Gravity. Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Gravity. Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields"

Transcription

1 Gravity Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields

2 Simulation Synchronous Rotation eg75q Sun-Earth-Moon System

3 Newton s Law of Gravitation r m 2 m 1 There is a force of gravity between any pair of objects anywhere. The force is proportional to each mass and inversely proportional to the square of the distance between the two objects. Its equation is: F G = G m 1 m 2 r 2 The constant of proportionality is G, the universal gravitation constant. G = N m 2 / kg 2. Note how the units of G all cancel out except for the Newtons, which is the unit needed on the left side of the equation.

4 F G = G m 1 m 2 r 2 Gravity Example How hard do two planets pull on each other if their masses are kg and kg and they 230 million kilometers apart? = ( N m 2 / kg 2 ) ( kg) ( kg) ( m) 2 = N This is the force each planet exerts on the other. Note the denominator is has a factor of 10 3 to convert to meters and a factor of 10 6 to account for the million. It doesn t matter which way or how fast the planets are moving.

5 3rd Law: Action-Reaction In the last example the force on each planet is the same. This is due to to Newton s third law of motion: the force on Planet 1 due to Planet 2 is just as strong but in the opposite direction as the force on Planet 2 due to Planet 1. The effects of these forces are not the same, however, since the planets have different masses. For the big planet: a = ( N) / ( kg) = m/s 2. For the little planet: a = ( N) / ( kg) = m/s kg N N kg

6 Inverse Square Law The law of gravitation is called an inverse square law because the magnitude of the force is inversely proportional to the square of the separation. If the masses are moved twice as far apart, the force of gravity between is cut by a factor of four. Triple the separation and the force is nine times weaker. F G = G m 1 m 2 r 2 What if each mass and the separation were all quadrupled? answer: no change in the force

7 Calculating the Gravitational Constant In 1798 Sir Henry Cavendish suspended a rod with two small masses (red) from a thin wire. Two larger mass (green) attract the small masses and cause the wire to twist slightly, since each force of attraction produces a torque in the same direction. By varying the masses and measuring the separations and the amount of twist, Cavendish was the first to calculate G. Since G is only N m 2 / kg 2, the measurements had to be very precise.

8 Calculating the mass of the Earth Knowing G, we can now actually calculate the mass of the Earth. All we do is write the weight of any object in two different ways and equate them. Its weight is the force of gravity between it and the Earth, which is F G in the equation below. M E is the mass of the Earth, R E is the radius of the Earth, and m is the mass of the object. The object s weight can also be written as mg. F G = G m 1 m 2 r 2 = G M E m R E 2 = mg The m s cancel in the last equation. g can be measured experimentally; Cavendish determined G s value; and R E can be calculated at m (see next slide). M E is the only unknown. Solving for M E we have: M E = g R E 2 G = kg

9 Calculating the radius of the Earth This is similar to the way the Greeks approximated Earth s radius over 2000 years ago: R E s Earth is also the central angle of the arc. s = R E R E = s / m

10 Net Force Gravity Problem 40 m kg 3 asteroids are positioned as shown, forming a right triangle. Find the net force on the 2.5 million kg asteroid kg kg 60 m Steps: 1. Find each force of gravity on it and draw in the vectors. 2. Find the angle at the lower right. 3. One force vector is to the left; break the other one down into components. 4. Find the resultant vector: magnitude via Pythagorean theorem; direction via inverse tangent. answer: N at 14.6 above horizontal (N of W)

11 Falling Around the Earth y = 0.5 g t 2 { x = vt v Newton imagined a cannon ball fired horizontally from a mountain top at a speed v. In a time t it falls a distance y = 0.5 g t 2 while moving horizontally a distance x = vt. If fired fast enough (about 8 km/s), the Earth would curve downward the same amount the cannon ball falls downward. Thus, the projectile would never hit the ground, and it would be in orbit. The moon falls around Earth in the exact same way but at a much greater altitude.. continued on next slide

12 Necessary Launch Speed for Orbit R = Earth s radius t = small amount of time after launch x = horiz. distance traveled in time t y = vertical distance fallen in time t (If t is very small, the red segment is nearly vertical.) y = gt 2 / 2 x = vt x 2 + R 2 = (R + y) 2 = R 2 + 2R y + y 2 Since y << R, x 2 + R 2 R 2 + 2R y x 2 2R y v 2 t 2 2R(g t 2 / 2) v 2 R g. So, R R v ( m 9.8 m/s 2 ) ½ v 7900 m/s

13 Early Astronomers In the 2 nd century AD the Alexandrian astronomer Ptolemy put forth a theory that Earth is stationary and at the center of the universe and that the sun, moon, and planets revolve around it. Though incorrect, it was accepted for centuries. In the early 1500 s the Polish astronomer Nicolaus Copernicus boldly rejected Ptolemy s geocentric model for a heliocentric one. His theory put the sun stated that the planets revolve around the sun in circular orbits and that Earth rotates daily on its axis. In the late 1500 s the Danish astronomer Tycho Brahe made better measurements of the planets and stars than anyone before him. The telescope had yet to be invented. He believed in a Ptolemaic-Coperican hybrid model in which the planets revolve around the sun, which in turn revolves around the Earth.

14 Early Astronomers Both Galileo and Kepler contributed greatly to work of the English scientist Sir Isaac Newton a generation later. In the late 1500 s and early 1600 s the Italian scientist Galileo was one of the very few people to advocate the Copernican view, for which the Church eventually had him placed under house arrest. After hearing about the invention of a spyglass in Holland, Galileo made a telescope and discovered four moons of Jupiter, craters on the moon, and the phases of Venus. The German astronomer Johannes Kepler was a contemporary of Galileo and an assistant to Tycho Brahe. Like Galileo, Kepler believed in the heliocentric system of Copernicus, but using Brahe s planetary data he deduced that the planets move in ellipses rather than circles. This is the first of three planetary laws that Kepler formulated based on Brahe s data.

15 Kepler s Laws of Planetary Motion Here is a summary of Kepler s 3 Laws: 1. Planets move around the sun in elliptical paths with the sun at one focus of the ellipse. 2. While orbiting, a planet sweep out equal areas in equal times. 3. The square of a planet s period (revolution time) is proportional to the cube of its mean distance from the sun: T 2 R 3 These laws apply to any satellite orbiting a much larger body.

16 Kepler s First Law Planets move around the sun in elliptical paths with the sun at one focus of the ellipse. F 1 F 2 Sun Planet An ellipse has two foci, F 1 and F 2. For any point P on the ellipse, F 1 P + F 2 P is a constant. The orbits of the planets are nearly circular (F 1 and F 2 are close together), but not perfect circles. A circle is a an ellipse with both foci at the same point--the center. Comets have very eccentric (highly elliptical) orbits. P

17 Kepler s Second Law (proven in advanced physics) While orbiting, a planet sweep out equal areas in equal times. A D Sun C B The blue shaded sector has the same area as the red shaded sector. Thus, a planet moves from C to D in the same amount of time as it moves from A to B. This means a planet must move faster when it s closer to the sun. For planets this affect is small, but for comets it s quite noticeable, since a comet s orbit is has much greater eccentricity.

18 Kepler s Third Law The square of a planet s period is proportional to the cube of its mean distance from the sun: T 2 R 3 Assuming that a planet s orbit is circular (which is not exactly correct but is a good approximation in most cases), then the mean distance from the sun is a constant--the radius. F is the force of gravity on the planet. F is also the centripetal force. If the orbit is circular, the planet s speed is constant, and v = 2 R / T. Therefore, M Sun F R m Planet G M m m v 2 R 2 = R Cancel m s and simplify: Rearrange: = m [2 R / T] 2 R G M R 2 = 4 T 2 = 2 R 3 G M 4 2 R T 2 Since G, M, and are constants, T 2 R 3.

19 Third Law Analysis 4 2 We just derived T 2 = R 3 GM It also shows that the orbital period depends on the mass of the central body (which for a planet is its star) but not on the mass of the orbiting body. In other words, if Mars had a companion planet the same distance from the sun, it would have the same period as Mars, regardless of its size. This shows that the farther away a planet is from its star, the longer it takes to complete an orbit. Likewise, an artificial satellite circling Earth from a great distance has a greater period than a satellite orbiting closer. There are two reasons for this: 1. The farther away the satellite is, the farther it must travel to complete an orbit; 2. The farther out its orbit is, the slower it moves, as shown: G M m m v 2 R 2 = G M R v = R

20 Third Law Example One astronomical unit (AU) is the distance between Earth and the sun (about 93 million miles). Jupiter is 5.2 AU from the sun. How long is a Jovian year? answer: Kepler s 3 rd Law says T 2 R 3, so T 2 = k R 3, where k is the constant of proportionality. Thus, for Earth and Jupiter we have: T E 2 = k R E 3 and T J2 = k R J 3 k s value matters not; since both planets are orbiting the same central body (the sun), k is the same in both equations. T E = 1 year, and R J / R E = 5.2, so dividing equations: T J 2 T E 2 R 3 J = R 3 T 2 J = (5.2) 3 T J = 11.9 years E continued on next slide

21 Third Law Example (cont.) What is Jupiter s orbital speed? answer: Since it s orbital is approximately circular, and it s speed is approximately constant: Jupiter is 5.2 AU from the sun (5.2 times farther than Earth is). v = d t = 2 (5.2)( miles) 1 year 11.9 years 365 days 1 day 24 hours 29,000 mph. Jupiter s period from last slide This means Jupiter is cruising through the solar system at about 13,000 m/s! Even at this great speed, though, Jupiter is so far away that when we observe it from Earth, we don t notice it s motion. Planets closer to the sun orbit even faster. Mercury, the closest planet, is traveling at about 48,000 m/s!

22 Third Law Practice Problem Venus is about AU from the sun, Mars AU. Venus takes days to circle the sun. Figure out how long a Martian year is. answer: 686 days

23 Uniform Gravitational Fields We live in what is essentially a uniform gravitational field. This means that the force of gravity near the surface of the Earth is pretty much constant in magnitude and direction. The green lines are gravitational field lines. They show the direction of the gravitational force on any object in the region (straight down). In a uniform field, the lines are parallel and evenly spaced. Near Earth s surface the magnitude of the gravitational field is 9.8 N/kg. That is, every kilogram of mass an object has experiences 9.8 N of force. Since a Newton is a kilogram meter per second squared, 1 N/kg = 1 m/s 2. So, the gravitational field strength is just the acceleration due to gravity, g. continued on next slide Earth s surface

24 Uniform Gravitational Fields (cont.) A 10 kg mass is near the surface of the Earth. Since the field strength is 9.8 N/ kg, each of the ten kilograms feels a 9.8 N force, for a total of 98 N. So, we can calculate the force of gravity by multiply mass and field strength. This is the same as calculating its weight (W = mg). 98 N 10 kg Earth s surface

25 Nonuniform Gravitational Fields Near Earth s surface the gravitational field is approximately uniform. Far from the surface it looks more like a sea urchin. The field lines are radial, rather than parallel, and point toward center of Earth. Earth get farther apart farther from the surface, meaning the field is weaker there. get closer together closer to the surface, meaning the field is stronger there.

Gravitation and the Motion of the Planets

Gravitation 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 information

Planetary Mechanics:

Planetary Mechanics: Planetary Mechanics: Satellites A satellite is an object or a body that revolves around another body due to the gravitational attraction to the greater mass. Ex: The planets are natural satellites of the

More information

Gravitation and the Waltz of the Planets

Gravitation 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 information

Gravitation and the Waltz of the Planets. Chapter Four

Gravitation 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 information

7.4 Universal Gravitation

7.4 Universal Gravitation Circular Motion Velocity is a vector quantity, which means that it involves both speed (magnitude) and direction. Therefore an object traveling at a constant speed can still accelerate if the direction

More information

January 19, notes.notebook. Claudius Ptolemaeus Second Century AD. Jan 5 7:37 AM

January 19, notes.notebook. Claudius Ptolemaeus Second Century AD. Jan 5 7:37 AM 8.1 notes.notebook Claudius Ptolemaeus Second Century AD Jan 5 7:7 AM Copernicus: The Foundation Nicholas Copernicus (Polish, 147 154): Proposed the first modern heliocentric model, motivated by inaccuracies

More information

Universal Gravitation

Universal Gravitation Universal Gravitation Johannes Kepler Johannes Kepler was a German mathematician, astronomer and astrologer, and key figure in the 17th century Scientific revolution. He is best known for his laws of planetary

More information

Announcements. Topics To Be Covered in this Lecture

Announcements. 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 information

9/12/2010. The Four Fundamental Forces of Nature. 1. Gravity 2. Electromagnetism 3. The Strong Nuclear Force 4. The Weak Nuclear Force

9/12/2010. The Four Fundamental Forces of Nature. 1. Gravity 2. Electromagnetism 3. The Strong Nuclear Force 4. The Weak Nuclear Force The Four Fundamental Forces of Nature 1. Gravity 2. Electromagnetism 3. The Strong Nuclear Force 4. The Weak Nuclear Force The Universe is made of matter Gravity the force of attraction between matter

More information

Lecture 13. Gravity in the Solar System

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

More information

Circular Motion. Gravitation

Circular Motion. Gravitation Circular Motion Gravitation Circular Motion Uniform circular motion is motion in a circle at constant speed. Centripetal force is the force that keeps an object moving in a circle. Centripetal acceleration,

More information

Introduction To Modern Astronomy I

Introduction To Modern Astronomy I ASTR 111 003 Fall 2006 Lecture 03 Sep. 18, 2006 Introduction To Modern Astronomy I Introducing Astronomy (chap. 1-6) Planets and Moons (chap. 7-17) Ch1: Astronomy and the Universe Ch2: Knowing the Heavens

More information

Astronomy- The Original Science

Astronomy- 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 information

AP Physics-B Universal Gravitation Introduction: Kepler s Laws of Planetary Motion: Newton s Law of Universal Gravitation: Performance Objectives:

AP Physics-B Universal Gravitation Introduction: Kepler s Laws of Planetary Motion: Newton s Law of Universal Gravitation: Performance Objectives: AP Physics-B Universal Gravitation Introduction: Astronomy is the oldest science. Practical needs and imagination acted together to give astronomy an early importance. For thousands of years, the motions

More information

ASTR 1010 Spring 2016 Study Notes Dr. Magnani

ASTR 1010 Spring 2016 Study Notes Dr. Magnani The Copernican Revolution ASTR 1010 Spring 2016 Study Notes Dr. Magnani The Copernican Revolution is basically how the West intellectually transitioned from the Ptolemaic geocentric model of the Universe

More information

PHYSICS. Chapter 13 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.

PHYSICS. 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 information

Gravity and the Orbits of Planets

Gravity 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 information

Planetary Orbits: Kepler s Laws 1/18/07

Planetary Orbits: Kepler s Laws 1/18/07 Planetary Orbits: Kepler s Laws Announcements The correct link for the course webpage http://www.lpl.arizona.edu/undergrad/classes/spring2007/giacalone_206-2 The first homework due Jan 25 (available for

More information

Chapter 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 information

14.1 Earth Satellites. The path of an Earth satellite follows the curvature of the Earth.

14.1 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 information

AP Physics Multiple Choice Practice Gravitation

AP Physics Multiple Choice Practice Gravitation AP Physics Multiple Choice Practice Gravitation 1. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each

More information

Physics Unit 7: Circular Motion, Universal Gravitation, and Satellite Orbits. Planetary Motion

Physics 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 information

PHYS 155 Introductory Astronomy

PHYS 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 information

Lecture #5: Plan. The Beginnings of Modern Astronomy Kepler s Laws Galileo

Lecture #5: Plan. The Beginnings of Modern Astronomy Kepler s Laws Galileo Lecture #5: Plan The Beginnings of Modern Astronomy Kepler s Laws Galileo Geocentric ( Ptolemaic ) Model Retrograde Motion: Apparent backward (= East-to-West) motion of a planet with respect to stars Ptolemy

More information

Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force

Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force This unit we will investigate the special case of kinematics and dynamics of objects in uniform circular motion. First let s consider

More information

Claudius Ptolemaeus Second Century AD. Jan 5 7:37 AM

Claudius Ptolemaeus Second Century AD. Jan 5 7:37 AM Claudius Ptolemaeus Second Century AD Jan 5 7:37 AM Copernicus: The Foundation Nicholas Copernicus (Polish, 1473 1543): Proposed the first modern heliocentric model, motivated by inaccuracies of the Ptolemaic

More information

Physics 12. Unit 5 Circular Motion and Gravitation Part 2

Physics 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 information

Intro to Astronomy. Looking at Our Space Neighborhood

Intro 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 information

Gravitation Part I. Ptolemy, Copernicus, Galileo, and Kepler

Gravitation Part I. Ptolemy, Copernicus, Galileo, and Kepler Gravitation Part I. Ptolemy, Copernicus, Galileo, and Kepler Celestial motions The stars: Uniform daily motion about the celestial poles (rising and setting). The Sun: Daily motion around the celestial

More information

Days of the week: - named after 7 Power (moving) objects in the sky (Sun, Moon, 5 planets) Models of the Universe:

Days of the week: - named after 7 Power (moving) objects in the sky (Sun, Moon, 5 planets)   Models of the Universe: Motions of the Planets ( Wanderers ) Planets move on celestial sphere - change RA, Dec each night - five are visible to naked eye Mercury, Venus, Mars, Jupiter, Saturn Days of the week: - named after 7

More information

6. Summarize Newton s Law of gravity and the inverse square concept. Write out the equation

6. Summarize Newton s Law of gravity and the inverse square concept. Write out the equation HW due Today. 1. Read p. 175 180. 2. Summarize the historical account of Brahe and Kepler 3. Write out Kepler s 3 laws. 1) Planets in orbit follow an elliptical path, the Sun is located at a focus of the

More information

Rotational Motion and the Law of Gravity 1

Rotational Motion and the Law of Gravity 1 Rotational Motion and the Law of Gravity 1 Linear motion is described by position, velocity, and acceleration. Circular motion repeats itself in circles around the axis of rotation Ex. Planets in orbit,

More information

Kepler, Newton, and laws of motion

Kepler, Newton, and laws of motion Kepler, Newton, and laws of motion First: A Little History Geocentric vs. heliocentric model for solar system (sec. 2.2-2.4)! The only history in this course is this progression: Aristotle (~350 BC) Ptolemy

More information

Johannes Kepler ( ) German Mathematician and Astronomer Passionately convinced of the rightness of the Copernican view. Set out to prove it!

Johannes 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 information

18. Kepler as a young man became the assistant to A) Nicolaus Copernicus. B) Ptolemy. C) Tycho Brahe. D) Sir Isaac Newton.

18. Kepler as a young man became the assistant to A) Nicolaus Copernicus. B) Ptolemy. C) Tycho Brahe. D) Sir Isaac Newton. Name: Date: 1. The word planet is derived from a Greek term meaning A) bright nighttime object. B) astrological sign. C) wanderer. D) nontwinkling star. 2. The planets that were known before the telescope

More information

Most of the time during full and new phases, the Moon lies above or below the Sun in the sky.

Most of the time during full and new phases, the Moon lies above or below the Sun in the sky. 6/16 Eclipses: We don t have eclipses every month because the plane of the Moon s orbit about the Earth is different from the plane the ecliptic, the Earth s orbital plane about the Sun. The planes of

More information

Early Theories. Early astronomers believed that the sun, planets and stars orbited Earth (geocentric model) Developed by Aristotle

Early Theories. Early astronomers believed that the sun, planets and stars orbited Earth (geocentric model) Developed by Aristotle Planetary Motion Early Theories Early astronomers believed that the sun, planets and stars orbited Earth (geocentric model) Developed by Aristotle Stars appear to move around Earth Observations showed

More information

CH 8. Universal Gravitation Planetary and Satellite Motion

CH 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 information

Unit 3 Lesson 2 Gravity and the Solar System. Copyright Houghton Mifflin Harcourt Publishing Company

Unit 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 information

The History of Astronomy. Theories, People, and Discoveries of the Past

The History of Astronomy. Theories, People, and Discoveries of the Past The History of Astronomy Theories, People, and Discoveries of the Past Early man recorded very little history. Left some clues in the form of petrographs. Stone drawings that show eclipses, comets, supernovae.

More information

Astronomy Notes Chapter 02.notebook April 11, 2014 Pythagoras Aristotle geocentric retrograde motion epicycles deferents Aristarchus, heliocentric

Astronomy 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 information

In so many and such important. ways, then, do the planets bear witness to the earth's mobility. Nicholas Copernicus

In so many and such important. ways, then, do the planets bear witness to the earth's mobility. Nicholas Copernicus In so many and such important ways, then, do the planets bear witness to the earth's mobility Nicholas Copernicus What We Will Learn Today What did it take to revise an age old belief? What is the Copernican

More information

History of Astronomy. PHYS 1411 Introduction to Astronomy. Tycho Brahe and Exploding Stars. Tycho Brahe ( ) Chapter 4. Renaissance Period

History of Astronomy. PHYS 1411 Introduction to Astronomy. Tycho Brahe and Exploding Stars. Tycho Brahe ( ) Chapter 4. Renaissance Period PHYS 1411 Introduction to Astronomy History of Astronomy Chapter 4 Renaissance Period Copernicus new (and correct) explanation for retrograde motion of the planets Copernicus new (and correct) explanation

More information

Unit 5 Gravitation. Newton s Law of Universal Gravitation Kepler s Laws of Planetary Motion

Unit 5 Gravitation. Newton s Law of Universal Gravitation Kepler s Laws of Planetary Motion Unit 5 Gravitation Newton s Law of Universal Gravitation Kepler s Laws of Planetary Motion Into to Gravity Phet Simulation Today: Make sure to collect all data. Finished lab due tomorrow!! Universal Law

More information

7 Study Guide. Gravitation Vocabulary Review

7 Study Guide. Gravitation Vocabulary Review Date Period Name CHAPTER 7 Study Guide Gravitation Vocabulary Review Write the term that correctly completes the statement. Use each term once. Kepler s second law Newton s law of universal gravitation

More information

Gravitation & Kepler s Laws

Gravitation & Kepler s Laws Gravitation & Kepler s Laws What causes YOU to be pulled down to the surface of the earth? THE EARTH.or more specifically the EARTH S MASS. Anything that has MASS has a gravitational pull towards it. F

More information

A Very Brief History of Statics and Dynamics

A Very Brief History of Statics and Dynamics UNIVERSAL GRAVITION A Very Brief History of Statics and Dynamics The idea that a force causes motion goes back to the 4 th century B.C., when the Greeks were developing ideas about science. Aristotle (384-33

More information

How big is the Universe and where are we in it?

How big is the Universe and where are we in it? Announcements Results of clicker questions from Monday are on ICON. First homework is graded on ICON. Next homework due one minute before midnight on Tuesday, September 6. Labs start this week. All lab

More information

Today. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws Laws of Motion. Laws of Motion

Today. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws Laws of Motion. Laws of Motion Today Planetary Motion Tycho Brahe s Observations Kepler s Laws Laws of Motion Laws of Motion In 1633 the Catholic Church ordered Galileo to recant his claim that Earth orbits the Sun. His book on the

More information

The Scientific Revolution

The Scientific Revolution The Scientific Revolution What is a Revolution? A Revolution is a complete change, or an overthrow of a government, a social system, etc. The Scientific Revolution In the 1500s and 1600s the Scientific

More information

Chapter 5 Review : Circular Motion; Gravitation

Chapter 5 Review : Circular Motion; Gravitation Chapter 5 Review : Circular Motion; Gravitation Conceptual Questions 1) Is it possible for an object moving with a constant speed to accelerate? Explain. A) No, if the speed is constant then the acceleration

More information

Learning Objectives. one night? Over the course of several nights? How do true motion and retrograde motion differ?

Learning Objectives. one night? Over the course of several nights? How do true motion and retrograde motion differ? Kepler s Laws Learning Objectives! Do the planets move east or west over the course of one night? Over the course of several nights? How do true motion and retrograde motion differ?! What are geocentric

More information

Chapter 13: universal gravitation

Chapter 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 information

Practice Test DeAnza College Astronomy 04 Test 1 Spring Quarter 2009

Practice Test DeAnza College Astronomy 04 Test 1 Spring Quarter 2009 Practice Test DeAnza College Astronomy 04 Test 1 Spring Quarter 2009 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Mark answer on Scantron.

More information

Eclipses and Forces. Jan 21, ) Review 2) Eclipses 3) Kepler s Laws 4) Newton s Laws

Eclipses and Forces. Jan 21, ) Review 2) Eclipses 3) Kepler s Laws 4) Newton s Laws Eclipses and Forces Jan 21, 2004 1) Review 2) Eclipses 3) Kepler s Laws 4) Newton s Laws Review Lots of motion The Moon revolves around the Earth Eclipses Solar Lunar the Sun, Earth and Moon must all be

More information

1 Astronomy: The Original Science

1 Astronomy: The Original Science CHAPTER 18 1 Astronomy: The Original Science SECTION Studying Space BEFORE YOU READ After you read this section, you should be able to answer these questions: How do astronomers define a day, a month,

More information

Exam #1 Study Guide (Note this is not all the information you need to know for the test, these are just SOME of the main points)

Exam #1 Study Guide (Note this is not all the information you need to know for the test, these are just SOME of the main points) Exam #1 Study Guide (Note this is not all the information you need to know for the test, these are just SOME of the main points) Moon Phases Moon is always ½ illuminated by the Sun, and the sunlit side

More information

Physics Test 7: Circular Motion page 1

Physics Test 7: Circular Motion page 1 Name Physics Test 7: Circular Motion page 1 hmultiple Choice Read each question and choose the best answer by putting the corresponding letter in the blank to the left. 1. The SI unit of angular speed

More information

Early Models of the Universe. How we explained those big shiny lights in the sky

Early Models of the Universe. How we explained those big shiny lights in the sky Early Models of the Universe How we explained those big shiny lights in the sky The Greek philosopher Aristotle (384 322 BCE) believed that the Earth was the center of our universe, and everything rotated

More information

By; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors

By; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors By; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors What is gravity? Gravity is defined as the force of attraction by which terrestrial bodies tend to fall

More information

Pull out a ½ sheet or use the back of your old quiz

Pull out a ½ sheet or use the back of your old quiz Pull out a ½ sheet or use the back of your old quiz Weekly Schedule Today Hw # 2 due Quiz # 2 Geocentric vs. Heliocentric models Kepler s Laws Astronomy InteracGves Newton and Gravity Lecture tutorials

More information

CIRCULAR MOTION AND UNIVERSAL GRAVITATION

CIRCULAR MOTION AND UNIVERSAL GRAVITATION CIRCULAR MOTION AND UNIVERSAL GRAVITATION Uniform Circular Motion What holds an object in a circular path? A force. String Friction Gravity What happens when the force is diminished? Object flies off in

More information

THE SUN AND THE SOLAR SYSTEM

THE SUN AND THE SOLAR SYSTEM Chapter 26 THE SUN AND THE SOLAR SYSTEM CHAPTER 26 SECTION 26.1: THE SUN S SIZE, HEAT, AND STRUCTURE Objectives: What is the Sun s structure and source of energy? Key Vocabulary: Fusion Photosphere Corona

More information

Space Notes Covers Objectives 1 & 2

Space Notes Covers Objectives 1 & 2 Space Notes Covers Objectives 1 & 2 Space Introduction Space Introduction Video Celestial Bodies Refers to a natural object out in space 1) Stars 2) Comets 3) Moons 4) Planets 5) Asteroids Constellations

More information

Chapter 13. Universal Gravitation

Chapter 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 information

What is a Revolution? A Revolution is a complete change, or an overthrow of a government, a social system, etc.

What is a Revolution? A Revolution is a complete change, or an overthrow of a government, a social system, etc. CW10 p374 Vocab What is a Revolution? A Revolution is a complete change, or an overthrow of a government, a social system, etc. The Scientific Revolution In the 1500s and 1600s the Scientific Revolution

More information

Chapter 2. The Rise of Astronomy. Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Chapter 2. The Rise of Astronomy. Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 2 The Rise of Astronomy Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Periods of Western Astronomy Western astronomy divides into 4 periods Prehistoric

More information

cosmogony geocentric heliocentric How the Greeks modeled the heavens

cosmogony geocentric heliocentric How the Greeks modeled the heavens Cosmogony A cosmogony is theory about ones place in the universe. A geocentric cosmogony is a theory that proposes Earth to be at the center of the universe. A heliocentric cosmogony is a theory that proposes

More information

,.~ Readlng ~ What,~,~~ is a geocentric system? Chapter3 J 73

,.~ Readlng ~ What,~,~~ is a geocentric system? Chapter3 J 73 Earth at the Center When the ancient Greeks watched the stars move across the sky, they noticed that the patterns of the stars didn t change. Although the stars seemed to move, they stayed in the same

More information

Chapter 4. The Origin Of Modern Astronomy. Is okay to change your phone? From ios to Android From Android to ios

Chapter 4. The Origin Of Modern Astronomy. Is okay to change your phone? From ios to Android From Android to ios Chapter 4 The Origin Of Modern Astronomy Slide 14 Slide 15 14 15 Is Change Good or Bad? Do you like Homer to look like Homer or with hair? Does it bother you when your schedule is changed? Is it okay to

More information

2.4 The Birth of Modern Astronomy

2.4 The Birth of Modern Astronomy 2.4 The Birth of Modern Astronomy Telescope invented around 1600 Galileo built his own, made observations: Moon has mountains and valleys Sun has sunspots, and rotates Jupiter has moons (shown): Venus

More information

Projectile Motion. Conceptual Physics 11 th Edition. Projectile Motion. Projectile Motion. Projectile Motion. This lecture will help you understand:

Projectile 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 information

INTRODUCTION: Ptolemy geo-centric theory Nicolas Copernicus Helio-centric theory TychoBrahe Johannes Kepler

INTRODUCTION: Ptolemy geo-centric theory Nicolas Copernicus Helio-centric theory TychoBrahe Johannes Kepler INTRODUCTION: Ptolemy in second century gave geo-centric theory of planetary motion in which the Earth is considered stationary at the centre of the universe and all the stars and the planets including

More information

Lecture 16. Gravitation

Lecture 16. Gravitation Lecture 16 Gravitation Today s Topics: The Gravitational Force Satellites in Circular Orbits Apparent Weightlessness lliptical Orbits and angular momentum Kepler s Laws of Orbital Motion Gravitational

More information

Section 37 Kepler's Rules

Section 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 information

Chapter 1 The Copernican Revolution

Chapter 1 The Copernican Revolution Chapter 1 The Copernican Revolution The Horse Head nebula in the Orion constellation (Reading assignment: Chapter 1) Learning Outcomes How the geocentric model accounts for the retrograde motion of planets?

More information

Chapter 02 The Rise of Astronomy

Chapter 02 The Rise of Astronomy Chapter 02 The Rise of Astronomy Multiple Choice Questions 1. The moon appears larger when it rises than when it is high in the sky because A. You are closer to it when it rises (angular-size relation).

More information

Conceptual Physics 11 th Edition

Conceptual 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 information

Chapter. Origin of Modern Astronomy

Chapter. Origin of Modern Astronomy Chapter Origin of Modern Astronomy 22.1 Early Astronomy Ancient Greeks Astronomy is the science that studies the universe. It includes the observation and interpretation of celestial bodies and phenomena.

More information

http://radicalart.info/physics/vacuum/index.html The Scientific Revolution In the 1500s and 1600s the Scientific Revolution changed the way Europeans looked at the world. People began to make conclusions

More information

Gravitation. Makes the World Go Round

Gravitation. Makes the World Go Round Gravitation Makes the World Go Round Gravitational Force The Force of gravity is an attractive force felt between all objects that have mass. G=6.67x10-11 N m 2 /kg 2 Example 1: What is the Force of Gravity

More information

Earth Science, 13e Tarbuck & Lutgens

Earth Science, 13e Tarbuck & Lutgens Earth Science, 13e Tarbuck & Lutgens Origins of Modern Astronomy Earth Science, 13e Chapter 21 Stanley C. Hatfield Southwestern Illinois College Early history of astronomy Ancient Greeks Used philosophical

More information

Name: 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 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 information

The History of Astronomy. Please pick up your assigned transmitter.

The History of Astronomy. Please pick up your assigned transmitter. The History of Astronomy Please pick up your assigned transmitter. When did mankind first become interested in the science of astronomy? 1. With the advent of modern computer technology (mid-20 th century)

More information

Today. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws of Planetary Motion. Laws of Motion. in physics

Today. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws of Planetary Motion. Laws of Motion. in physics Planetary Motion Today Tycho Brahe s Observations Kepler s Laws of Planetary Motion Laws of Motion in physics Page from 1640 text in the KSL rare book collection That the Earth may be a Planet the seeming

More information

Basics of Kepler and Newton. Orbits of the planets, moons,

Basics 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 information

How Astronomers Learnt that The Heavens Are Not Perfect

How Astronomers Learnt that The Heavens Are Not Perfect 1 How Astronomers Learnt that The Heavens Are Not Perfect Introduction In this packet, you will read about the discoveries and theories which changed the way astronomers understood the Universe. I have

More information

6.1 Newtonian Gravitation

6.1 Newtonian Gravitation 6.1 Newtonian Gravitation Early in the formation of our galaxy, tiny gravitational effects between particles began to draw matter together into slightly denser configurations. Those, in turn, exerted even

More information

5. Universal Laws of Motion

5. Universal Laws of Motion 5. Universal Laws of Motion If I have seen farther than others, it is because I have stood on the shoulders of giants. Sir Isaac Newton (164 177) Physicist Image courtesy of NASA/JPL Sir Isaac Newton (164-177)

More information

Ch. 22 Origin of Modern Astronomy Pretest

Ch. 22 Origin of Modern Astronomy Pretest Ch. 22 Origin of Modern Astronomy Pretest Ch. 22 Origin of Modern Astronomy Pretest 1. True or False: Early Greek astronomers (600 B.C. A.D. 150) used telescopes to observe the stars. Ch. 22 Origin of

More information

Astr 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) 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 information

Chapter 12 Gravity. Copyright 2010 Pearson Education, Inc.

Chapter 12 Gravity. Copyright 2010 Pearson Education, Inc. Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation

More information

Observational Astronomy - Lecture 4 Orbits, Motions, Kepler s and Newton s Laws

Observational 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 information

Models of the Solar System. The Development of Understanding from Ancient Greece to Isaac Newton

Models of the Solar System. The Development of Understanding from Ancient Greece to Isaac Newton Models of the Solar System The Development of Understanding from Ancient Greece to Isaac Newton Aristotle (384 BC 322 BC) Third in line of Greek thinkers: Socrates was the teacher of Plato, Plato was the

More information

KNOWLEDGE TO GET FROM TODAY S CLASS MEETING

KNOWLEDGE TO GET FROM TODAY S CLASS MEETING KNOWLEDGE TO GET FROM TODAY S CLASS MEETING Class Meeting #6, Monday, February 1 st, 2016 1) GRAVITY: finish up from Fri, Jan 29 th (pages 111-112, 123) 2) Isaac Newton s LAWS of MOTION (briefly) (pages

More information

Gravity and the Laws of Motion

Gravity and the Laws of Motion Gravity and the Laws of Motion Mass Mass is the amount of stuff (matter) in an object. Measured in grams (kg, mg, cg, etc.) Mass will not change unless matter is added or taken away. Weight Weight is the

More information

Physics General Physics. Lecture 8 Planetary Motion. Fall 2016 Semester Prof. Matthew Jones

Physics General Physics. Lecture 8 Planetary Motion. Fall 2016 Semester Prof. Matthew Jones Physics 22000 General Physics Lecture 8 Planetary Motion Fall 2016 Semester Prof. Matthew Jones 1 First Midterm Exam Tuesday, October 4 th, 8:00-9:30 pm Location: PHYS 112 and WTHR 200. Covering material

More information

Chapter 5 Lecture Notes

Chapter 5 Lecture Notes Formulas: a C = v 2 /r a = a C + a T F = Gm 1 m 2 /r 2 Chapter 5 Lecture Notes Physics 2414 - Strauss Constants: G = 6.67 10-11 N-m 2 /kg 2. Main Ideas: 1. Uniform circular motion 2. Nonuniform circular

More information

Test Bank for Life in the Universe, Third Edition Chapter 2: The Science of Life in the Universe

Test 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 information

Astronomy 101 Exam 2 Form Akey

Astronomy 101 Exam 2 Form Akey Astronomy 101 Exam 2 Form Akey Name: Lab section number: (In the format M0**. See back page; if you get this wrong you may not get your exam back!) Exam time: one hour and twenty minutes Please put bags

More information