Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe
More informationCONSERVATION OF ANGULAR MOMENTUM
CONSERVATION OF ANGULAR MOMENTUM Introduction Picture 1. Animation Two weights connected to pistons. Hydraulic machinery (not shown) pulls the weights closer to the center of rotation, causing angular
More informationlightyears observable universe astronomical unit po- laris perihelion Milky Way
1 Chapter 1 Astronomical distances are so large we typically measure distances in lightyears: the distance light can travel in one year, or 9.46 10 12 km or 9, 600, 000, 000, 000 km. Looking into the sky
More information5.1. Accelerated Coordinate Systems:
5.1. Accelerated Coordinate Systems: Recall: Uniformly moving reference frames (e.g. those considered at 'rest' or moving with constant velocity in a straight line) are called inertial reference frames.
More informationA SIMULATION OF THE MOTION OF AN EARTH BOUND SATELLITE
DOING PHYSICS WITH MATLAB A SIMULATION OF THE MOTION OF AN EARTH BOUND SATELLITE Download Directory: Matlab mscripts mec_satellite_gui.m The [2D] motion of a satellite around the Earth is computed from
More informationAstronomy 1143 Final Exam Review Answers
Astronomy 1143 Final Exam Review Answers Prof. Pradhan April 24, 2015 What is Science? 1. Explain the difference between astronomy and astrology. 2. What number is the metric system based around? What
More informationChapter 13. Gravitation. PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow
Chapter 13 Gravitation PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Next one week Today: Ch 13 Wed: Review of Ch 8-11, focusing
More informationUse conserved quantities to reduce number of variables and the equation of motion (EOM)
Physics 106a, Caltech 5 October, 018 Lecture 8: Central Forces Bound States Today we discuss the Kepler problem of the orbital motion of planets and other objects in the gravitational field of the sun.
More informationDownloaded from
Chapter 8 (Gravitation) Multiple Choice Questions Single Correct Answer Type Q1. The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on
More informationName: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016 Why are celestial motions and forces important? They explain the world around us.
More informationChapter 4 Thrills and Chills +Math +Depth Acceleration of the Moon +Concepts The Moon is 60 times further away from the center of Earth than objects on the surface of Earth, and moves about Earth in an
More informationMaking Sense of the Universe (Chapter 4) Why does the Earth go around the Sun? Part, but not all, of Chapter 4
Making Sense of the Universe (Chapter 4) Why does the Earth go around the Sun? Part, but not all, of Chapter 4 Based on part of Chapter 4 This material will be useful for understanding Chapters 8 and 11
More informationGravity and the Orbits of Planets
Gravity and the Orbits of Planets 1. Gravity Galileo Newton Earth s Gravity Mass v. Weight Einstein and General Relativity Round and irregular shaped objects 2. Orbits and Kepler s Laws ESO Galileo, Gravity,
More information14.1 Earth Satellites. The path of an Earth satellite follows the curvature of the Earth.
The path of an Earth satellite follows the curvature of the Earth. A stone thrown fast enough to go a horizontal distance of 8 kilometers during the time (1 second) it takes to fall 5 meters, will orbit
More informationNm kg. The magnitude of a gravitational field is known as the gravitational field strength, g. This is defined as the GM
Copyright FIST EDUCATION 011 0430 860 810 Nick Zhang Lecture 7 Gravity and satellites Newton's Law of Universal Gravitation Gravitation is a force of attraction that acts between any two masses. The gravitation
More informationOutline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy
PHY131H1F - Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe
More informationParticles in Motion; Kepler s Laws
CHAPTER 4 Particles in Motion; Kepler s Laws 4.. Vector Functions Vector notation is well suited to the representation of the motion of a particle. Fix a coordinate system with center O, and let the position
More informationASTR 150. Planetarium Shows begin Sept 9th. Register your iclicker! Last time: The Night Sky Today: Motion and Gravity. Info on course website
Planetarium Shows begin Sept 9th Info on course website Register your iclicker! Last time: The Night Sky Today: Motion and Gravity ASTR 150 Hang on tight! Most math all semester-- get it over with right
More information1 The Solar System. 1.1 a journey into our galaxy
1 The Solar System Though Pluto, and the far-flung depths of the Solar System, is the focus of this book, it is essential that Pluto is placed in the context of the planetary system that it inhabits our
More informationWelcome Aboard!! CHANGE OF KOMATSU S OFFICE HOURS. Briefing Welcome to the Cosmic Tour: Some Guide Lines. Lecture 1 Our Place in the Universe
CHANGE OF KOMATSU S OFFICE HOURS (Previous) Tuesdays & Thursdays 3:30 to 4:30 (New) Tuesdays 4:45 to 5:30 Thursdays 3:30 to 4:30 YOURNAME 31AUG Welcome Aboard!! AUSTIN AST 301 YOURNAME 31AUG 2.5 MILLION
More informationD. A system of assumptions and principles applicable to a wide range of phenomena that has been repeatedly verified
ASTRONOMY 1 EXAM 1 Name Identify Terms - Matching (20 @ 1 point each = 20 pts.) 1 Solar System G 7. aphelion N 14. eccentricity M 2. Planet E 8. apparent visual magnitude R 15. empirical Q 3. Star P 9.
More informationAstr 2320 Tues. Jan. 24, 2017 Today s Topics Review of Celestial Mechanics (Ch. 3)
Astr 2320 Tues. Jan. 24, 2017 Today s Topics Review of Celestial Mechanics (Ch. 3) Copernicus (empirical observations) Kepler (mathematical concepts) Galileo (application to Jupiter s moons) Newton (Gravity
More informationPHYS 155 Introductory Astronomy
PHYS 155 Introductory Astronomy - observing sessions: Sunday Thursday, 9pm, weather permitting http://www.phys.uconn.edu/observatory - Exam - Tuesday March 20, - Review Monday 6:30-9pm, PB 38 Marek Krasnansky
More information21/11/ /11/2017 Space Physics AQA Physics topic 8
Space Physics AQA Physics topic 8 8.1 Solar System, Orbits and Satellites The eight planets of our Solar System Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune As well as the eight planets, the
More informationPHYS 106 Fall 2151 Homework 3 Due: Thursday, 8 Oct 2015
PHYS 106 Fall 2151 Homework 3 Due: Thursday, 8 Oct 2015 When you do a calculation, show all your steps. Do not just give an answer. You may work with others, but the work you submit should be your own.
More informationTest 1 Review Chapter 1 Our place in the universe
Test 1 Review Bring Gator 1 ID card Bring pencil #2 with eraser No use of calculator or any electronic device during the exam We provide the scantrons Formulas will be projected on the screen You can use
More informationFormation of the Universe
A. The Universe 1. 2. 3. How did the universe begin? Only one exists or are there more? Composed of space and 100 billion galaxies A galaxy is a grouping of millions or billions of stars kept together
More informationFORCE. The 4 Fundamental Forces of Nature
FORCE - Force a push or pull. Results only from interaction with another object. Without interaction, forces cannot be present. - Measured in Newtons (N) 1 Newton is the amount of force required to give
More informationElliptic orbits and mercury perihelion advance as evidence for absolute motion
Elliptic orbits and mercury perihelion advance as evidence for absolute motion bstract March 03, 2013 Henok Tadesse, Electrical Engineer, BSc. ddress: Ethiopia, Debrezeit, Mobile phone: +251 910 751339
More informationBasics of Kepler and Newton. Orbits of the planets, moons,
Basics of Kepler and Newton Orbits of the planets, moons, Kepler s Laws, as derived by Newton. Kepler s Laws Universal Law of Gravity Three Laws of Motion Deriving Kepler s Laws Recall: The Copernican
More informationA CASE STUDY OF HIGH SCHOOL STUDENTS ASTROPHY- S ICAL CONCEPTION SURVEY ON THE KEPLER S SECOND LAW OF MOTIONS AND NEWTONIAN MECHANICS IN PHAYAO
Suranaree J. Sci. Technol. Vol. 22 No. 2; April - June 2015 135 A CASE STUDY OF HIGH SCHOOL STUDENTS ASTROPHY- S ICAL CONCEPTION SURVEY ON THE KEPLER S SECOND LAW OF MOTIONS AND NEWTONIAN MECHANICS IN
More informationSection 37 Kepler's Rules
Section 37 Kepler's Rules What is the universe made out of and how do the parts interact? That was our goal in this course While we ve learned that objects do what they do because of forces, energy, linear
More informationAstronomy- The Original Science
Astronomy- The Original Science Imagine that it is 5,000 years ago. Clocks and modern calendars have not been invented. How would you tell time or know what day it is? One way to tell the time is to study
More informationPosition 3. None - it is always above the horizon. Agree with student 2; star B never crosses horizon plane, so it can t rise or set.
Position 3 None - it is always above the horizon. N E W S Agree with student 2; star B never crosses horizon plane, so it can t rise or set. Imaginary plane No; the Earth blocks the view. Star A at position
More informationCircular Motion and Gravity Lecture 5
Circular Motion and Gravity Lecture 5 ˆ Today we talk about circular motion. There are two reasons to do this... ˆ Last week we talked about Newton s laws in problems dealing with straight-line motion.
More informationAstronomy A BEGINNER S GUIDE TO THE UNIVERSE EIGHTH EDITION
Astronomy A BEGINNER S GUIDE TO THE UNIVERSE EIGHTH EDITION CHAPTER 1 The Copernican Revolution Lecture Presentation 1.0 Have you ever wondered about? Where are the stars during the day? What is the near
More informationPhysical Science 1 Chapter 16 INTRODUCTION. Astronomy is the study of the universe, which includes all matter, energy, space and time.
INTRODUCTION Astronomy is the study of the universe, which includes all matter, energy, space and time. Although the universe is vast and almost beyond imagination, much is known about its make-up and
More informationOrbital Mechanics Laboratory
Team: Orbital Mechanics Laboratory Studying the forces of nature the interactions between matter is the primary quest of physics. In this celestial experiment, you will measure the force responsible for
More informationPHYS 160 Astronomy Test #1 Fall 2017 Version B
PHYS 160 Astronomy Test #1 Fall 2017 Version B 1 I. True/False (1 point each) Circle the T if the statement is true, or F if the statement is false on your answer sheet. 1. An object has the same weight,
More informationIntro to Astronomy. Looking at Our Space Neighborhood
Intro to Astronomy Looking at Our Space Neighborhood Astronomy: The Original Science Ancient cultures used the movement of stars, planets and the moon to mark time Astronomy: the study of the universe
More informationUnit 1: The Earth in the Universe
Unit 1: The Earth in the Universe 1. The Universe 1.1. First ideas about the Universe 1.2. Components and origin 1.3. Sizes and distances 2. The Solar System 3. The planet Earth 3.1. Movements of the Earth
More informationChapter 13. Universal Gravitation
Chapter 13 Universal Gravitation Planetary Motion A large amount of data had been collected by 1687. There was no clear understanding of the forces related to these motions. Isaac Newton provided the answer.
More informationEARTH SCIENCE UNIT 9 -NOTES ASTRONOMY
EARTH SCIENCE UNIT 9 -NOTES ASTRONOMY UNIT 9- ASTRONOMY 2 THE SOLAR SYSTEM I. The Solar System:. a. Celestial Body:. i. Examples:. b. MAIN COMPONENTS/MEMBERS OF THE SOLAR SYSTEM: i. 1. Planets are objects
More informationGravitation. Objectives. The apple and the Moon. Equations 6/2/14. Describe the historical development of the concepts of gravitational force.
Gravitation Objectives Describe the historical development of the concepts of gravitational force. Describe and calculate how the magnitude of the gravitational force between two objects depends on their
More information1 Summary of Chapter 2
General Astronomy (9:61) Fall 01 Lecture 7 Notes, September 10, 01 1 Summary of Chapter There are a number of items from Chapter that you should be sure to understand. 1.1 Terminology A number of technical
More informationChapter 13 Gravity Pearson Education, Inc. Slide 13-1
Chapter 13 Gravity Slide 13-1 The plan Lab this week: there will be time for exam problems Final exam: sections posted today; some left out Final format: all multiple choice, almost all short problems,
More informationWhat is a Satellite? A satellite is an object that orbits another object. Ex. Radio satellite, moons, planets
Planetary Orbit Planetary Orbits What shape do planets APPEAR to orbit the sun? Planets APPEAR to orbit in a circle. What shape do the planets orbit the sun??? Each planet Orbits the Sun in an ellipse
More informationRadial Acceleration. recall, the direction of the instantaneous velocity vector is tangential to the trajectory
Radial Acceleration recall, the direction of the instantaneous velocity vector is tangential to the trajectory 1 Radial Acceleration recall, the direction of the instantaneous velocity vector is tangential
More informationFirst exam next Wednesday. Today in class Review: Motion, Gravity. Gravity and Orbits. Review: Motion. Newton s Laws of Motion. Gravity and Orbits
Review: s of First exam next Wednesday Today in class Review:, Gravity Gravity and Gravity and Review: s of Review: Gravity and Newton s laws of motion Review: s of 1. Momentum (qualitative) 2. Force and
More informationExplanation: The escape velocity and the orbital velocity for a satellite are given by
1. A satellite orbits at a height h above the Earth's surface. Let R be the Earth's radius. If Ve is the escape velocity and Vo is the orbital velocity of the satellite orbiting at a height h
More information