Chapter 5. Determining Masses of Astronomical Objects

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Chapter 5. Determining Masses of Astronomical Objects"

Transcription

1 Chapter 5. Determining Masses of Astronomical Objects One of the most fundamental and important properties of an object is its mass. On Earth we can easily weigh objects, essentially measuring how much force the Earth is exerting on them, which depends on their mass. For astronomical objects we can only watch their motions in response to the gravitational interactions. A common event is when one object orbits another (or, more precisely, they orbit each other). This occurs for planets orbiting a star or two stars orbiting each other. It also occurs for binary galaxies although the details of how the mass can be determined in this case are different because the orbital period of two galaxies tends to be millions of years much longer than can be measured on human time scales! To determine masses of objects in the Solar System awaited to two advances beyond Newton: determination of distances within the Solar System (i.e. beyond the Moon, which the Greeks knew) and the calibration of big gee (G) the Gravitational Constant. 1. Distances within the Solar System Kepler s Third Law, P 2 = a 3, related something we could determine, sidereal periods of planets, to something we wished to know, a, the semi-major axis (or size) of their orbits. Unfortunately, the relation was in terms of the Earth s value for a, which is called the Astronomical Unit, or AU. The AU is defined as the semi-major axis of the Earth s orbit. But how can we determine it? (Note that because the Earth s orbit is nearly a circle, the AU is also nearly the mean distance of the Sun from the Earth. However, the precise definition of the AU is, as given above, the value of the semi-major axis of the Earth s orbit). One approach to calibrating the AU in physical units such as meters, would be to determine the distance to the Sun directly at any given time. However, this turns out not to be easy to do. A simpler method is to get some other distance within the Solar System to a planet (or asteroid) that obeys Kepler s Third Law and effectively then, one has determined the scale of the Solar System. That is, we know instantaneously the distance between any two objects orbiting the Sun from Kepler s Laws, and if we can get the actual distance (in meters, not in AU!) between these objects then we can calibrate the AU. This was first done by Giovanni Cassini in His method is known as the parallax method of distance determination and is widely used in astronomy even today, although not for Solar System objects. He used observations of the planet Mars obtained simultaneously from two locations on the Earth that were greatly spaced in distance. One was in Europe and the other in South America. Mars appeared to be in slightly different directions against the

2 2 fixed stars when viewed from these two different locations on Earth. By measuring the angle through which Mars appeared to move when viewed from the two different locations, knowing the distance between those locations on Earth, Cassini could employ simple geometry to get the distance to Mars. He achieved an accuracy of about 7% and calibrated distances within the Solar System (i.e. calibrated the AU in terms of meters). Today we have much more accuracy in our value of the AU. Distances to planets are routinely determined by bouncing radar signals off of them and timing how long the signal takes to return to Earth. 2. Calibrating the Gravitational Constant To make progress in determining masses of objects, we must first directly measure how strong gravity is. That is we must determine the value of big gee (G), the Universal constant of gravity in Newton s equations. Surprisingly, this was not done until well after Sir Isaac Newton s work. It was first accomplished by the British physicist Lord Cavendish (see link on course page). He used a very sensitive instrument called a torsion balance to measure the force exerted by large masses on each other. His experiment yielded the mass (and, therefore density) of the Earth for the first time. Once G was known, it was possible to use little gee (g), the gravitational acceleration at the surface of the Earth to determine M, the mass of the Earth. From Newton s theory, we have F = ma = mg = GMm R 2 where g is the acceleration of an object at the surface of the Earth and R is the radius of the Earth and M is the mass of the Earth. From this, it follows that g = GM R 2 so that with g known (9.8 m/s/s) and R known and G now known, M is determined. From the mass of the Earth, its mean density (ρ) follows immediately as its mass divided by its volume. Since the Earth is a sphere (to a good approximation!) its volume is 4 3 πr3 so ρ = 3M 4πR 3 = 5.5 gm/cm3. 3. Two-Body with m << M For objects besides the Earth we normally cannot measure their surface accelerations directly, so we need to use their gravitational affect on nearby objects (e.g. moon, planet,

3 3 companion star, etc.) to determine their mass. The simplest case to analyze and determine a mass for is when m << M and the motion of the large object can be ignored. Note that since the motion of m is independent of its actual mass, this method can only be used to determine M, not m. In reality, the method determines the sum of the masses M+m, but since m << M this is essentially the same as determining M. The relevant equation is Kepler s Third Law as formulated by Newton, namely P 2 = 4π2 GM a3. It is clear from this equation that if we can measure P and a we can solve for M, because the other quantities in the equation are known constants. Normally, P is pretty easy to determine for any cyclical motion just by watching it. For example, we can determine the period of the Moon around the Earth just by watching its motion against the fixed stars. We can get P for Earth orbiting the Sun from the time it takes the Sun to go around the sky once. The orbital period of other planets is derived from their Synodic period (S) as described in an earlier chapter. As an example, the mass of the Sun might be found from this equation by using the data for the Earth s orbit. We know that the period is 1 year (or sec) and we know that the AU is 150 million km (or cm). Therefore, we know all quantities in the equation above except M, the mass of the Sun, and we can solve for it, being careful to use values with the same units. Using the AU in cm and P in sec, we need G in cgs units, and its value is G = Plugging in, we find the mass of the Sun to be about gm. Once a mass is determined for an object, its mean density again follows easily, assuming we know how big the object is. The diameter of the Sun is easy to determine from Earth, in part by the fact that the Moon happens to just fit right over it during a solar eclipse! Hence, the Moon and Sun have close to the same angular size, which is about one-half of a degree or 30 arc-minutes. Knowing the angular diameter of the Sun and its actual distance (the AU) allows us to calculate its actual diameter in terms of meters and, therefore, its radius. From its radius, and the fact that it is a sphere (as closely as we can tell!) its volume follows. From its mass and volume, its mean density follows, and is about 1.4 gm/cm 3. Note that the mean density of the Sun is much smaller than that of the Earth which, of course, reflects the fact that its composition is much different. The Sun is primarily made of Hydrogen, while the Earth is primarily made of Oxygen (bound to silicon, known as silicates or rocks ). Masses of planets with moons are very easy to determine by this method. A good example is Jupiter, which has 4 easily visible moons, discovered by Galileo. By observing any one of the moons motion one can determine its period and its maximum separation from Jupiter, in terms of angle. The period can be converted to seconds and the angular

4 4 separation can be converted to a size of orbit (around Jupiter) using the known distance to Jupiter. Hence, with P and a known for that moon, we can use Kepler s Third Law (Newton s form) to determine the value of M, which is here the mass of Jupiter, since it is the central massive object about which its moons are orbiting. Again, once the mass of the planet is found, we can calculate its mean density. For Jupiter this turns out to be close to that of the Sun, about 1.33 gm/cm 3. This is an indication that Jupiter is a much different kind of planet than the Earth being composed primarily of Hydrogen, like the Sun, not oxygen and heavier elements like the Earth. This method can be used to determine the masses of any planets (or even some nonplanets) that have moons orbiting them. This applies to all the planets now except Mercury. Venus also does not have a moon but it does have an artificial satellite (which we put there) orbiting it. Some asteroids even have moons of their own and this method can be used to get their masses. A famous non-planet known as Pluto has a moon and its mass (and density) can therefore be determined. Densities of objects in the Solar System are (note that liquid water and pure ice have a density of about 1 gm/cm 3 and typical rocks on the Earth s surface have a density of about 3 gm/cm 3 : Sun (1.4), Mercury (5.4), Venus (5.2), Earth (5.5), Moon (3.4), Mars (3.9), Jupiter (1.3), Saturn (0.7), Pluto (2.0). Based on this we can divide object in Solar System into those composed primarily of the light elements Hydrogen and Helium (Sun, Jupiter, Saturn), those composed of rocks including silicates and iron (Earth, Venus, Mercury), rocky planets with less iron (Moon, Mars) and icy objects (Pluto). 4. General Two Body Orbits Often it turns out that the difference in masses between the two orbiting objects, m and M are not that different, in which case M must be replaced by m+m and a must be replaced by the sum of the semi-major axes in Kepler s Third Law. So, knowing the period and total size of the orbit only gives the sum of the masses, not the individual masses. To get individual masses we must get the relative sizes of the orbits of the two objects, remembering that they will both orbit the center of mass. They obey the relation that m 1 a 1 = m 2 a 2. It is generally the case for binary stars that we need to know the motions of both stars in order to determine the individual masses. A beautiful example of this effect, where the motion of the more massive object must be taken into account, is the discover of exoplanets, planets around other stars (see link on course page). Planets do exert a gravitational influence on their host stars and so their presence can be dettected by the small orbit, or wobble that the central star undergoes as it responds to the gravitational pull of the planet. This motion may be very small (only meters/second

5 5 in terms of velocity), yet it can be detected with modern techniques. Hundreds of planets have now been detected around nearby stars by this method. From the amplitude of the motions of the stars we can determine the mass of the object they are orbiting i.e. the planets. So far, this method has detected objects as small in mass as Neptune (about 15 Earth-masses), but it is not capable of finding Earth-sized planets. 5. Unbound Orbits It is also possible to determine the mass of an object with nothing orbiting it, just by the gravitational deflection it causes on an object passing close to it. In other words, one can use the shape of the unbound (hyperbolic) orbit to get the mass of the deflecting objecting. This is how the mass of Mercury must be determined, since it has not orbiting satellites, even artificial ones, however we have done fly bys of satellites passing close to it along unbound orbits. This is also how we can determine the masses of moons of other planets (e.g. Jupiter) by having a satellite pass close to the Moon and seeing how much deflection there is). We can also get masses of asteroids in this way as our probes fly by them by measuring the amount of deflection of the orbit. 6. Perturbations The gravitational interactions between the smaller objects (e.g. planets) orbiting a larger object (e.g. star) produce so-called perturbations to the elliptical orbits that the planets would otherwise follow. This effect can be quite pronounced and add up over time to change the characteristics (e.g. eccentricity) of orbits. It was actually key to the discovery of a new planet in our own solar system Neptune. The planet Uranus was discovered entirely by chance in the late 1700 s by Sir William Herschel. When its motion was followed carefully, it was found not to be obeying Kepler s Laws precisely. This was attributed to the existence of an additional planet, as yet unseen. In the mid 1800 s the exact location of Neptune was calculated using the perturbation effect it must be having on Uranus. The planet was then discovered in one night at very close to its predicted position. This was a triumph for Newton s law of gravity and for science in general. In some cases, the mass of an orbiting object can be determined by the amount of perturbation it produces in the orbit of another object. Pluto was originally thought to be having a significant perturbing effect on Neptune, making it much more massive than we now know it is. This was leading to the absurd conclusion that the density of Pluto was so high that it must be made of gold! (or something like that). We now know that the small discrepancies thought to be

6 6 measured in Neptune s orbit and attributed to Pluto s influence were actually only noise in the measurements. 7. Non-Keplerian Motions, Virial Theorem and Dark Matter We will come back to this later in the course, but it is worth mentioning here that this same concepts of orbits of objects around each other or motion in response to the presence of another mass is the central idea throughout astronomy in determining mass. For example, stars orbiting around the center of a galaxy can be used to determine the mass of the matter inside their orbiting position. The discovery of rapidly orbiting stars near the center of our own galaxy led to the realization that there is a central black hole there. The fact that orbital speed increases (or stays the same) as one moves further out in a galaxy, rather than decreasing, as in the solar system, led to the discovery of Dark Matter in galaxies (not the same as black holes). The Virial theorem states that twice the total kinetic energy in a gravitationally bound cluster (of stars or galaxies) is equal to the total potential energy. This concept is used to measure masses of whole clusters of stars and galaxies and also indicates that there is much more mass than expected based on the visible light. This is additional strong evidence for dark matter in the Universe. We will come back to these concepts later in the course but wanted to mention them here because they are all related to the same basic idea of how mass is determined, that starts with Newton s laws.

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.

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. 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 increased,

More information

Newton s Universal Law of Gravitation The Apple and the Moon Video

Newton s Universal Law of Gravitation The Apple and the Moon Video Name Date Pd Newton s Universal Law of Gravitation The Apple and the Moon Video Objectives Recognize that a gravitational force exists between any two objects and that the force is directly proportional

More information

The orbit of Halley s Comet

The orbit of Halley s Comet The orbit of Halley s Comet Given this information Orbital period = 76 yrs Aphelion distance = 35.3 AU Observed comet in 1682 and predicted return 1758 Questions: How close does HC approach the Sun? What

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

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

Newton s Law of Gravity

Newton s Law of Gravity Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has

More information

UCM-Gravity. 2. The diagram shows two bowling balls, A and B, each having a mass of 7 kilograms, placed 2 meters apart.

UCM-Gravity. 2. The diagram shows two bowling balls, A and B, each having a mass of 7 kilograms, placed 2 meters apart. 1. A space probe is launched into space from Earth s surface. Which graph represents the relationship between the magnitude of the gravitational force exerted on Earth by the space probe and the distance

More information

Chapter 6: Our Solar System and Its Origin

Chapter 6: Our Solar System and Its Origin Chapter 6: Our Solar System and Its Origin What does our solar system look like? The planets are tiny compared to the distances between them (a million times smaller than shown here), but they exhibit

More information

1 The Nine Planets. What are the parts of our solar system? When were the planets discovered? How do astronomers measure large distances?

1 The Nine Planets. What are the parts of our solar system? When were the planets discovered? How do astronomers measure large distances? CHAPTER 4 1 The Nine Planets SECTION A Family of Planets BEFORE YOU READ After you read this section, you should be able to answer these questions: What are the parts of our solar system? When were the

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

LESSON 3 THE SOLAR SYSTEM. Chapter 8, Astronomy

LESSON 3 THE SOLAR SYSTEM. Chapter 8, Astronomy LESSON 3 THE SOLAR SYSTEM Chapter 8, Astronomy OBJECTIVES Identify planets by observing their movement against background stars. Explain that the solar system consists of many bodies held together by gravity.

More information

THE SOLAR SYSTEM NAME. I. Physical characteristics of the solar system

THE SOLAR SYSTEM NAME. I. Physical characteristics of the solar system NAME I. Physical characteristics of the solar system THE SOLAR SYSTEM The solar system consists of the sun and 9 planets. Table 2 lists a number of the properties and characteristics of the sun and the

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

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

Name Class Date. true

Name Class Date. true Exercises 131 The Falling Apple (page 233) 1 Describe the legend of Newton s discovery that gravity extends throughout the universe According to legend, Newton saw an apple fall from a tree and realized

More information

EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1

EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 Instructor: L. M. Khandro EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 1. An arc second is a measure of a. time interval between oscillations of a standard clock b. time

More information

Newton s Law of Gravity

Newton s Law of Gravity Newton s Law of Gravity Example 4: What is this persons weight on Earth? Earth s mass = 5.98 10 24 kg Mar s mass = 6.4191 10 23 kg Mar s radius = 3400 km Earth s radius = 6378 km Newton s Form of Kepler

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

Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X?

Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? Solar System 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? A) Earth B) Sun C) Moon D) Polaris 2. Which object orbits Earth in both the Earth-centered

More information

UNIT V. Earth and Space. Earth and the Solar System

UNIT V. Earth and Space. Earth and the Solar System UNIT V Earth and Space Chapter 9 Earth and the Solar System EARTH AND OTHER PLANETS A solar system contains planets, moons, and other objects that orbit around a star or the star system. The solar system

More information

Motion and Gravity in Space

Motion and Gravity in Space Motion and Gravity in Space Each planet spins on its axis. The spinning of a body, such a planet, on its axis is called rotation. The orbit is the path that a body follows as it travels around another

More information

Homework #3 Solutions

Homework #3 Solutions Chap. 7, #40 Homework #3 Solutions ASTR100: Introduction to Astronomy Fall 2009: Dr. Stacy McGaugh Which of the following is a strong greenhouse gas? A) Nitrogen. B) Water Vapor. C) Oxygen) The correct

More information

Class 2 Solar System Characteristics Formation Exosolar Planets

Class 2 Solar System Characteristics Formation Exosolar Planets Class 1 Introduction, Background History of Modern Astronomy The Night Sky, Eclipses and the Seasons Kepler's Laws Newtonian Gravity General Relativity Matter and Light Telescopes Class 2 Solar System

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

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

Grade 6 Standard 3 Unit Test A Astronomy. 1. The four inner planets are rocky and small. Which description best fits the next four outer planets?

Grade 6 Standard 3 Unit Test A Astronomy. 1. The four inner planets are rocky and small. Which description best fits the next four outer planets? Grade 6 Standard 3 Unit Test A Astronomy Multiple Choice 1. The four inner planets are rocky and small. Which description best fits the next four outer planets? A. They are also rocky and small. B. They

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

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

Chapter 5: Circular Motion, the Planets, and Gravity

Chapter 5: Circular Motion, the Planets, and Gravity Chapter 5: Circular Motion, the Planets, and Gravity 1. Earth s gravity attracts a person with a force of 120 lbs. The force with which the Earth is attracted towards the person is A. Zero. B. Small but

More information

A. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great.

A. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great. Q12.1 The mass of the Moon is 1/81 of the mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth is A. 81 2

More information

The Hidden Lives of Galaxies. Jim Lochner, USRA & NASA/GSFC

The Hidden Lives of Galaxies. Jim Lochner, USRA & NASA/GSFC The Hidden Lives of Galaxies Jim Lochner, USRA & NASA/GSFC What is a Galaxy? Solar System Distance from Earth to Sun = 93,000,000 miles = 8 light-minutes Size of Solar System = 5.5 light-hours What is

More information

The University of Texas at Austin. Gravity and Orbits

The University of Texas at Austin. Gravity and Orbits UTeach Outreach The University of Texas at Austin Gravity and Orbits Time of Lesson: 60-75 minutes Content Standards Addressed in Lesson: TEKS6.11B understand that gravity is the force that governs the

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

Chapter 7 Reading Quiz Clickers. The Cosmic Perspective Seventh Edition. Our Planetary System Pearson Education, Inc.

Chapter 7 Reading Quiz Clickers. The Cosmic Perspective Seventh Edition. Our Planetary System Pearson Education, Inc. Reading Quiz Clickers The Cosmic Perspective Seventh Edition Our Planetary System 7.1 Studying the Solar System What does the solar system look like? What can we learn by comparing the planets to one another?

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

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

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

Name: Date: Period: Gravity Study Guide

Name: Date: Period: Gravity Study Guide Vocabulary: Define the following terms. Law of Universal Gravitation Gravity Study Guide Weight Weightlessness Gravitational Field Black hole Escape velocity Math: Be able to use the equation for the law

More information

Aphelion The point in the orbit of a planet or other celestial body where it is furthest from the Sun.

Aphelion The point in the orbit of a planet or other celestial body where it is furthest from the Sun. SKYTRACK Glossary of Terms Angular distance The angular separation between two objects in the sky as perceived by an observer, measured in angles. The angular separation between two celestial objects in

More information

Introduction to the Solar System

Introduction to the Solar System Introduction to the Solar System Lesson Objectives Describe some early ideas about our solar system. Name the planets, and describe their motion around the Sun. Explain how the solar system formed. Introduction

More information

THE SOLAR SYSTEM - EXERCISES 1

THE SOLAR SYSTEM - EXERCISES 1 THE SOLAR SYSTEM - EXERCISES 1 THE SUN AND THE SOLAR SYSTEM Name the planets in their order from the sun. 1 2 3 4 5 6 7 8 The asteroid belt is between and Which planet has the most moons? About how many?

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

Lecture 5: Newton s Laws. Astronomy 111

Lecture 5: Newton s Laws. Astronomy 111 Lecture 5: Newton s Laws Astronomy 111 Isaac Newton (1643-1727): English Discovered: three laws of motion, one law of universal gravitation. Newton s great book: Newton s laws are universal in scope,

More information

The Origin of the Solar System and Other Planetary Systems

The Origin of the Solar System and Other Planetary Systems The Origin of the Solar System and Other Planetary Systems Modeling Planet Formation Boundary Conditions Nebular Hypothesis Fixing Problems Role of Catastrophes Planets of Other Stars Modeling Planet Formation

More information

Solar System Fundamentals. What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System

Solar System Fundamentals. What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System Solar System Fundamentals What is a Planet? Planetary orbits Planetary temperatures Planetary Atmospheres Origin of the Solar System Properties of Planets What is a planet? Defined finally in August 2006!

More information

Astronomy 114 Summary of Important Concepts #1 1

Astronomy 114 Summary of Important Concepts #1 1 Astronomy 114 Summary of Important Concepts #1 1 1 Kepler s Third Law Kepler discovered that the size of a planet s orbit (the semi-major axis of the ellipse) is simply related to sidereal period of the

More information

The Formation of Planetary Systems. Astronomy 1-1 Lecture 20-1

The Formation of Planetary Systems. Astronomy 1-1 Lecture 20-1 The Formation of Planetary Systems Astronomy 1-1 Lecture 20-1 Modeling Planet Formation Any model for solar system and planet formation must explain 1. Planets are relatively isolated in space 2. Planetary

More information

Study Guide: Solar System

Study Guide: Solar System Study Guide: Solar System 1. How many planets are there in the solar system? 2. What is the correct order of all the planets in the solar system? 3. Where can a comet be located in the solar system? 4.

More information

Name Class Period. F = G m 1 m 2 d 2. G =6.67 x 10-11 Nm 2 /kg 2

Name Class Period. F = G m 1 m 2 d 2. G =6.67 x 10-11 Nm 2 /kg 2 Gravitational Forces 13.1 Newton s Law of Universal Gravity Newton discovered that gravity is universal. Everything pulls on everything else in the universe in a way that involves only mass and distance.

More information

GRAVITY CONCEPTS. Gravity is the universal force of attraction between all matter

GRAVITY CONCEPTS. Gravity is the universal force of attraction between all matter IT S UNIVERSAL GRAVITY CONCEPTS Gravity is the universal force of attraction between all matter Weight is a measure of the gravitational force pulling objects toward Earth Objects seem weightless when

More information

Chapter 13 Other Planetary Systems: The New Science of Distant Worlds

Chapter 13 Other Planetary Systems: The New Science of Distant Worlds Chapter 13 Other Planetary Systems: The New Science of Distant Worlds 13.1 Detecting Extrasolar Planets Our goals for learning: Why is it so difficult to detect planets around other stars? How do we detect

More information

Names of Group Members:

Names of Group Members: Names of Group Members: Using telescopes and spacecraft, astronomers can collect information from objects too big or too far away to test and study in a lab. This is fortunate, because it turns out that

More information

Exercise: Estimating the Mass of Jupiter Difficulty: Medium

Exercise: Estimating the Mass of Jupiter Difficulty: Medium Exercise: Estimating the Mass of Jupiter Difficulty: Medium OBJECTIVE The July / August observing notes for 010 state that Jupiter rises at dusk. The great planet is now starting its grand showing for

More information

Planets and Dwarf Planets by Shauna Hutton

Planets and Dwarf Planets by Shauna Hutton Name: Wow! Technology has improved so well in the last several years that we keep finding more and more objects in our solar system! Because of this, scientists have had to come up with new categories

More information

Lab 6: Kepler's Laws. Introduction. Section 1: First Law

Lab 6: Kepler's Laws. Introduction. Section 1: First Law Lab 6: Kepler's Laws Purpose: to learn that orbit shapes are ellipses, gravity and orbital velocity are related, and force of gravity and orbital period are related. Materials: 2 thumbtacks, 1 pencil,

More information

Page 1 of 2

Page 1 of 2 Kinesthetic Solar System Kinesthetic Solar System Demonstration Materials Students Pictures or signs representing each body in the solar system, including comets, and asteroids. Large outside open area,

More information

15.6 Planets Beyond the Solar System

15.6 Planets Beyond the Solar System 15.6 Planets Beyond the Solar System Planets orbiting other stars are called extrasolar planets. Until 1995, whether or not extrasolar planets existed was unknown. Since then more than 300 have been discovered.

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

Lecture Outlines. Chapter 15. Astronomy Today 7th Edition Chaisson/McMillan. 2011 Pearson Education, Inc.

Lecture Outlines. Chapter 15. Astronomy Today 7th Edition Chaisson/McMillan. 2011 Pearson Education, Inc. Lecture Outlines Chapter 15 Astronomy Today 7th Edition Chaisson/McMillan Chapter 15 The Formation of Planetary Systems Units of Chapter 15 15.1 Modeling Planet Formation 15.2 Terrestrial and Jovian Planets

More information

The Solar System. Source http://starchild.gsfc.nasa.gov/docs/starchild/solar_system_level1/solar_system.html

The Solar System. Source http://starchild.gsfc.nasa.gov/docs/starchild/solar_system_level1/solar_system.html The Solar System What is the solar system? It is our Sun and everything that travels around it. Our solar system is elliptical in shape. That means it is shaped like an egg. Earth s orbit is nearly circular.

More information

The Motions of Celestial Bodies, and Newton s Laws of Motion

The Motions of Celestial Bodies, and Newton s Laws of Motion The Motions of Celestial Bodies, and Newton s Laws of Motion Announcements The results of Quiz 1 are posted in OWL Looking ahead: Homework 1 is on-going, and is due on Thu, Sept. 29 th ; Homework 2 will

More information

MODULE P7: FURTHER PHYSICS OBSERVING THE UNIVERSE OVERVIEW

MODULE P7: FURTHER PHYSICS OBSERVING THE UNIVERSE OVERVIEW OVERVIEW More than ever before, Physics in the Twenty First Century has become an example of international cooperation, particularly in the areas of astronomy and cosmology. Astronomers work in a number

More information

Chapter 13 Other Planetary Systems The New Science of Distant Worlds. Why is it so difficult to detect planets around other stars?

Chapter 13 Other Planetary Systems The New Science of Distant Worlds. Why is it so difficult to detect planets around other stars? Chapter 13 Other Planetary Systems The New Science of Distant Worlds 13.1 Detecting Extrasolar Planets Our goals for learning Why is it so difficult to detect planets around other stars? How do we detect

More information

Putting The Distance Between The Earth And Moon In Perspective

Putting The Distance Between The Earth And Moon In Perspective Putting The Distance Between The Earth And Moon In Perspective In a spaceship, how long does it take to get to the moon? It depends on how fast the spaceship can travel. When the Apollo.astronauts went

More information

Chapter 13. Newton s Theory of Gravity

Chapter 13. Newton s Theory of Gravity Chapter 13. Newton s Theory of Gravity The beautiful rings of Saturn consist of countless centimeter-sized ice crystals, all orbiting the planet under the influence of gravity. Chapter Goal: To use Newton

More information

Chapter 6 Formation of Planetary Systems Our Solar System and Beyond

Chapter 6 Formation of Planetary Systems Our Solar System and Beyond Chapter 6 Formation of Planetary Systems Our Solar System and Beyond The solar system exhibits clear patterns of composition and motion. Sun Over 99.9% of solar system s mass Made mostly of H/He gas (plasma)

More information

tps Q: If the Earth were located at 0.5 AU instead of 1 AU, how would the Sun s gravitational force on Earth change?

tps Q: If the Earth were located at 0.5 AU instead of 1 AU, how would the Sun s gravitational force on Earth change? tps Q: If the Earth were located at 0.5 AU instead of 1 AU, how would the Sun s gravitational force on Earth change? A. It would be one-fourth as strong. B. It would be one-half as strong. C. It would

More information

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION

DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION 1 DIRECT ORBITAL DYNAMICS: USING INDEPENDENT ORBITAL TERMS TO TREAT BODIES AS ORBITING EACH OTHER DIRECTLY WHILE IN MOTION Daniel S. Orton email: dsorton1@gmail.com Abstract: There are many longstanding

More information

Use the following information to deduce that the gravitational field strength at the surface of the Earth is approximately 10 N kg 1.

Use the following information to deduce that the gravitational field strength at the surface of the Earth is approximately 10 N kg 1. IB PHYSICS: Gravitational Forces Review 1. This question is about gravitation and ocean tides. (b) State Newton s law of universal gravitation. Use the following information to deduce that the gravitational

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

Page. ASTRONOMICAL OBJECTS (Page 4).

Page. ASTRONOMICAL OBJECTS (Page 4). Star: ASTRONOMICAL OBJECTS ( 4). Ball of gas that generates energy by nuclear fusion in its includes white dwarfs, protostars, neutron stars. Planet: Object (solid or gaseous) that orbits a star. Radius

More information

Exemplar Problems Physics

Exemplar Problems Physics Chapter Eight GRAVITATION MCQ I 8.1 The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration

More information

1.1 A Modern View of the Universe" Our goals for learning: What is our place in the universe?"

1.1 A Modern View of the Universe Our goals for learning: What is our place in the universe? Chapter 1 Our Place in the Universe 1.1 A Modern View of the Universe What is our place in the universe? What is our place in the universe? How did we come to be? How can we know what the universe was

More information

Chapter 13 Other Planetary Systems. Detecting Extrasolar Planets Brightness Difference. How do we detect planets around other stars?

Chapter 13 Other Planetary Systems. Detecting Extrasolar Planets Brightness Difference. How do we detect planets around other stars? Chapter 13 Other Planetary Systems The New Science of Distant Worlds Detecting Extrasolar Planets Brightness Difference A Sun-like star is about a billion times brighter than the sunlight reflected from

More information

The Solar System. Unit 4 covers the following framework standards: ES 10 and PS 11. Content was adapted the following:

The Solar System. Unit 4 covers the following framework standards: ES 10 and PS 11. Content was adapted the following: Unit 4 The Solar System Chapter 7 ~ The History of the Solar System o Section 1 ~ The Formation of the Solar System o Section 2 ~ Observing the Solar System Chapter 8 ~ The Parts the Solar System o Section

More information

The following questions refer to Chapter 19, (PAGES 259 278 IN YOUR MANUAL, 7 th ed.)

The following questions refer to Chapter 19, (PAGES 259 278 IN YOUR MANUAL, 7 th ed.) GEOLOGY 306 Laboratory Instructor: TERRY J. BOROUGHS NAME: Locating the Planets (Chapter 19) and the Moon and Sun (Chapter 21) For this assignment you will require: a calculator, colored pencils, a metric

More information

Newton s Laws. Newton s Imaginary Cannon. Michael Fowler Physics 142E Lec 6 Jan 22, 2009

Newton s Laws. Newton s Imaginary Cannon. Michael Fowler Physics 142E Lec 6 Jan 22, 2009 Newton s Laws Michael Fowler Physics 142E Lec 6 Jan 22, 2009 Newton s Imaginary Cannon Newton was familiar with Galileo s analysis of projectile motion, and decided to take it one step further. He imagined

More information

This paper is also taken for the relevant Examination for the Associateship. For Second Year Physics Students Wednesday, 4th June 2008: 14:00 to 16:00

This paper is also taken for the relevant Examination for the Associateship. For Second Year Physics Students Wednesday, 4th June 2008: 14:00 to 16:00 Imperial College London BSc/MSci EXAMINATION June 2008 This paper is also taken for the relevant Examination for the Associateship SUN, STARS, PLANETS For Second Year Physics Students Wednesday, 4th June

More information

where G is the universal gravitational constant (approximately 6.67 10 11 Nm 2 /kg 2 ) and M is the sun s mass (approximately 2 10 24 kg).

where G is the universal gravitational constant (approximately 6.67 10 11 Nm 2 /kg 2 ) and M is the sun s mass (approximately 2 10 24 kg). Kepler s Third Law ID: 8515 By Michele Impedovo Time required 2 hours Activity Overview Johannes Kepler (1571-1630) is remembered for laying firm mathematical foundations for modern astronomy through his

More information

Astro 110-01 Lecture 10 Newton s laws

Astro 110-01 Lecture 10 Newton s laws Astro 110-01 Lecture 10 Newton s laws Twin Sungrazing comets 9/02/09 Habbal Astro110-01 Lecture 10 1 http://umbra.nascom.nasa.gov/comets/movies/soho_lasco_c2.mpg What have we learned? How do we describe

More information

CHAPTER 11. The total energy of the body in its orbit is a constant and is given by the sum of the kinetic and potential energies

CHAPTER 11. The total energy of the body in its orbit is a constant and is given by the sum of the kinetic and potential energies CHAPTER 11 SATELLITE ORBITS 11.1 Orbital Mechanics Newton's laws of motion provide the basis for the orbital mechanics. Newton's three laws are briefly (a) the law of inertia which states that a body at

More information

Other Planetary Systems

Other Planetary Systems Other Planetary Systems Other Planetary Systems Learning goals How do we detect planets around other stars? What have other planetary systems taught us about our own? Extrasolar planet search

More information

Earth Is Not the Center of the Universe

Earth Is Not the Center of the Universe Earth Is Not the Center of the Universe Source: Utah State Office of Education Introduction Have you ever looked up at the night sky and wondered about all the pinpoint lights? People through the ages

More information

Chapter 13. Gravitation

Chapter 13. Gravitation Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G = 6.67

More information

356 CHAPTER 12 Bob Daemmrich

356 CHAPTER 12 Bob Daemmrich Standard 7.3.17: Investigate that an unbalanced force, acting on an object, changes its speed or path of motion or both, and know that if the force always acts toward the same center as the object moves,

More information

Section II: Grades 3-4 Lessons

Section II: Grades 3-4 Lessons Section II: Grades 3-4 Lessons Lesson One: The Solar System Introduction: We live on planet Earth. Earth is just one member in a family of eight major planets. All of these planets orbit the Sun, which

More information

Study Guide due Friday, 1/29

Study Guide due Friday, 1/29 NAME: Astronomy Study Guide asteroid chromosphere comet corona ellipse Galilean moons VOCABULARY WORDS TO KNOW geocentric system meteor gravity meteorite greenhouse effect meteoroid heliocentric system

More information

Chapter 13 Other Planetary Systems: The New Science of Distant Worlds

Chapter 13 Other Planetary Systems: The New Science of Distant Worlds Chapter 13 Other Planetary Systems: The New Science of Distant Worlds 13.1 Detecting Extrasolar Planets Our goals for learning: Why is it so difficult to detect planets around other stars? How do we detect

More information

Formation of the Solar System

Formation of the Solar System Formation of the Solar System Any theory of formation of the Solar System must explain all of the basic facts that we have learned so far. 1 The Solar System The Sun contains 99.9% of the mass. The Solar

More information

Kepler s Laws and Gravity. Ian Morison

Kepler s Laws and Gravity. Ian Morison Kepler s Laws and Gravity Ian Morison Observations of a supernova. Tycho made detailed observations of the supernova of 1572 now called Tycho s supernova. It was initially brighter than Venus and was visible

More information

Version A Page 1. 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart.

Version A Page 1. 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart. Physics Unit Exam, Kinematics 1. The diagram shows two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters apart. What is the magnitude of the gravitational force exerted by

More information

DWARF PLANETS A S T R O N O M Y. The Academic Support Daytona State College (Science 109, Page 1 of 33)

DWARF PLANETS A S T R O N O M Y. The Academic Support Daytona State College (Science 109, Page 1 of 33) DWARF PLANETS A S T R O N O M Y The Academic Support Center @ Daytona State College (Science 109, Page 1 of 33) DWARF PLANETS The Academic Support Center @ Daytona State College (Science 109, Page 2 of

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

SURFACE ACTIVITY LESSON

SURFACE ACTIVITY LESSON SURFACE ACTIVITY LESSON Ronald Wilhelm & Jennifer Wilhelm, University of Kentucky 2007 Surface Activity on Planets and Moons The Earth and the Moon: Investigations of the Earth and the Moon show that both

More information

Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007. Name:

Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007. Name: Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007 Name: Directions: Listed below are twenty (20) multiple-choice questions based on the material covered by the lectures this past week. Choose

More information

RETURN TO THE MOON. Lesson Plan

RETURN TO THE MOON. Lesson Plan RETURN TO THE MOON Lesson Plan INSTRUCTIONS FOR TEACHERS Grade Level: 9-12 Curriculum Links: Earth and Space (SNC 1D: D2.1, D2.2, D2.3, D2.4) Group Size: Groups of 2-4 students Preparation time: 1 hour

More information

Related Standards and Background Information

Related Standards and Background Information Related Standards and Background Information Earth Patterns, Cycles and Changes This strand focuses on student understanding of patterns in nature, natural cycles, and changes that occur both quickly and

More information

Chapter 7 Our Planetary System. Agenda. Intro Astronomy. Intro Astronomy. What does the solar system look like? A. General Basics

Chapter 7 Our Planetary System. Agenda. Intro Astronomy. Intro Astronomy. What does the solar system look like? A. General Basics Chapter 7 Our Planetary System Agenda Pass back & discuss Test 2 Where we are (at) Ch. 7 Our Planetary System Finish Einstein s Big Idea Earth, as viewed by the Voyager spacecraft A. General Basics Intro

More information

Homework 4. problems: 5.61, 5.67, 6.63, 13.21

Homework 4. problems: 5.61, 5.67, 6.63, 13.21 Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find

More information

Newton s Law of Gravity and Kepler s Laws

Newton s Law of Gravity and Kepler s Laws Newton s Law of Gravity and Kepler s Laws Michael Fowler Phys 142E Lec 9 2/6/09. These notes are partly adapted from my Physics 152 lectures, where more mathematical details can be found. The Universal

More information