2 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 describe the motions of planets in the solar system? 3. How does Newton s law of universal gravitation explain the motions of the planets?
3 13.1 Overview: from Copernicus to Newton The motions of the planets in the solar system provide one of the best examples of how physical laws to understand nature develop from observations. Copernicus first devised the framework of heliocentric model to explain the motions of the planets. Tyco s invaluable precise measurements were corner stones for Kepler and Newton s laws. Kepler established three laws to describe motions in the solar system Newton s law of universal gravitation
4 Copernicus used a geometric method to determine the distances of the planets relative to the Sun-Earth distance, i.e., in units of AU. He also figured out the synodic period from observations, and calculated the sidereal period of each planet. The sidereal period (P) of a planet, its true orbital period, is measured with respect to the stars. Its synodic period (S) is measured with respect to the Earth and the Sun (for example, from one conjunction to the next) A planet further from the Sun has a longer sidereal period.
5 Tycho Brahe s astronomical observations disproved ancient ideas about the heavens Tycho Brahe observing Tycho tried to find the distance of stars by observing parallax shifts. His comprehensive measurements of positions of planets put the heliocentric model on a solid foundation.
6 13.2 Kepler s Three Laws Johannes Kepler proposed elliptical paths for the planets about the Sun. Using data collected by Tycho Brahe, Kepler deduced three laws of planetary motion: 1. the orbits are ellipses 2. a planet s speed varies as it moves around its elliptical orbit 3. the orbital period of a planet is related to the size of its orbit Kepler s laws are a landmark in the history of astronomy. They are not only useful to understand planetary orbits, but are applied to celestial objects outside the solar system.
7 Kepler s First Law: the orbit of a planet is an ellipse with the Sun at one focus. semiminor semimajor ( ) e = (R a R p ) (R a + R p ) = R a R p 2a R a = distance at Aphelion R p = distance at Perihelion for a circle : R a = R p, e = 0 e: eccentricity
8 R P + R A = 2a perihelion R P R A aphelion A planet is at the Aphelion where it is farthest from the Sun, and at Perihelion when it is closest.
9 R P = b,r A = a perihelion b a aphelion This diagram is WRONG.
10 Kepler s Second Law: a line joining a planet and the Sun sweeps out equal areas in equal intervals of time. The speed of the orbital motion varies. It is smaller at Aphelion than at Perihelion. Ex 1: longitudinal libration of the Moon.
11 Kepler s Third Law: the square of the sidereal period of a planet is directly proportional to the cube of the semimajor axis of the orbit. P 2 = a 3 P = planet s sidereal period, in years a = planet s semimajor axis, in AU
12 Ex 2: A comet has a very long thin elliptical orbit. It is 2 AU from the Sun at the aphelion. What is its sidereal period? (a) 2.8 years (b) A bit shorter than 1 year (c) A bit longer than 1 year (d) cannot tell
13 Ex 3: Comet Halley orbits the Sun with a sidereal period of 76 years. (a) Find the semi-major axis of its orbit. (b) At aphelion, the comet is 35.4 AU away from the Sun. How far is it from the Sun at perihelion? (c ) what s the eccentricity of its orbit? (a) P 2 = 76 2 = 5776 = a 3, a = /3 = 18 (AU) R A + R P = 2a, R P = 2a - R A = 0.6 (AU) R A R P )/(R A + R P ) = ( )/36 = Comet Halley s orbit is very eccentric: the comet is 0.6 AU from the Sun at perihelion and 35.4 AU at aphelion.
14 13.3 Galileo s Discoveries Galileo s discoveries with a telescope strongly supported a heliocentric model. The invention of the telescope led Galileo to new discoveries that supported a heliocentric model. These included his observations of the phases of Venus and of the motions of four moons around Jupiter. Galileo s telescopic observations constituted the first fundamentally new astronomical data in almost 2000 years. His discoveries strongly suggested a heliocentric structure of the universe.
15 The phases of Venus: one of Galileo s most important discoveries with his telescope. Venus exhibits phases like those of the Moon. The apparent size of Venus is related to the planet s phase. Venus looks small at gibbous phase and large at crescent phase
16 A heliocentric model, in which both the Earth and Venus orbit the Sun, provides a natural explanation for the changing appearance of Venus.
17 Jupiter and its Largest Moons The orbital motions of Jupiter s moons around Jupiter resemble the motions of the planets around the Sun.
18 13.4 Newton s Law of Universal Gravitation Newton s Law of Universal Gravitation accounts for Kepler s laws and explains the motions of the planets. F G = G mm r 2 F = gravitational force between two objects (in newtons) m = mass of the planet (in kilograms) M = mass of the Sun (in kilograms) r = distance between planet and Sun (in meters) G = newton m 2 /kg 2, universal constant of gravitation F G ~ M, m F G ~ 1/r 2
19 Newton s form of Kepler s third law The gravitational (pull or attractive) force keeps the planets orbiting the Sun and satellites orbiting the planets. F = mω 2 r = 4π 2 mr P 2 = F G Newton demonstrated that Kepler s third law follows logically the law of gravity, and can be re-written as: a 3 = GM 4π 2 P 2 P = sidereal period, in seconds a = semimajor axis, in meters M = mass of the Sun, in kg G = universal constant of gravitation = 6.67 x Scaling the equation to Sun-Earth system: Kepler s third law.
20 Ex 4: Sun s gravitational force to Earth is F 1. The gravitational force of Earth to Sun is F 2. F 1 is 300,000 times F 2, since the mass of Sun is 300,000 times the mass of Earth. True or false? However, acceleration of an object by a force is inversely proportional to its mass; therefore, subject to the same amount of gravitational force, the Sun (star) only wobbles a little bit. An object in an orbital motion, such as the planet revolving about the Sun, is accelerated by the gravitational force. An acceleration changes the magnitude and/or direction of a velocity.
21 Gravitational force by the Sun provides the centripetal force that maintains the orbital motion of a planet around the Sun. Ex 5: (assume the orbit is circular) If the mass of the Sun were greater by a factor of 4, while a planet s orbit size remained the same, would the planet revolve faster or slower? By how much? a 3 = GM 4π 2 P 2 Ex 6: (assume the orbit is circular) If the mass of the Sun were greater by a factor of 4, and a planet s sidereal period remained the same, would the planet be closer to the Sun or farther away from the Sun? By how much? Would the planet move faster on its orbit?
22 Scaling Newton s law of planet motion to the Sun-Earth system, we obtain Kepler s third law. a 3 Planet = GM Sun 4π 2 a 3 Earth = GM Sun 4π 2 a Planet a Earth 3 P Planet P Earth = P Planet P Earth This same scaling relation applies to asteroids and comets that revolve around the Sun
23 Newton s form of Kepler s third law applies to all situations where two objects orbit each other solely under the influence of their mutual gravitational attraction. Ex 7: Europa s orbital period around Jupiter is twice that of Io. Calculate the distance of Europa from Jupiter relative to Io s distance to Jupiter. a 3 Io = GM Jupiter 2 4π 2 P Io a 3 Europa = GM Jupiter 4π 2 a Europa =1.6a Io = GM Jupiter 4π 2 2 P Europa 2P Io ( ) 2 = 4a Io 3
24 Ex 8: The distance of the outer edge of Saturn s A ring is about twice the distance of the inner edge of Saturn s C ring. a. A ring particle (A) at the outer edge of A ring revolves faster than a ring particle (C) at the inner edge of C ring by a factor of about 3. b. (A) revolves slower than (C) by a factor of 3. c. (A) revolves faster by a factor of 2. d. (A) revolves slower by a factor of 2.
25 Ex 9 [previous year s final exam]: Suppose that we discover another moon called Koon orbiting the Earth in an elliptical orbit with a period of 8 months. It is further found that the apparent size of Koon at perihelion is 3 times its apparent size at aphelion. Find the semi-major axis, aphelion distance, and perihelion distance of Koon s orbit as how many times the Earth-Moon distance. [HW A1] Hint: (a) Kepler s third law but scaled to Earth-Moon system; (b) Kepler s first law. a 3 Moon = GM Earth 4π 2 P Moon a 3 Koon = GM Earth 4π 2 P Koon 2 2 a Koon a Moon 3 = P Koon P Moon 2
26 Newton s form of Kepler s third law may be used to find the mass of celestial objects in a binary system. Ex 10: astronomers discovered an exoplanet orbiting a star. They measured the distance of the planet to the star to be 5 AU and the orbit period of the planet to be 2 earth years. From these measurements, can you tell what is the mass of the star in units of solar mass? using Newton's form of Kepler's third law for the exoplanet : a 3 p = GM star 4π 2 P p And for Earth : a 3 E = GM sun 4π 2 P E scale the two equations, we get : a p a E 3 = M star P p M sun P E 2, so : 2 M star M sun = a p ae P p PE 3 2 = 31 2
27 (optional) Ex 11: precisely, in a binary system, both objects orbit about their center of mass with the same angular speed star wobbles due to planet perturbation! The exact Newton s form of Kepler s laws yields the total mass of the binary system. Exact Newton's form of Kepler's third law : a 3 = G(m + m ) 1 2 4π 2 P 2 P : orbital period of the binary a : semi - major axis of the ellipse made by the separation of the objects Motion of each of the binary members is given by the ellipse of the same eccentricity, but scaled down according to their mass ratio. P 1 = P 2, a 1 = m 2 m 1 + m 2 a, a 2 = m 1 m 1 + m 2 a, a 1 a 2 = m 2 m 1, v 1 v 2 = m 2 m 1
28 13.5 Gravity in the Solar System Solar/stellar system is formed by gravitational contraction. gravitational force between two objects: F G = G mm d 2 gravitational energy in a binary system: U = - G mm d gravitational energy of a mass M and radius R : U= 3 5 M 2 G R With decreasing R, U is converted to internal heat. Kelvin-Helmholtz contraction provides energy for protostars before fusion ignition, and is still converting gravitational energy to internal heat in Jupiter.
29 Particles with low speed are retained by gravity. 1 2 mv 2 G Mm (R + h) 2 v esc = 2GM R + h 2GM R Ex 12: launching satellite on Earth Ex 13: capture of the atmosphere by a planet (N.B.: compare 6v th and v esc )
30 Tidal force (differential gravitational force) accounts for many phenomena in the solar system. The tidal force by a planet mass M on the unit mass at two edges of a satellite of radius R and distance d. f tidal = G 4MR d 3 Ex 14: examples of tidal force effect in the solar system. - tides on earth; tidal bulges of planets and moons; - synchronous rotation of many moons in the solar system - 3-to-2 spin-to-orbit coupling of Mercury s motion - future of Moon and Triton - tidal heating of Jovian moons - Roche limit and Jovian rings
31 Gravity shapes the solar system in many ways. Ex 15: shepherd satellites and gaps in Saturn s rings. Ex 16: formation and configuration of asteroid belt. Ex 17: At Lagrange points L1 and L2, an object and Mass2 orbit Mass1 with the same rate. How does that happen? HW-A2
32 Key Words ellipse gravitational force heliocentric model Kepler s laws law of equal areas law of universal gravitation major axis Newton s form of Kepler s third law semimajor axis sidereal period synodic period universal constant of gravitation
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
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
Solar Eclipses The Sun disappears behind the Moon The Moon is always in the New phase during a solar eclipse Can only be seen from certain places on Earth These events are even more rare than lunar eclipses
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
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
Today Galileo Planetary Motion Tycho Brahe s Observations Kepler s Laws 1 Galileo c. 1564-1642 First telescopic astronomical observations 2 First use of telescope for astronomy in 1609 400 years ago! 3
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
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
Vocabulary - Understanding Revolution in Universe Galaxy Solar system Planet Moon Comet Asteroid Meteor(ite) Heliocentric Geocentric Satellite Terrestrial planets Jovian (gas) planets Gravity our Solar
Exam 1 Ast 4 - Chapter 2 - Newton s Laws Exam 1 is scheduled for the week of Feb 19th Bring Pencil Scantron 882-E (available in the Bookstore) A scientific calculator (you will not be allowed to use you
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
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!
Chapter 7 Circular Motion and Gravitation 7.1 Calculate force of gravity using Newton s Law of Universal Gravitation. 5. What is the gravitational force between the Earth and the Sun? (Mass of Earth: 5.98
Kepler s Laws and our Solar System The Astronomical Unit, AU Kepler s Empirical Laws of Planetary mo=on The mass of the Sun, M O. A very brief tour of the solar system Major planets Dwarf planets (defini=on)
USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION Ian Cooper School of Physics The University of Sydney firstname.lastname@example.org Introduction The numerical calculations performed by scientists and engineers
Unit 4 The Solar System Chapter 7 ~ The History of the Solar System o Section 1 ~ The Formation of the Solar System o Section 2 ~ Observing the Solar System Chapter 8 ~ The Parts the Solar System o Section
Chapter 13 Newton s Theory of Gravity Chapter Goal: To use Newton s theory of gravity to understand the motion of satellites and planets. Slide 13-2 Chapter 13 Preview Slide 13-3 Chapter 13 Preview Slide
Orbital Mechanics The objects that orbit earth have only a few forces acting on them, the largest being the gravitational pull from the earth. The trajectories that satellites or rockets follow are largely
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
Newton s Law of Gravity Example 4: What is this persons weight on Earth? Earth s mass = 5.98 10 24 kg Mar s mass = 6.4191 10 23 kg Mar s radius = 3400 km Earth s radius = 6378 km Newton s Form of Kepler
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.
Chapter 5: Circular Motion, the Planets, and Gravity 1. Earth s gravity attracts a person with a force of 120 lbs. The force with which the Earth is attracted towards the person is A. Zero. B. Small but
Exercises 131 The Falling Apple (page 233) 1 Describe the legend of Newton s discovery that gravity extends throughout the universe According to legend, Newton saw an apple fall from a tree and realized
AE554 Applied Orbital Mechanics Hafta 1 Egemen Đmre A bit of history the beginning Astronomy: Science of heavens. (Ancient Greeks). Astronomy existed several thousand years BC Perfect universe (like circles
Chapter 3 The Science of Astronomy Days of the week were named for Sun, Moon, and visible planets. What did ancient civilizations achieve in astronomy? Daily timekeeping Tracking the seasons and calendar
Newton's Laws Before Isaac Newton Newton's Laws There were facts and laws about the way the physical world worked, but no explanations After Newton There was a unified system that explained those facts
LESSON 3 THE SOLAR SYSTEM Chapter 8, Astronomy OBJECTIVES Identify planets by observing their movement against background stars. Explain that the solar system consists of many bodies held together by gravity.
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.
The moon is essentially gray, no color. It looks like plaster of Paris, like dirty beach sand with lots of footprints in it. -James A. Lovell (from the Apollo 13 mission) David J. Starling Penn State Hazleton
Copyright 2011 Study Island - All rights reserved. Directions: Challenge yourself! Print out the quiz or get a pen/pencil and paper and record your answers to the questions below. Check your answers with
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
Exam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti INSTRUCTIONS: Please, use the `bubble sheet and a pencil # 2 to answer the exam questions, by marking
Periods of Western Astronomy Chapter 1 History of Astronomy Western astronomy divides into 4 periods Prehistoric (before 500 B.C.) Cyclical motions of Sun, Moon and stars observed Keeping time and determining
Tidal Forces and their Effects in the Solar System Richard McDonald September 10, 2005 Introduction For most residents of Earth, tides are synonymous with the daily rise and fall of sea levels, and there
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.
The Motions of Celestial Bodies, and Newton s Laws of Motion Announcements The results of Quiz 1 are posted in OWL Looking ahead: Homework 1 is on-going, and is due on Thu, Sept. 29 th ; Homework 2 will
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
SKYTRACK Glossary of Terms Angular distance The angular separation between two objects in the sky as perceived by an observer, measured in angles. The angular separation between two celestial objects in
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
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
Newton s Law of Gravity and Kepler s Laws Michael Fowler Phys 142E Lec 9 2/6/09. These notes are partly adapted from my Physics 152 lectures, where more mathematical details can be found. The Universal
1 DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION Daniel S. Orton email: email@example.com Abstract: There are many longstanding
Celestial Mechanics: The Why of Planetary Motions Attempts to Describe How Celestial Objects Move Aristotle, Hipparchus, and Ptolemy: The Ptolemaic System Aristarchus, Copernicus, and Kepler: The Copernican
Lab 7: Gravity and Jupiter's Moons Image of Galileo Spacecraft Gravity is the force that binds all astronomical structures. Clusters of galaxies are gravitationally bound into the largest structures in
Understanding the motion of the Universe Motion, Force, and Gravity Laws of Motion Stationary objects do not begin moving on their own. In the same way, moving objects don t change their movement spontaneously.
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
Solar System Formation Background Information System: Many pieces that make up a whole Solar System: Anything that orbits the Sun Just like in the formation of of stars.. Gravity plays a major role. Gravitational
IB PHYSICS: Gravitational Forces Review 1. This question is about gravitation and ocean tides. (b) State Newton s law of universal gravitation. Use the following information to deduce that the gravitational
Kepler s Laws and Gravity Ian Morison Observations of a supernova. Tycho made detailed observations of the supernova of 1572 now called Tycho s supernova. It was initially brighter than Venus and was visible
THE SOLAR SYSTEM - EXERCISES 1 THE SUN AND THE SOLAR SYSTEM Name the planets in their order from the sun. 1 2 3 4 5 6 7 8 The asteroid belt is between and Which planet has the most moons? About how many?
Star: ASTRONOMICAL OBJECTS ( 4). Ball of gas that generates energy by nuclear fusion in its includes white dwarfs, protostars, neutron stars. Planet: Object (solid or gaseous) that orbits a star. Radius
Chap. 7, #40 Homework #3 Solutions ASTR100: Introduction to Astronomy Fall 2009: Dr. Stacy McGaugh Which of the following is a strong greenhouse gas? A) Nitrogen. B) Water Vapor. C) Oxygen) The correct
The Solar System What is the solar system? It is our Sun and everything that travels around it. Our solar system is elliptical in shape. That means it is shaped like an egg. Earth s orbit is nearly circular.
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.
Unit 11: Gravity & the Solar System Inquiry Physics www.inquiryphysics.org Historical development Kepler s Laws Newton s Universal Gravitation Next 11: Gravity & the Solar System Historical development
CHAPTER 4 1 The Nine Planets SECTION A Family of Planets BEFORE YOU READ After you read this section, you should be able to answer these questions: What are the parts of our solar system? When were the
Monografías de la Real Academia de Ciencias de Zaragoza. 25: 115 120, (2004). Extra-solar massive planets with small semi-major axes? S. Fernández, D. Giuliodori and M. A. Nicotra Observatorio Astronómico.
The Formation of Planetary Systems Astronomy 1-1 Lecture 20-1 Modeling Planet Formation Any model for solar system and planet formation must explain 1. Planets are relatively isolated in space 2. Planetary
Lecture Outlines Chapter 15 Astronomy Today 7th Edition Chaisson/McMillan Chapter 15 The Formation of Planetary Systems Units of Chapter 15 15.1 Modeling Planet Formation 15.2 Terrestrial and Jovian Planets
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
Figure 12.4 physics of biomolecular chemistry and structures under stress e.g. protein conformations protein-protein bonds cell membranes unfolding/refolding single bond kinetics pore formation strength
Computer Practical: Solar System Model Paul Connolly, September 015 1 Overview In this computer practical, a solar system model implemented in MATLAB is used to demonstrate analysis of time-series data
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
Tidal forces in the Solar System Introduction As anywhere else in the Universe, gravity is the basic and fundamental principle that rules the shape and permanent motion of all the celestial bodies inside
FOCUS Book Design a test to find out whether Earth s gravity always pulls straight down. A pendulum is a weight that hangs from a string or rod that can swing back and forth. Use string and metal washers
Astronomy 114 Summary of Important Concepts #1 1 1 Kepler s Third Law Kepler discovered that the size of a planet s orbit (the semi-major axis of the ellipse) is simply related to sidereal period of the
NOTES: GEORGIA HIGH SCHOOL SCIENCE TEST THE SOLAR SYSTEM 1.What is a Solar system? A solar system consists of: * one central star, the Sun and * nine planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn,
Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G = 6.67
14b. Pluto, Kuiper Belt & Oort Cloud Pluto Pluto s moons The Kuiper Belt Resonant Kuiper Belt objects Classical Kuiper Belt objects Pluto Data: Numbers Diameter: 2,290.km 0.18. Earth Mass: 1.0. 10 22 kg
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:
8.5 Motions of, the, and Planets axis axis North Pole South Pole rotation Figure 1 s axis is an imaginary line that goes through the planet from pole-to-pole. orbital radius the average distance between
Chapter 7 Our Planetary System Agenda Pass back & discuss Test 2 Where we are (at) Ch. 7 Our Planetary System Finish Einstein s Big Idea Earth, as viewed by the Voyager spacecraft A. General Basics Intro
Imperial College London BSc/MSci EXAMINATION June 2008 This paper is also taken for the relevant Examination for the Associateship SUN, STARS, PLANETS For Second Year Physics Students Wednesday, 4th June
Grade 6 Standard 3 Unit Test A Astronomy Multiple Choice 1. The four inner planets are rocky and small. Which description best fits the next four outer planets? A. They are also rocky and small. B. They
CELESTIAL MOTIONS Stars appear to move counterclockwise on the surface of a huge sphere the Starry Vault, in their daily motions about Earth Polaris remains stationary. In Charlottesville we see Polaris
Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007 Name: Directions: Listed below are twenty (20) multiple-choice questions based on the material covered by the lectures this past week. Choose
Newton s derivation of Kepler s laws (outline) 1. Brief history. The first known proposal for a heliocentric solar system is due to Aristarchus of Samos (ancient Greece, c. 270 BC). Following a long period
1. A space probe is launched into space from Earth s surface. Which graph represents the relationship between the magnitude of the gravitational force exerted on Earth by the space probe and the distance
Lecture 3: Motions of the and Moon ecliptic (path of ) ecliptic (path of ) The 23.5 degree tilt of Earth s spin axis relative to its orbital axis around the causes the seasons Celestial Sphere Celestial
15.6 Planets Beyond the Solar System Planets orbiting other stars are called extrasolar planets. Until 1995, whether or not extrasolar planets existed was unknown. Since then more than 300 have been discovered.