Astro 109 Lecture 6: Kepler s Laws of (Planetary) Mo=on September 19, 2014

Size: px
Start display at page:

Download "Astro 109 Lecture 6: Kepler s Laws of (Planetary) Mo=on September 19, 2014"

Transcription

1 Astro 109 Lecture 6: Kepler s Laws of (Planetary) Mo=on September 19, 2014

2 Constella=on of the day: Gemini Zodiac constella=on most easily visible at night in January/ February. Named aqer the twins Castor (mortal) and Pollux (immortal), because of the two bright stars that now bear the same names. Image credit: IAU/Sky & Telescope

3 Why astronomers like Gemini It contains the nearby Geminga pulsar, a rapidly spinning neutron star leq behind aqer a supernova. Geminga is one of the brightest sources of gamma rays in the en=re sky. Image credit: Bill Saxton (NRAO/AUI/NSF) Image credit: NASA/Fermi

4 Organiza=onal reminders In- person office hours are today 3:00-4:30pm in Scob Hall 102 but cancelled next Tuesday 9/23. Availability in the Sakai chat room will be limited through Tuesday, while I m in Texas. Reading for Wednesday: Sec=ons 3.1 (again, this =me focusing on Newton), 3.3, T6. Homework for next Friday: 10 ques=ons, available in Sakai Tests & Quizzes, due before class. Please submit your homework and don t just save it! Please register your clicker in Sakai! Currently at 122/127.

5 All weekly study groups scheduled! LA DAY TIME CAMPUS ROOM Elsie Lee Monday 1:10-2:30pm College Ave Kreeger 117 Isabel Kennedy Monday 6:40-8:00pm Livingston Tilleb 111 Ryan DeGregorio Tuesday 8:10-9:30pm Busch ARC 326 Adrian Casper Wednesday 1:10-2:30pm College Ave Kreeger 117 Zac Csorny Wednesday 2:50-4:10pm College Ave Kreeger 117 Ragen Patel Thursday 2:50-4:10pm College Ave Kreeger 117 Anthony Xing Thursday 5:00-6:20pm Livingston Tilleb 111 All students are welcome to abend, but if you are genng 6/10 or less on homeworks, you are strongly encouraged to abend.

6 Sign up for study groups in Sakai All study groups next week are now available for signup via the Sign- up tab in Sakai (note: you do need to sign up again for each separate week). Tips: When you sign up, you should get a confirma=on . Please cancel your slot if you re not going to use it! Bring textbook and copy of last year s midterm. Ques=ons to prepare to discuss with LAs next week: How do the geocentric model and the heliocentric model explain the mo=ons of the Sun, stars, and planets in the sky? What are examples of Kepler s laws in ac=on in the solar system? Ques=ons from last year s midterm you should be able to answer aqer today s lecture: #15 (52%), #23 (26%).

7 Homework # 2 Ques=on 10 When we can see a full moon from the Earth s northern hemisphere, what lunar phase is visible from the Earth s southern hemisphere? A. Either first quarter or third quarter; it is not possible to say which without more informa=on. B. The moon will not be visible at all from the southern hemisphere, because the Earth will be in the away. C. New. D. Full. Lunar phase depends only on where the moon is in its orbit around the Earth not on where on the Earth we are observing the moon from!

8 Johannes Kepler ( ) Sept. 18

9 Kepler s Laws: based on data 1. The orbit of a planet about the Sun is an ellipse with the Sun at one focus.

10 Conic sec=ons Circle Ellipse Wikipedia focus (plural foci)

11 How to draw an ellipse Pick two points (foci). Take a piece of string that is longer than the distance between the foci, and nail the ends of the string to the foci. Ellipse = all points you can stretch the string out to: sum of distances to foci = length of string = constant. Longer string rela=ve to the distance between the foci gives a more circular (less eccentric) ellipse. Ellipse

12 Ellip=cal orbit Can t fit the data? Change your hypothesis! If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight minutes pointed the road to a complete reforma?on in astronomy. - - Kepler

13 Terminology major axis semimajor axis minor axis Note: we measure semimajor axis from the center, but remember the Sun is at a focus.

14 Specifying a circle or ellipse Circle: radius r Ellipse: semimajor axis a, semiminor axis b - OR - semimajor axis a, eccentricity e

15 Example: comets Halley s comet is about 0.6 AU from the Sun at perihelion, and 35 AU from the Sun at aphelion. What is its semimajor axis? major axis = 35.6 AU semimajor axis = 17.8 AU 0.6 AU 35 AU Not to scale!

16 Kepler s Laws: based on data 1. The orbit of a planet about the Sun is an ellipse with the Sun at one focus. 2. A line joining a planet and the Sun sweeps out equal areas in equal intervals of =me.

17

18 Clicker ques=on # 1 Suppose a comet orbits the Sun such that its semimajor axis is 5 AU and the closest it gets to the Sun is 1 AU. At the point in its orbit when it is moving slowest, how far is the comet from the Sun? Not to scale! A. 1 AU B. 5 AU C. 6 AU D. 9 AU E. Not far enough. 1 AU 5 AU

19 Why does Kepler s second law hold? Casual ice skater effect (or: dizzy professor effect ) Physics conserva=on of angular momentum: objects that are rota=ng/revolving want to con=nue to rotate/revolve around the same axis and with the same angular momentum

20 Orbital angular momentum Mass doesn t change, so we have a tradeoff between distance and velocity as Earth (or any planet) goes around the Sun.

21 Group clicker ques=on # 2 Suppose we plot the shape of planetary orbits and the corresponding speed versus =me. Which of the following combina=ons is correct? A B C D

22 Kepler s Laws: based on data 1. The orbit of a planet about the Sun is an ellipse with the Sun at one focus. 2. A line joining a planet and the Sun sweeps out equal areas in equal intervals of =me. 3. The square of the orbital period of a planet is directly propor=onal to the cube of the semimajor axis of its orbit.

23 Kepler s original formula=on Express the semimajor axis, a, in AU. Express the period, P, in yr. Then P 2 = a 3 where the nota=on means P x P = a x a x a. Note: depends on semimajor axis not eccentricity not planet mass

24 Planets in the solar system: data! Planet a (AU) a 2 a 3 P (yr) P 2 P 3 Mercury Venus Earth Mars Jupiter Saturn

25 Example Halley s comet is about 0.6 AU from the Sun at perihelion, and its orbital period is 75.3 yr. How far is it from the Sun at aphelion? a 3 = P 2 = 5670 a = 17.8 AU perihelion + aphelion = 2a = 35.6 AU - - > aphelion = 35 AU

26 Clicker ques=on # 3 If Earth were 9 =mes its current distance from the Sun, the =me it would take Earth to complete one orbit of the Sun would be A. 3 years. B. 9 years. C. 27 years. D. 81 years. E. Pie. (π years.) P 2 = a 3

27 Working with Kepler s third law If Earth were 9 =mes its current distance from the Sun, the =me it would take Earth to complete one orbit of the Sun would be P x P = a x a x a = 9 x 9 x 9 = (3 x 3) x (3 x 3) x (3 x 3) = (3 x 3 x 3) x (3 x 3 x 3) = 27 x years.

28 Looking at Kepler s third law in detail The simplest form of the third law contains a hidden dependence on the mass of the Sun (not the mass of whatever planet we re looking at). Let s un- hide it: [P (yr)] 2 = [a (AU)]3 M (M )

29 How does this help us? We can now use Kepler s third law to analyze objects that don t revolve around the Sun! [P (yr)] 2 = [a (AU)]3 M (M )

30 Working with Kepler s third law If a planet has two moons whose orbital periods are 8 days and 1 day, what is the ra=o of their orbits semi- major axes? P 1 2 = a 13 /M P 2 2 = a 23 /M Dividing one equa=on by the other: (P 1 /P 2 ) 2 = (a 1 /a 2 ) 3 = 8 x 8 = (2 x 2 x 2) x (2 x 2 x 2) = (2 x 2) x (2 x 2) x (2 x 2) = 4 x 4 x 4 We know the ra=o of the semi- major axes a 1 /a 2 = 4, even though we don t know what either a 1 or a 2 is separately!

31 Clicker ques=on # 4 If Earth were in an orbit around a star with 9 =mes the mass of the Sun, but s=ll at a distance of 1 AU from that star, the =me it would take to complete one orbit would be A years. B years. C. 1 year. D. 3 years. E. 9 years. [P (yr)] 2 = [a (AU)]3 M (M )

32 Clicker ques=on # 5 If Earth were 9 =mes its current mass but s=ll orbi=ng the Sun at its current (1 AU) distance, the =me it would take to complete one orbit would be A years. B years. C. 1 year. D. 3 years. E. 9 years. [P (yr)] 2 = [a (AU)]3 M (M )

33 We can also analyze orbits around planets We re allowed to change units for convenience Express the semimajor axis, a, in km. Express the period, P, in s. Then [P (s)] 2 = 10 4 [a (km)]3 M (M )

34 Sept. 18 Jupiter s moons

35 Jupiter s moons Moon a (km) a a 3 P (d) P (s) P 2 Io Europa Ganymede Callisto [P (s)] 2 = [a (km)] 3 Depends on the mass of Jupiter.

36 Clicker ques=on # 6 Which two pieces of informa=on could be used to determine the mass of Saturn? A. Saturn s distance from the Sun and how long it takes to orbit the Sun. B. The semimajor axes of any two moons of Saturn. C. The orbital periods of any two moons of Saturn. D. The orbital period and mass of any single moon of Saturn. E. The orbital period and semimajor axis of any single moon of Saturn.

37 Universality (or: why Kepler was awesome) Kepler s laws apply to: planets orbi=ng the Sun moons orbi=ng planets planets orbi=ng other stars stars orbi=ng black holes

38 The Center of the Milky Way

39 Image credit: MPE Garching in the direc=on of Sagibarius

40 Example There is a black hole at the center of the Milky Way. A star orbits it with a semimajor axis a = 920 AU and period P = 14.5 yr. What is the mass of the black hole (in units of M sun )? [P (yr)] 2 = M (M ) = [a (AU)]3 M (M ) [a (AU)]3 [P (yr)] 2 = = =

41 One more layer of complica=on The versions of the third law that contain only one mass work well when the orbitee is much more massive than the orbiter (e.g., Sun is 333,000 =mes more massive than Earth). However: these are only approxima=ons of Newton s version of Kepler s third law (see textbook T6): Image credit: OSU/R. Pogge

42 What happens for more equal masses? Center of mass of the two objects (imagine trying to balance a see- saw/teeter- tober ) is a focus of each object s ellip=cal orbit. Center of mass can be inside the larger of the two. Image credit: Char=ng the Heavens

43 > 2 objects revolve around barycenter Barycenter = fancy name for center of mass of the en=re solar system: + some=mes (not always) inside Sun + moves with =me as the planets (especially Jupiter) orbit the Sun + orbits (including Sun s) are more complicated than simple ellipses Image credit: Wikipedia

Astro 109 Lecture 4: Learning from the Sun and Moon. September 12, 2014

Astro 109 Lecture 4: Learning from the Sun and Moon. September 12, 2014 Astro 109 Lecture 4: Learning from the Sun and Moon September 12, 2014 Constella@on of the day: Aquarius A zodiac constella@on visible in the night sky about now; one of 48 constella@ons tabulated by Ptolemy.

More information

Lecture 4: Kepler and Galileo. Astronomy 111 Wednesday September 6, 2017

Lecture 4: Kepler and Galileo. Astronomy 111 Wednesday September 6, 2017 Lecture 4: Kepler and Galileo Astronomy 111 Wednesday September 6, 2017 Reminders Online homework #2 due Monday at 3pm Johannes Kepler (1571-1630): German Was Tycho s assistant Used Tycho s data to discover

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

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

[05] Historical Perspectives (9/12/17)

[05] Historical Perspectives (9/12/17) 1 [05] Historical Perspectives (9/12/17) Upcoming Items 1. Homework #2 due now. 2. Read Ch. 4.1 4.2 and do self-study quizzes. 3. Homework #3 due in one week. Ptolemaic system http://static.newworldencyclopedia.org/thumb/3/3a/

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

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

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

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

KEPLER S LAWS OF PLANETARY MOTION

KEPLER S LAWS OF PLANETARY MOTION KEPLER S LAWS OF PLANETARY MOTION In the early 1600s, Johannes Kepler culminated his analysis of the extensive data taken by Tycho Brahe and published his three laws of planetary motion, which we know

More information

Astro 109 Lecture 11: Energy, Density, and Pressure October 8, 2014

Astro 109 Lecture 11: Energy, Density, and Pressure October 8, 2014 Astro 109 Lecture 11: Energy, Density, and Pressure October 8, 2014 Constella@on of the day: Scorpius Zodiac constella@on visible in the sky at night in northern summer; Antares is the 15th brightest star

More information

AST 105. Introduction to Astronomy: The Solar System. Announcement: First Midterm this Thursday 02/25

AST 105. Introduction to Astronomy: The Solar System. Announcement: First Midterm this Thursday 02/25 AST 105 Introduction to Astronomy: The Solar System Announcement: First Midterm this Thursday 02/25 REVIEW Newton s 3 Laws of Motion 1. An object moves at constant velocity if there is no net force acting

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

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

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

Introduction To Modern Astronomy II

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

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

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

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

The Revolution of the Moons of Jupiter

The Revolution of the Moons of Jupiter The Revolution of the Moons of Jupiter Overview: During this lab session you will make use of a CLEA (Contemporary Laboratory Experiences in Astronomy) computer program generously developed and supplied

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

4π 2 G(M1+M2 ) p2 = Newton s 3 Laws of Motion AST 105. Introduction to Astronomy: The Solar System. Newton's Version of Kepler's Third Law

4π 2 G(M1+M2 ) p2 = Newton s 3 Laws of Motion AST 105. Introduction to Astronomy: The Solar System. Newton's Version of Kepler's Third Law REVIEW Newton s 3 Laws of Motion AST 105 Introduction to Astronomy: The Solar System Announcement: First Midterm this Thursday 02/25 Newton's Version of Kepler's Third Law Newton's Version of Kepler's

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

Origin of Modern Astronomy Chapter 21

Origin of Modern Astronomy Chapter 21 Origin of Modern Astronomy Chapter 21 Early history of astronomy Ancient Greeks Used philosophical arguments to explain natural phenomena Also used some observa:onal data (looking at the night sky) Ancient

More information

Lab 6: The Planets and Kepler

Lab 6: The Planets and Kepler Lab 6: The Planets and Kepler The Motion of the Planets part I 1. Morning and Evening Stars. Start up Stellarium, and check to see if you have the Angle Tool installed it looks like a sideways A ( ) in

More information

Kepler s laws. Astronomy 101 Syracuse University, Fall 2018 Walter Freeman. October 2, Astronomy 101 Kepler s laws October 2, / 23

Kepler s laws. Astronomy 101 Syracuse University, Fall 2018 Walter Freeman. October 2, Astronomy 101 Kepler s laws October 2, / 23 Kepler s laws Astronomy 101 Syracuse University, Fall 2018 Walter Freeman October 2, 2018 Astronomy 101 Kepler s laws October 2, 2018 1 / 23 And yet it moves. Galileo (attributed), on the Earth Astronomy

More information

The Watershed : Tycho & Kepler

The Watershed : Tycho & Kepler The Watershed : Tycho & Kepler Key Ideas: Tycho Brahe Amassed 20 years of precise planetary data. Johannes Kepler Brilliant theorist who analyzed Tycho s data Kepler s Three Laws of Planetary Motion: 1st

More information

The Law of Ellipses (Kepler s First Law): all planets orbit the sun in a

The Law of Ellipses (Kepler s First Law): all planets orbit the sun in a Team Number Team Members Present Learning Objectives 1. Practice the Engineering Process a series of steps to follow to design a solution to a problem. 2. Practice the Five Dimensions of Being a Good Team

More information

ASTRO 1050 LAB #3: Planetary Orbits and Kepler s Laws

ASTRO 1050 LAB #3: Planetary Orbits and Kepler s Laws ASTRO 1050 LAB #3: Planetary Orbits and Kepler s Laws ABSTRACT Johannes Kepler (1571-1630), a German mathematician and astronomer, was a man on a quest to discover order and harmony in the solar system.

More information

Chapter 16 The Solar System

Chapter 16 The Solar System Chapter 16 The Solar System Finding the Standard Time and Date at Another Location Example When it is 12 noon in London, what is the standard time in Denver, Colorado (40 N, 105 W)? Section 15.3 Finding

More information

Astro 210 Lecture 6 Jan 29, 2018

Astro 210 Lecture 6 Jan 29, 2018 Astro 210 Lecture 6 Jan 29, 2018 Announcements HW2 due online in PDF, Friday 5:00 pm HW1 extended until 11:59pm today register your iclicker; link on course webpage first Planetarium shows Mon Feb 5 and

More information

PHYS 106 Fall 2151 Homework 3 Due: Thursday, 8 Oct 2015

PHYS 106 Fall 2151 Homework 3 Due: Thursday, 8 Oct 2015 PHYS 106 Fall 2151 Homework 3 Due: Thursday, 8 Oct 2015 When you do a calculation, show all your steps. Do not just give an answer. You may work with others, but the work you submit should be your own.

More 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

D. A system of assumptions and principles applicable to a wide range of phenomena that has been repeatedly verified

D. A system of assumptions and principles applicable to a wide range of phenomena that has been repeatedly verified ASTRONOMY 1 EXAM 1 Name Identify Terms - Matching (20 @ 1 point each = 20 pts.) 1 Solar System G 7. aphelion N 14. eccentricity M 2. Planet E 8. apparent visual magnitude R 15. empirical Q 3. Star P 9.

More information

If Earth had no tilt, what else would happen?

If Earth had no tilt, what else would happen? A more in depth explanation from last week: If Earth had no tilt, what else would happen? The equator would be much hotter due to the direct sunlight which would lead to a lower survival rate and little

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

PHYS 160 Astronomy Test #1 Fall 2017 Version B

PHYS 160 Astronomy Test #1 Fall 2017 Version B PHYS 160 Astronomy Test #1 Fall 2017 Version B 1 I. True/False (1 point each) Circle the T if the statement is true, or F if the statement is false on your answer sheet. 1. An object has the same weight,

More information

Unit 1 Astronomy: Kepler s Laws Of Planetary Motion Assessed Activity (66 marks total)

Unit 1 Astronomy: Kepler s Laws Of Planetary Motion Assessed Activity (66 marks total) Name: Solutions & Marking Scheme 2009 TG: PF Unit 1 Astronomy: Kepler s Laws Of Planetary Motion Assessed Activity (66 marks total) Aim: To investigate Kepler s three laws planetary motion. Apparatus:

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

Astronomy Section 2 Solar System Test

Astronomy Section 2 Solar System Test is really cool! 1. The diagram below shows one model of a portion of the universe. Astronomy Section 2 Solar System Test 4. Which arrangement of the Sun, the Moon, and Earth results in the highest high

More information

Phys 214. Planets and Life

Phys 214. Planets and Life Phys 214. Planets and Life Dr. Cristina Buzea Department of Physics Room 259 E-mail: cristi@physics.queensu.ca (Please use PHYS214 in e-mail subject) Lecture 13. Midterm review February 4th, 2008 1. Astronomy

More information

Tycho Brahe

Tycho Brahe Tycho Brahe 1546-1601 At the time of Shakespeare and Elizabeth I and Champlain Lost part of his nose in a duel over who was the best mathematician At 27 he measured the distance of a supernova and a comet

More information

HOMEWORK AND EXAMS. Homework Set 13 due Wednesday November 29. Exam 3 Monday December 4. Homework Set 14 due Friday December 8

HOMEWORK AND EXAMS. Homework Set 13 due Wednesday November 29. Exam 3 Monday December 4. Homework Set 14 due Friday December 8 HOMEWORK AND EXAMS Homework Set 13 due Wednesday November 29 Exam 3 Monday December 4 Homework Set 14 due Friday December 8 Final Exam Tuesday December 12 1 Section 8.6. The Kepler orbits Read Section

More information

Position 3. None - it is always above the horizon. Agree with student 2; star B never crosses horizon plane, so it can t rise or set.

Position 3. None - it is always above the horizon. Agree with student 2; star B never crosses horizon plane, so it can t rise or set. Position 3 None - it is always above the horizon. N E W S Agree with student 2; star B never crosses horizon plane, so it can t rise or set. Imaginary plane No; the Earth blocks the view. Star A at position

More 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

Assignment 1. Due Feb. 11, 2019

Assignment 1. Due Feb. 11, 2019 Assignment 1 Due Feb. 11, 2019 Show all work and turn in answers on separate pages, not on these pages. Circle your final answers for clarity. Be sure to show/explain all of your reasoning and that your

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

Goals of this course. Welcome to Stars, Galaxies & the Universe. Grading for Stars, Galaxies & Universe. Other things you need to know: Course Website

Goals of this course. Welcome to Stars, Galaxies & the Universe. Grading for Stars, Galaxies & Universe. Other things you need to know: Course Website Welcome to Stars, Galaxies & the Universe Grading for Stars, Galaxies & Universe One-hour exams (3 exams, dates on syllabus) 300 Final exam (16 December 2010) 150 Homework (10 of 12 ICON assignments) 100

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

Astronomy 1 Fall 2016

Astronomy 1 Fall 2016 Astronomy 1 Fall 2016 Comet Halley Edmund Halley, a friend of Newton s used Newton s math to predict the return of a comet seen at intervals of 76 years. Lecture 3; September 29, 2016 Previously on Astro-1

More information

1UNIT. The Universe. What do you remember? Key language. Content objectives

1UNIT. The Universe. What do you remember? Key language. Content objectives 1UNIT The Universe What do you remember? What are the points of light in this photo? What is the difference between a star and a planet? a moon and a comet? Content objectives In this unit, you will Learn

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

2. See FIGURE B. This person in the FIGURE discovered that this planet had phases (name the planet)?

2. See FIGURE B. This person in the FIGURE discovered that this planet had phases (name the planet)? ASTRONOMY 2 MIDTERM EXAM PART I SPRING 2019 60 QUESTIONS 50 POINTS: Part I of the midterm constitutes the Take-Home part of the entire Midterm Exam. Additionally, this Take-Home part is divided into two

More information

Lecture 2: Motions of the Earth and Moon. Astronomy 111 Wednesday August 30, 2017

Lecture 2: Motions of the Earth and Moon. Astronomy 111 Wednesday August 30, 2017 Lecture 2: Motions of the Earth and Moon Astronomy 111 Wednesday August 30, 2017 Reminders Online homework #1 due Monday at 3pm Labs start next week Motions of the Earth ASTR111 Lecture 2 Observation:

More information

1. The Moon appears larger when it rises than when it is high in the sky because

1. The Moon appears larger when it rises than when it is high in the sky because 2-1 Copyright 2016 All rights reserved. No reproduction or distribution without the prior written consent of 1. The Moon appears larger when it rises than when it is high in the sky because A. you are

More information

Astronomy A BEGINNER S GUIDE TO THE UNIVERSE EIGHTH EDITION

Astronomy A BEGINNER S GUIDE TO THE UNIVERSE EIGHTH EDITION Astronomy A BEGINNER S GUIDE TO THE UNIVERSE EIGHTH EDITION CHAPTER 1 The Copernican Revolution Lecture Presentation 1.0 Have you ever wondered about? Where are the stars during the day? What is the near

More information

Name Period Date Earth and Space Science. Solar System Review

Name Period Date Earth and Space Science. Solar System Review Name Period Date Earth and Space Science Solar System Review 1. is the spinning a planetary object on its axis. 2. is the backward motion of planets. 3. The is a unit less number between 0 and 1 that describes

More 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

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

VISUAL PHYSICS ONLINE

VISUAL PHYSICS ONLINE VISUAL PHYSICS ONLINE PRACTICAL ACTIVITY HOW DO THE PANETS MOVE? One of the most important questions historically in Physics was how the planets move. Many historians consider the field of Physics to date

More information

Kepler s Laws of Orbital Motion. Lecture 5 January 24, 2013

Kepler s Laws of Orbital Motion. Lecture 5 January 24, 2013 Kepler s Laws of Orbital Motion Lecture 5 January 24, 2013 Team Extra Credit Two teams: Io & Genius Every class (that is not an exam/exam review) will have a question asked to a random member of each team

More information

PTYS/ASTR 206 Section 2 Spring 2007 Homework #1 (Page 1/4)

PTYS/ASTR 206 Section 2 Spring 2007 Homework #1 (Page 1/4) PTYS/ASTR 206 Section 2 Spring 2007 Homework #1 (Page 1/4) NAME: KEY Due Date: start of class 1/25/2007 5 pts extra credit if turned in before 9:00AM (early!) (To get the extra credit, the assignment must

More information

You should have finished reading Chapter 3, and started on chapter 4 for next week.

You should have finished reading Chapter 3, and started on chapter 4 for next week. Announcements Homework due on Sunday at 11:45pm. Thank your classmate! You should have finished reading Chapter 3, and started on chapter 4 for next week. Don t forget your out of class planetarium show

More information

Kepler s Laws of Orbital Motion. Lecture 5 January 30, 2014

Kepler s Laws of Orbital Motion. Lecture 5 January 30, 2014 Kepler s Laws of Orbital Motion Lecture 5 January 30, 2014 Parallax If distance is measured in parsecs then d = 1 PA Where PA is the parallax angle, in arcsec NOTE: The distance from the Sun to the Earth

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

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

Unit: Planetary Science

Unit: Planetary Science Orbital Motion Kepler s Laws GETTING AN ACCOUNT: 1) go to www.explorelearning.com 2) click on Enroll in a class (top right hand area of screen). 3) Where it says Enter class Code enter the number: MLTWD2YAZH

More information

1. The bar graph below shows one planetary characteristic, identified as X, plotted for the planets of our solar system.

1. The bar graph below shows one planetary characteristic, identified as X, plotted for the planets of our solar system. 1. The bar graph below shows one planetary characteristic, identified as X, plotted for the planets of our solar system. Which characteristic of the planets in our solar system is represented by X? A)

More information

A. The moon B. The sun C. Jupiter D. Earth A. 1 B. 2 C. 3 D. 4. Sky Science Unit Review Konrad. Here is a selection of PAT style questions.

A. The moon B. The sun C. Jupiter D. Earth A. 1 B. 2 C. 3 D. 4. Sky Science Unit Review Konrad. Here is a selection of PAT style questions. Sky Science Unit Review Konrad Here is a selection of PAT style questions. Use the following information to answer the next question 1. 2. The source of light that allows astronimors to see Jupitor through

More information

GEOL212 Due 9/24/18 Homework 4

GEOL212 Due 9/24/18 Homework 4 GEOL212 Due 9/24/18 Homework 4 General instructions: Although you are allowed to discuss homework questions with your classmates, your work must be uniquely your own. Thus, please answer all questions

More information

PHYS1002: Founda0ons of Astronomy

PHYS1002: Founda0ons of Astronomy PHYS1002: Founda0ons of Astronomy Simon.Driver@icrar.org Course Text: Astronomy: A Physical Perspec0ve, Marc Kutner 9 Lectures + 2 Assessments + Final Exam New course component Exams will be similar to

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

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

5.1. Accelerated Coordinate Systems:

5.1. Accelerated Coordinate Systems: 5.1. Accelerated Coordinate Systems: Recall: Uniformly moving reference frames (e.g. those considered at 'rest' or moving with constant velocity in a straight line) are called inertial reference frames.

More information

2. See FIGURE B. In the Renaissance times, he proposed this model of the solar system (name this person).

2. See FIGURE B. In the Renaissance times, he proposed this model of the solar system (name this person). ASTRONOMY 5 MIDTERM EXAM PART I SPRING 2019 60 QUESTIONS 50 POINTS: Part I of the midterm constitutes the Take-Home part of the entire Midterm Exam. Additionally, this Take-Home part is divided into two

More information

Assignment 1. Due Jan. 31, 2017

Assignment 1. Due Jan. 31, 2017 Assignment 1 Due Jan. 31, 2017 Show all work and turn in answers on separate pages, not on these pages. Circle your final answers for clarity. Be sure to show/explain all of your reasoning and that your

More information

Tycho Brahe ( )

Tycho Brahe ( ) Tycho Brahe (1546-1601) Foremost astronomer after the death of Copernicus. King Frederick II of Denmark set him up at Uraniborg, an observatory on the island of Hveen. With new instruments (quadrant),

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

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

The Mass of Jupiter Student Guide

The Mass of Jupiter Student Guide The Mass of Jupiter Student Guide Introduction: In this lab, you will use astronomical observations of Jupiter and its satellites to measure the mass of Jupiter. We will use the program Stellarium to simulate

More information

The Heliocentric Model of Copernicus

The Heliocentric Model of Copernicus Celestial Mechanics The Heliocentric Model of Copernicus Sun at the center and planets (including Earth) orbiting along circles. inferior planets - planets closer to Sun than Earth - Mercury, Venus superior

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

Kepler correctly determined the motion of the planets giving his 3 Laws which still hold today for the planets and other orbital motion: moons around

Kepler correctly determined the motion of the planets giving his 3 Laws which still hold today for the planets and other orbital motion: moons around Kepler correctly determined the motion of the planets giving his 3 Laws which still hold today for the planets and other orbital motion: moons around planets, exoplanets around other stars, stars in the

More information

a. 0.5 AU b. 5 AU c. 50 AU d.* AU e AU

a. 0.5 AU b. 5 AU c. 50 AU d.* AU e AU 1 AST104 Sp04: WELCOME TO EXAM 1 Multiple Choice Questions: Mark the best answer choice. Read all answer choices before making selection. (No credit given when multiple answers are marked.) 1. A galaxy

More information

Astronomy 100 Section 2 MWF Greg Hall. Outline. Total Lunar Eclipse Time Lapse. Homework #1 is due Friday, 11:50 a.m.!!!!!

Astronomy 100 Section 2 MWF Greg Hall. Outline. Total Lunar Eclipse Time Lapse. Homework #1 is due Friday, 11:50 a.m.!!!!! Astronomy 100 Section 2 MWF 1200-1300 100 Greg Hall Leslie Looney Phone: 217-244-3615 Email: lwl @ uiuc. edu Office: Astro Building #218 Office Hours: MTF 10:30-11:30 a.m. or by appointment Homework #1

More information

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

DeAnza College Winter First Midterm Exam MAKE ALL MARKS DARK AND COMPLETE. FAMILY NAME : (Please PRINT!) GIVEN NAME : (Please PRINT!) Signature: ASTRONOMY 4 DeAnza College Winter 2018 First Midterm Exam MAKE ALL MARKS DARK AND COMPLETE. Instructions: 1. On your Parscore sheet

More information

Astronomy 291. Professor Bradley M. Peterson

Astronomy 291. Professor Bradley M. Peterson Astronomy 291 Professor Bradley M. Peterson The Sky As a first step, we need to understand the appearance of the sky. Important points (to be explained): The relative positions of stars remain the same

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

APS 1030 Astronomy Lab 79 Kepler's Laws KEPLER'S LAWS

APS 1030 Astronomy Lab 79 Kepler's Laws KEPLER'S LAWS APS 1030 Astronomy Lab 79 Kepler's Laws KEPLER'S LAWS SYNOPSIS: Johannes Kepler formulated three laws that described how the planets orbit around the Sun. His work paved the way for Isaac Newton, who derived

More information

I. Introduction. II. An Introduction to Starry Night NAME: ORBITAL MOTION

I. Introduction. II. An Introduction to Starry Night NAME: ORBITAL MOTION NAME: ORBITAL MOTION What will you learn in this Lab? You will be using some special software to simulate the motion of planets in our Solar System and across the night sky. You will be asked to try and

More information

Astronomy 101 Exam 2 Form AC-key

Astronomy 101 Exam 2 Form AC-key Astronomy 101 Exam 2 Form AC-key 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

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

Thursday is last Planetarium observing. Nighttime observing starts next week.

Thursday is last Planetarium observing. Nighttime observing starts next week. Homework #2 is due at 11:50am this Friday! Thursday is last Planetarium observing. Solar Observing is happening now! Check out webpage to see if it is canceled due to weather. Nighttime observing starts

More information

Coriolis Effect - the apparent curved paths of projectiles, winds, and ocean currents

Coriolis Effect - the apparent curved paths of projectiles, winds, and ocean currents Regents Earth Science Unit 5: Astronomy Models of the Universe Earliest models of the universe were based on the idea that the Sun, Moon, and planets all orbit the Earth models needed to explain how the

More information

ASTR : Stars & Galaxies (Spring 2019)... Study Guide for Midterm 1

ASTR : Stars & Galaxies (Spring 2019)... Study Guide for Midterm 1 ASTR-1200-01: Stars & Galaxies (Spring 2019)........................ Study Guide for Midterm 1 The first midterm exam for ASTR-1200 takes place in class on Wednesday, February 13, 2019. The exam covers

More information

Name and Student ID Section Day/Time:

Name and Student ID Section Day/Time: AY2 - Overview of the Universe - Midterm #1 - Instructor: Maria F. Duran Name and Student ID Section Day/Time: 1) Imagine we ve discovered a planet orbiting another star at 1 AU every 6 months. The planet

More information

astronomy A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times.

astronomy A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times. astronomy 2008 1. A planet was viewed from Earth for several hours. The diagrams below represent the appearance of the planet at four different times. 5. If the distance between the Earth and the Sun were

More information

UNIT 1: EARTH AND THE SOLAR SYSTEM.

UNIT 1: EARTH AND THE SOLAR SYSTEM. UNIT 1: EARTH AND THE SOLAR SYSTEM. 1) A BRIEF HISTORY Theories of the Universe In the second century BC, the astronomer Ptolemy proposed that the Earth was the centre of the Universe, and that the Sun,

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

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