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

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 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.

3 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.

4 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

5 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

6 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.

7 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 = m g 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: g R 2 M E E = = G 24 kg

8 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

9 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)

10 Falling Around the Earth y = 0.5 g t 2 { x = v t 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 = v t. 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

11 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 = g t 2 / 2 x = v t x 2 + R 2 = (R + y) 2 = R R y + y 2 Since y << R, x 2 + R 2 R R y x 2 2 R y v 2 t 2 2 R (g t 2 / 2) v 2 R g. So, R R v ( m 9.8 m/s 2 ) ½ v 7900 m/s

12 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.

13 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.

14 Kepler s Laws of Planetary Motion 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 Here is a summary of Kepler s 3 Laws: These laws apply to any satellite orbiting a much larger body.

15 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

16 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.

17 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 R 2 = m v 2 R Cancel m s and simplify: Rearrange: = m [2 R / T] 2 R G M R 2 = 4 2 T 2 = R 3 G M 4 2 R T 2 Since G, M, and are constants, T 2 R 3.

18 Third Law Analysis 4 2 T 2 = R 3 We just derived G M 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 R 2 m v = 2 R v = G M R

19 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 J 2 = 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 E = T J 2 = (5.2) 3 T J = 11.9 years continued on next slide

20 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) 11.9 years 1 year 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!

21 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

22 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

23 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

24 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

Chapter 5. Kepler s Laws. 5.1 Purpose. 5.2 Introduction

Chapter 5. Kepler s Laws. 5.1 Purpose. 5.2 Introduction Chapter 5 Kepler s Laws 5.1 Purpose In this lab, we will investigate the properties of planetary orbits. The motion of the planets had intrigued people throughout history. Johannes Kepler found three empirical

More information

Chapter 5 Circular Motion, the Planets, and Gravity

Chapter 5 Circular Motion, the Planets, and Gravity Chapter 5 Circular Motion, the Planets, and Gravity Does the circular motion of the moon around the Earth...... have anything in common with circular motion on Earth? A ball is whirled on the end of a

More information

Gravity, Orbital Motion,& Relativity

Gravity, Orbital Motion,& Relativity Gravity, Orbital Motion,& Relativity Early Astronomy Early Times As far as we know, humans have always been interested in the motions of objects in the sky. Not only did early humans navigate by means

More information

14 Satellite Motion. The path of an Earth satellite follows the curvature of the Earth.

14 Satellite Motion. The path of an Earth satellite follows the curvature of the Earth. The path of an Earth satellite follows the curvature of the Earth. 14.1 Earth Satellites A stone thrown fast enough to go a horizontal distance of 8 kilometers during the time (1 second) it takes to fall

More information

Kepler, Newton and Gravitation

Kepler, Newton and Gravitation Kepler, Newton and Gravitation Kepler, Newton and Gravity 1 Using the unit of distance 1 AU = Earth-Sun distance PLANETS COPERNICUS MODERN Mercury 0.38 0.387 Venus 0.72 0.723 Earth 1.00 1.00 Mars 1.52

More information

Newton s Law of Universal Gravitation (Ch 13) Law of Gravitation, cont. Notation. More About Forces. This is an example of an inverse square law

Newton s Law of Universal Gravitation (Ch 13) Law of Gravitation, cont. Notation. More About Forces. This is an example of an inverse square law Newton s Law of Universal Gravitation (Ch 13) Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional

More information

Let s say you were able to build a tunnel through the center of the Earth to the opposite side. If you were to jump in, you would accelerate toward

Let s say you were able to build a tunnel through the center of the Earth to the opposite side. If you were to jump in, you would accelerate toward Let s say you were able to build a tunnel through the center of the Earth to the opposite side. If you were to jump in, you would accelerate toward the center. However your acceleration decrease as your

More information

Lecture Outlines. Chapter 2. Astronomy Today 7th Edition Chaisson/McMillan Pearson Education, Inc.

Lecture Outlines. Chapter 2. Astronomy Today 7th Edition Chaisson/McMillan Pearson Education, Inc. Lecture Outlines Chapter 2 Astronomy Today 7th Edition Chaisson/McMillan Chapter 2 The Copernican Revolution Units of Chapter 2 2.1 Ancient Astronomy 2.2 The Geocentric Universe 2.3 The Heliocentric Model

More information

History of Gravity. Name: Date: Period:

History of Gravity. Name: Date: Period: History of Gravity Name: Date: Period: I. ANCIENT ASTRONOMY Imagine what it was like for the first humans to look up at the night sky. This is well before the invention of modern technology. There were

More information

From Aristotle to Newton

From Aristotle to Newton From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. The Geocentric Model Ancient Greek astronomers

More information

Kepler s Laws & Satellite Motion

Kepler s Laws & Satellite Motion Kepler s Laws & Satellite Motion Johannes Kepler (1571-1630) Tycho Brahe (1546 1601) built the first modern astronomical observatories. His instruments like the mural quandrant enabled him to measure the

More information

Circular Motion and Gravitation

Circular Motion and Gravitation Nicholas J. Giordano www.cengage.com/physics/giordano Circular Motion and Gravitation Introduction Circular motion Acceleration is not constant Cannot be reduced to a one-dimensional problem Examples Car

More information

A Little History. PHYS-1408-H01 Lecture 21. Chapter 13. Universal Gravitation. April. 8, Announcement

A Little History. PHYS-1408-H01 Lecture 21. Chapter 13. Universal Gravitation. April. 8, Announcement Announcement PHYS-1408-H01 Lecture 1 April. 8, 013 Course webpage http://highenergy.phys.ttu.edu/~slee/1408/ Homework.9 HW due 4/3 (next-to-next Tuesday) Ch.1 3, 9, 13, 3, 7, 3 Ch. 13 7, 1, 14, 17,, 7,

More information

Universal Law of Gravitation Honors Physics

Universal Law of Gravitation Honors Physics Universal Law of Gravitation Honors Physics 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

More information

The Main Point. The Scientific Method. Laws of Planetary Motion. Lecture #3: Orbits and Gravity. Laws of Planetary Motion:

The Main Point. The Scientific Method. Laws of Planetary Motion. Lecture #3: Orbits and Gravity. Laws of Planetary Motion: Lecture #3: Orbits and Gravity Laws of Planetary Motion: Kepler's Laws. Newton's Laws. Gravity. Planetary Orbits. Spacecraft Orbits. The Main Point Motions of planets, moons, and asteroids can be very

More information

Announcements. Eclipses 2/1/12. HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework!

Announcements. Eclipses 2/1/12. HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework! Announcements HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework! TA Qufei Gu will be in RH111 4:00-5:00PM Wednesday to help with homework. Email: zyx88@unm.edu Feb

More information

Introduction to Gravity and Orbits. Isaac Newton. Newton s Laws of Motion

Introduction to Gravity and Orbits. Isaac Newton. Newton s Laws of Motion Introduction to Gravity and Orbits Isaac Newton Born in England in 1642 Invented calculus in early twenties Finally published work in gravity in 1687 The Principia Newton s Laws of Motion 1: An object

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

QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION

QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION I. One mark Questions: 1. State Kepler s law of orbits. 2. State Kepler s law of areas. 3. State Kepler s law of periods. 4. Which physical quantity is conserved

More information

Astronomy Ch. 2 The Copernican Revolution. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Astronomy Ch. 2 The Copernican Revolution. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Name: Period: Date: Astronomy Ch. 2 The Copernican Revolution MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The principal culture that transferred

More information

Gravity and the Motion of the Planets

Gravity and the Motion of the Planets Gravity and the Motion of the Planets Foundations of Modern Science More than 2500 years ago Pythagoras put forth the idea that nature can be described with mathematics. Aristotle asserted that the Universe

More information

Chapter 13 Newton s Theory of Gravity

Chapter 13 Newton s Theory of Gravity 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

More information

The Planets. Saturn. Venus. Jupiter Mercury.

The Planets. Saturn. Venus. Jupiter Mercury. 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

Renaissance Astronomy. Astronomy 1-1 Lecture 04-1

Renaissance Astronomy. Astronomy 1-1 Lecture 04-1 Renaissance Astronomy Astronomy 1-1 Lecture 04-1 Cast of Characters Nicolaus Copernicus (1473-1543) Circular motion of planets around sun Tycho Brahe (1546-1601) Recorded planets' positions Johannes Kepler

More information

Website: Reading: Homework: Discussion:

Website: Reading: Homework: Discussion: Reminders! Website: http://starsarestellar.blogspot.com/ Lectures 1-5 are available for download as study aids. Reading: You should have Chapters 1-4 read, Chapter 5 by the end of today, and Chapters 6

More information

Astro Lecture 8 The Copernican Revolution (Cont d)

Astro Lecture 8 The Copernican Revolution (Cont d) Astro110-01 Lecture 8 The Copernican Revolution (Cont d) or the revolutionaries: Nicolas Copernicus (1473-1543) Tycho Brahe (1546-1601) Johannes Kepler (1571-1630) Galileo Galilei (1564-1642) Isaac Newton

More information

Newton s Law of Universal Gravitation

Newton s Law of Universal Gravitation Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just two different versions of the same thing.

More information

First Midterm Exam. Physics General Physics Lecture 8 Planetary Motion 9/18/2016. Fall 2016 Semester Prof. Matthew Jones

First Midterm Exam. Physics General Physics Lecture 8 Planetary Motion 9/18/2016. 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

Sir Isaac and Universal Gravitation. ... so what really happened?

Sir Isaac and Universal Gravitation. ... so what really happened? Sir Isaac and Universal Gravitation... so what really happened? Apr 11 11:51 AM For the Aztecs, who lived in central Mexico, Tonatiuh was a Sun god. Aztecs believed that four suns had been created in four

More information

6. CIRCULAR MOTION; GRAVITATION.

6. CIRCULAR MOTION; GRAVITATION. 6. CIRCULAR MOTION; GRAVITATION. Key words: Uniform Circular Motion, Period of rotation, Frequency, Centripetal Acceleration, Centripetal Force, Kepler s Laws of Planetary Motion, Gravitation, Newton s

More information

TAKEN FROM HORIZONS 7TH EDITION CHAPTER 4 TUTORIAL QUIZ

TAKEN FROM HORIZONS 7TH EDITION CHAPTER 4 TUTORIAL QUIZ TAKEN FROM HORIZONS 7TH EDITION CHAPTER 4 TUTORIAL QUIZ 1. The Greek astronomer Hipparchus is noted for a. naming all of the stars. b. developing the concept of the light-year. c. recognizing and recording

More information

Newton s Laws and Gravity 1/29/2013

Newton s Laws and Gravity 1/29/2013 Newton s Laws and Gravity 1/29/2013 Announcements Today: Homework Collection: The Seasons & Kepler s Laws Rules for Lecture Tutorials Work with a partner!! this is the whole point. it is NOT acceptable

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

Observations from Earth

Observations from Earth Observations from Earth Sun Constellation Orion Constellation Orion All objects in the heavens rise in the east and set in the west. The Sun and stars all moved across the sky in a regular, predictable

More information

Chapter 13: Universal Gravitation

Chapter 13: Universal Gravitation Chapter 13: Universal Gravitation I. The Falling Apple (13.1) A. Isaac Newton (1642-1727) 1. Formulated ideas based on earlier work by Galileo (concept of inertia) 2. Concept if object undergoes change

More information

Assignment 3. Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.

Assignment 3. Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Assignment 3 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The scientist who formulated the three laws of planetary motion by analyzing

More information

Physics 130 Astronomy Exam #1 July 19, 2004

Physics 130 Astronomy Exam #1 July 19, 2004 Physics 130 Astronomy Exam #1 July 19, 2004 Name Multiple Choice: 1. A scientist observes a new phenomenon that disagrees with his explanation or hypothesis. Following the scientific methods, he should

More information

From Essential University Physics 3 rd Edition by Richard Wolfson, Middlebury College 2016 by Pearson Education, Inc.

From Essential University Physics 3 rd Edition by Richard Wolfson, Middlebury College 2016 by Pearson Education, Inc. PreClass Notes: Chapter 8 From Essential University Physics 3 rd Edition by Richard Wolfson, Middlebury College 2016 by Pearson Education, Inc. Narration and extra little notes by Jason Harlow, University

More information

PHYS-1000 Chapter 3 Homework Solutions Due: September 9, 2012

PHYS-1000 Chapter 3 Homework Solutions Due: September 9, 2012 1. In the Greek geocentric model, the retrograde motion of a planet occurs when A. Earth is about to pass the planet in its orbit around the Sun. B. the planet actually goes backward in its orbit around

More information

The Copernican Revolution. Kelper s Three Laws 3/4/09

The Copernican Revolution. Kelper s Three Laws 3/4/09 The Copernican Revolution The Copernican Revolution is about astronomers struggling with two related problems Earth s place in the cosmos The motion of the planets Copernicus revolutionized humanity s

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 Galileo c. 1564-1640 Galileo s telescopic discoveries Stars in the Milky Way Mountains on the

More information

1 Kepler s Laws of Planetary Motion

1 Kepler s Laws of Planetary Motion Name: 1 Kepler s Laws of Planetary Motion 1.1 Introduction Johannes Kepler published three laws of planetary motion, the first two in 1609 and the third in 1619. The laws were made possible by planetary

More information

Gravitation. Gravity & Planetary Motion. A. Aristotle vs. Galileo. B. Tycho & Kepler. C. Newton & Halley. D. Einstein

Gravitation. Gravity & Planetary Motion. A. Aristotle vs. Galileo. B. Tycho & Kepler. C. Newton & Halley. D. Einstein Gravitation Dr. Bill Pezzaglia Gravity & Planetary Motion A. Aristotle vs. Galileo B. Tycho & Kepler C. Newton & Halley D. Einstein 2 Osher Meeting #5, March 26, 2007 2a.7 Laws of Inertia 3 Aristotle:

More information

Newton s Law of Universal Gravitation

Newton s Law of Universal Gravitation Newton s Law of Universal Gravitation Gravitational Field Strength Uniform Circular Motion Centripetal Force and Acceleration Vertical Circular Motion Horizontal Circular Motion Kepler s Laws Planetary

More information

7.2 Calculate force of gravity at a given distance given the force of gravity at another distance (making use of the inverse square relationship).

7.2 Calculate force of gravity at a given distance given the force of gravity at another distance (making use of the inverse square relationship). 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

More information

Student Exploration: Orbital Motion Kepler s Laws

Student Exploration: Orbital Motion Kepler s Laws Name: Date: Student Exploration: Orbital Motion Kepler s Laws Vocabulary: astronomical unit, eccentricity, ellipse, force, gravity, Kepler s first law, Kepler s second law, Kepler s third law, orbit, orbital

More information

Chapter 25.1: Models of our Solar System

Chapter 25.1: Models of our Solar System Chapter 25.1: Models of our Solar System Objectives: Compare & Contrast geocentric and heliocentric models of the solar sytem. Describe the orbits of planets explain how gravity and inertia keep the planets

More information

What s going on during a solar eclipse. Solar Eclipses. Total Solar Eclipse on March 29, 2006 (viewed from Turkey) Partial, Total, and Annular

What s going on during a solar eclipse. Solar Eclipses. Total Solar Eclipse on March 29, 2006 (viewed from Turkey) Partial, Total, and Annular 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

More information

1 Kepler s Laws of Planetary Motion

1 Kepler s Laws of Planetary Motion 1 Kepler s Laws of Planetary Motion 1.1 Introduction Johannes Kepler published three laws of planetary motion, the first two in 1609 and the third in 1619. The laws were made possible by planetary data

More information

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

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

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

Kepler, Newton, and laws of motion

Kepler, Newton, and laws of motion Kepler, Newton, and laws of motion !! " The only history in this course:!!!geocentric vs. heliocentric model (sec. 2.2-2.4)" The important historical progression is the following:!! Ptolemy (~140 AD) Copernicus

More information

Next: The Science of Astronomy. Geocentric vs Heliocentric. ASTR 105 Intro Astronomy: The Solar System

Next: The Science of Astronomy. Geocentric vs Heliocentric. ASTR 105 Intro Astronomy: The Solar System Next: The Science of Astronomy ASTR 105 Intro Astronomy: The Solar System Geocentric vs Heliocentric Astronomically Important Historians a.k.a. Famous Dead White Guys The Greeks (600 B.C. ~ 200 A.D.) Plato

More information

1 Astronomy: The Original Science

1 Astronomy: The Original Science CHAPTER 1 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, and

More information

Lecture 5 Galileo and Brahe September 21, 2015

Lecture 5 Galileo and Brahe September 21, 2015 Lecture 5 Galileo and Brahe September 21, 2015 1 2 Galileo Galilei (1564-1642) Supported Copernican model. Used telescope to observe sky (1610). Mountains on the moon Rings of Saturn Sunspots Milky Way

More information

Astron 100 Sample Exam 1 1. Solar eclipses occur only at (A) New moon (B) 1 st quarter moon (C) Full moon (D) 3 rd quarter moon (E) The equinoxes 2.

Astron 100 Sample Exam 1 1. Solar eclipses occur only at (A) New moon (B) 1 st quarter moon (C) Full moon (D) 3 rd quarter moon (E) The equinoxes 2. Astron 100 Sample Exam 1 1. Solar eclipses occur only at (A) New moon (B) 1 st quarter moon (C) Full moon (D) 3 rd quarter moon (E) The equinoxes 2. If the Moon is at first quarter tonight in Amherst,

More information

ASTR 105 Intro Astronomy: The Solar System

ASTR 105 Intro Astronomy: The Solar System ASTR 105 Intro Astronomy: The Solar System Next: The Science of Astronomy Geocentric vs Heliocentric Earth-Centered (Geocentric) Sun-Centered (Heliocentric) Astronomically Important Historians a.k.a. Famous

More information

DYNAMICS OF UNIFORM CIRCULAR MOTION

DYNAMICS OF UNIFORM CIRCULAR MOTION chapter DYNAMICS OF UNIFORM CIRCULAR MOTION Section 5.1 Uniform Circular Motion Section 5.2 Centripetal Acceleration 1. A ball moves with a constant speed of 4 m/s around a circle of radius 0.25 m. What

More information

Chapter 6 The Gravitational Force and the Gravitational Field

Chapter 6 The Gravitational Force and the Gravitational Field Chapter 6 The Gravitational Force and the Gravitational Field Newton s Law of Universal Gravitation F GMm = 2 r F is the force of an object with mass M on an object with mass m r is a unit vector pointing

More information

Physics Announcement I. Announcement II. Principles of Physics. Chapter 6. Moon s Acceleration. Gravitation & Newton s Synthesis

Physics Announcement I. Announcement II. Principles of Physics. Chapter 6. Moon s Acceleration. Gravitation & Newton s Synthesis Announcement I Physics 1408-00 Lecture note is on the web Handout (6 slides/page) Principles of Physics Lecture 10 Chapter 6 February 1, 008 Sung-Won Lee Sungwon.Lee@ttu.edu Announcement II SI session

More information

Today. The Copernican Revolution. Galileo. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws

Today. The Copernican Revolution. Galileo. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws Today The Copernican Revolution Galileo Planetary Motion Tycho Brahe s Observations Kepler s Laws Galileo c. 1564-1640 First telescopic astronomical observations Galileo s observations of phases of Venus

More information

Lesson 5 Rotational and Projectile Motion

Lesson 5 Rotational and Projectile Motion Lesson 5 Rotational and Projectile Motion Introduction: Connecting Your Learning The previous lesson discussed momentum and energy. This lesson explores rotational and circular motion as well as the particular

More information

M OTION. Chapter2 OUTLINE GOALS

M OTION. Chapter2 OUTLINE GOALS Chapter2 M OTION OUTLINE Describing Motion 2.1 Speed 2.2 Vectors 2.3 Acceleration 2.4 Distance, Time, and Acceleration Acceleration of Gravity 2.5 Free Fall 2.6 Air Resistence Force and Motion 2.7 First

More information

Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015

Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 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

More information

SPH4U - Unit One - Day 14 - Planetary and Satellite Motion

SPH4U - Unit One - Day 14 - Planetary and Satellite Motion SPH4U - Unit One - Day 14 - Planetary and Satellite Motion Learning Goals state and use Kepler's Laws to analyze the motion of satellites and planets in orbital motion correctly use the following vocabulary

More information

THE SCIENTIFIC METHOD

THE SCIENTIFIC METHOD Chapter1 THE SCIENTIFIC METHOD OUTLINE How Scientists Study Nature 1.1 The Scientific Method 1.2 Why Science Is Successful The Solar System 1.3 A Survey of the Sky 1.4 The Ptolemaic System 1.5 The Copernican

More information

Unit 8 Lesson 2 Gravity and the Solar System

Unit 8 Lesson 2 Gravity and the Solar System Unit 8 Lesson 2 Gravity and the Solar System Gravity What is gravity? Gravity is a force of attraction between objects that is due to their masses and the distances between them. Every object in the universe

More information

Astronomy 1140 Quiz 1 Review

Astronomy 1140 Quiz 1 Review Astronomy 1140 Quiz 1 Review Prof. Pradhan September 15, 2015 What is Science? 1. Explain the difference between astronomy and astrology. (a) Astrology: nonscience using zodiac sign to predict the future/personality

More information

Chapter 4: Renaissance Astronomy

Chapter 4: Renaissance Astronomy Chapter 4: Renaissance Astronomy Astronomy after Ptolemy [http://www.thenagain.info/webchron/westciv/westciv.html] Decline of Western Civilization (extended) knowledge of ancient astronomy lost Islamic

More information

Lecture Outline Chapter 12. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 12. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc. Lecture Outline Chapter 12 Physics, 4 th Edition James S. Walker Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws

More information

Astronomy 1 Winter 2011

Astronomy 1 Winter 2011 Astronomy 1 Winter 2011 Lecture 4; January 10 2011 Previously on Astro-1 Lunar Phases: How do they arise? Length of the Month: How long does it take for the moon to go around the Earth? The Moon s Orbit:

More information

Lecture 6: Newton & Kepler. Tycho Brahe ( ) Johannes Kepler

Lecture 6: Newton & Kepler. Tycho Brahe ( ) Johannes Kepler Lecture 6: Newton & Kepler Johannes Kepler (1600) was employed by Tycho to develop a mathematical theory to explain the observations made by Tycho Kepler was a pure theorist; Tycho a pure observer Issac

More information

Gravitation. Physics 1425 Lecture 11. Michael Fowler, UVa

Gravitation. Physics 1425 Lecture 11. Michael Fowler, UVa Gravitation Physics 1425 Lecture 11 Michael Fowler, UVa The Inverse Square Law Newton s idea: the centripetal force keeping the Moon circling the Earth is the same gravitational force that pulls us to

More information

Name: Class: Date: ID: A

Name: Class: Date: ID: A Name: Class: _ Date: _ Astro Quiz 3 (ch3) Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following people did NOT accept a heliocentric model

More information

5. How did Copernicus s model solve the problem of some planets moving backwards?

5. How did Copernicus s model solve the problem of some planets moving backwards? PACKET #5 - MODELS OF THE SOLAR SYSTEM Reading Guide: Chapter 27.2 (read text pages 691-694) 1k. Recognize the cumulative nature of scientific evidence. 1n. Know that when an observation does not agree

More information

Lecture Outlines PowerPoint. Chapter 21 Earth Science 11e Tarbuck/Lutgens

Lecture Outlines PowerPoint. Chapter 21 Earth Science 11e Tarbuck/Lutgens Lecture Outlines PowerPoint Chapter 21 Earth Science 11e Tarbuck/Lutgens 2006 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors

More information

G = N m 2 /kg 2

G = N m 2 /kg 2 PH2213 : Examples from Chapter 6 : Gravitation Key Concepts Two point-mass objects of masses m 1 and m 2 separated by a distance of r will attract each other with a gravitational force of magnitude F =

More information

The Heliocentric Model of the Solar System

The Heliocentric Model of the Solar System The Heliocentric Model of the Solar System Hypothesis: The Sun is the center of the solar system. Only Moon orbits around Earth; Planets orbit around Sun. Aristarchus of Samos was the first to propose

More information

Physics General Physics

Physics General Physics Physics 1403-001 General Physics Lecture 16 Chapter 5 & 6 Feb 4, 014 Announcements Course webpage: http://highenergy.phys.ttu.edu/~slee/1403 Syllabus, lecture note, etc Online homework: http://webassign.net/login.html

More information

THE FORCE OF GRAVITY

THE FORCE OF GRAVITY THE FORCE OF GRAVITY By looking at phenomena known to everyone, like the motion of bodies in free fall, or object's weight, we will understand the general notion of gravitational field. We will then try

More information

Chapter 13 - Gravity. David J. Starling Penn State Hazleton Fall Chapter 13 - Gravity. Objectives (Ch 13) Newton s Law of Gravitation

Chapter 13 - Gravity. David J. Starling Penn State Hazleton Fall Chapter 13 - Gravity. Objectives (Ch 13) Newton s Law of Gravitation 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

More information

Making Sense of the Universe: Understanding Motion, Energy, and Gravity

Making Sense of the Universe: Understanding Motion, Energy, and Gravity Making Sense of the Universe: Understanding Motion, Energy, and Gravity 1. Newton s Laws 2. Conservation Laws Energy Angular momentum 3. Gravity Review from last time Ancient Greeks: Ptolemy; the geocentric

More information

Understanding the motion of the Universe. Motion, Force, and Gravity

Understanding the motion of the Universe. Motion, Force, and Gravity 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.

More information

Gravitation and Newton s Synthesis

Gravitation and Newton s Synthesis Gravitation and Newton s Synthesis Vocabulary law of unviversal Kepler s laws of planetary perturbations casual laws gravitation motion casuality field graviational field inertial mass gravitational mass

More information

DeAnza College Fall First Midterm Exam MAKE ALL MARKS DARK AND COMPLETE.

DeAnza College Fall First Midterm Exam MAKE ALL MARKS DARK AND COMPLETE. FAMILY NAME : (Please PRINT!) GIVEN NAME : (Please PRINT!) Signature: ASTRONOMY 4 DeAnza College Fall 2016 First Midterm Exam MAKE ALL MARKS DARK AND COMPLETE. Instructions: 1. On your Parscore sheet (using

More information

Monday, October 3, 2011

Monday, October 3, 2011 the shuttle blasts off Then comes the tremendous pressure of three G s and the sudden release into weightlessness as the ship leaves the gravitational field behind -from The Arizona Republic 1 Quiz #3:

More information

If I have seen further it is by standing on the. shoulders of giants. Sir Isaac Newton

If I have seen further it is by standing on the. shoulders of giants. Sir Isaac Newton If I have seen further it is by standing on the shoulders of giants. Sir Isaac Newton What We Will Learn Today What are the basic elements of motion? What are Newton s laws of motion? What are the three

More information

Earth/Moon as seen from Mars

Earth/Moon as seen from Mars Earth/Moon as seen from Mars Homeworks Bit of Administration. Bless, pp. 105-139 139 BNSV, pp. 70-83 Observing Lab Nice Work on Lab 1! Start Lab 2 on Saturday Timing Matters! 10 minutes every clear night

More information

1 Newton s Laws of Motion

1 Newton s Laws of Motion 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

More information

PARAMETRIC EQUATIONS AND POLAR COORDINATES

PARAMETRIC EQUATIONS AND POLAR COORDINATES 10 PARAMETRIC EQUATIONS AND POLAR COORDINATES PARAMETRIC EQUATIONS & POLAR COORDINATES In Section 10.5, we defined the parabola in terms of a focus and directrix. However, we defined the ellipse and hyperbola

More information

Understanding the motion of the Universe. Motion, Force, and Gravity

Understanding the motion of the Universe. Motion, Force, and Gravity 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.

More information

The Science of Astronomy Pearson Education, Inc.

The Science of Astronomy Pearson Education, Inc. The Science of Astronomy Why does modern science trace its roots to the Greeks? Greeks were the first people known to make models of nature. They tried to explain patterns in nature without resorting to

More information

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law

More information

Is velocity constant? A = πr 2

Is velocity constant? A = πr 2 Physics R Date: Circular Motion & Gravity Uniform Circular Motion What does uniform mean? Equations: (on reference table) Uniform circular motion means circular motion with C = 2πr = Is velocity constant?

More information

Newton s Law of Universal Gravitation

Newton s Law of Universal Gravitation 12.1 Newton s Law of Universal Gravitation SECTION Explain Kepler s laws. Describe Newton s law of universal gravitation. Apply Newton s law of universal gravitation quantitatively. KEY TERMS OUTCOMES

More information

Circular Motion. Physics 1425 Lecture 9. Michael Fowler, UVa.

Circular Motion. Physics 1425 Lecture 9. Michael Fowler, UVa. Circular Motion Physics 1425 Lecture 9 Michael Fowler, UVa. A Cannon on a Mountain Back to Galileo one more time imagine a powerful cannon shooting horizontally from a high mountaintop: The path falls

More information

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13.

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. Chapter 5. Gravitation Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. 5.1 Newton s Law of Gravitation We have already studied the effects of gravity through the

More information

4.1 Describing Motion. How do we describe motion? Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

4.1 Describing Motion. How do we describe motion? Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion Our goals for learning:! How do we describe motion?! How is mass different from weight? How do we

More information