# Calculation of gravitational forces in a non-ideal sphere

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Gravitational Forces in a Non-Ideal Sphere 1 Calculation of gravitational forces in a non-ideal sphere A paper by: Dipl. Ing. Matthias Krause, (CID) Cosmological Independent Department, Germany, 2009 Objective The purpose of this paper is to analyze the calculation of gravitational fields in a non-ideal sphere. Following a discussion and comparison of results with examples from the calculation of ideal spheres, the consequences of the determined results for the standard model (big bang model) are evaluated. The figures and graphs used for demonstration were taken from an EXCEL datasheet, specifically designed to calculate the gravitational forces in a sphere. Fundamentals of the calculation The basis for the following calculations is the fact that on the inside of a hollow ideal sphere with an even distribution of surface mass, gravitational forces cannot be felt. In a homogenous non-hollow sphere, on the other hand, gravitational forces increase linearly toward the edge. The calculation of said gravitational forces is possible through the discrete calculation relative to a measuring point with the help of an EXCEL datasheet and is thoroughly explained in the paper about the gravitational forces of an ideal sphere by Dipl. Ing. Matthias Krause (2005) which can be found in this forum. The model of a gridded sphere is necessary for a discrete calculation. However, the grids cause a slight difference between the ideal result (with an infinite numbers of particles) and the discrete result (with a limited number of particles). This discrepancy is naturally taken into account when comparing results. Nevertheless, the gravitational forces in a hollow sphere equal zero. What happens if this area around zero gravity is further evaluated and discretely calculated? Is it possible to discover new effects that might change the calculation of gravitational forces? Figure 1 shows the gravitational field of an ideal hollow sphere and an ideal massive homogenous sphere, calculated discretely. Figure 1

2 Gravitational Forces in a Non-Ideal Sphere 2 The left graph illustrates the result of discrete calculation for a hollow sphere with an even distribution of mass on its surface. The right graph shows the gravitational field of a homogenously filled sphere. Even though the gravitation inside and outside of both spheres were calculated, only the gravitation on the inside of the spheres matters for this calculation. How do the gravitational forces change if they are calculated with the help of a non-ideally gridded model? In addition, it is interesting to determine what would happen to the gravitational forces if the sphere were not ideally hollow. These questions about the distribution of masses and gravity can easily be answered with discrete calculation. How is the discrete volume calculation of gravity realized in a sphere? The construction of a sphere model is derived from the gridded model of a circular plane. Instead of calculating only the area of a single plane, several stacked planes are taken into consideration. To ensure the symmetry of the sphere model, the mass of each plane is predetermined. It is possible to compare the model with an onion with its concentric layers. The sphere appears to be cut into slices, each of which will provide the single planes for the discrete calculation. Two symmetrical planes are combined to calculate the gravitational forces with the help of two coordinates on the planes. Figure 2 The slices of the sphere model are clearly visible here. The plane of symmetry is red, and the upper dome and lower half sphere are cut into seven symmetrical slices. Even though the model is similar to an onion, the layers resemble more a stack of differently sized coins with steps between the planes. The more slices or planes a model has, the smaller the steps turn out to be. Hence, it pays off to create a model with a larger amount of planes, for example, 21, which provides 10 measuring points. Though the work is tedious, the results of the calculation are more accurate.

3 Gravitational Forces in a Non-Ideal Sphere 3 Figure 3 A sphere with 10 measuring points (MPs) has 5065 mass points. Multiplication with 10 MPs results in a proud sum of 50,650 calculations. As a sphere is symmetrical to the middle plane, and each plane itself is symmetrical to its diameter, it is only necessary to calculate half of the middle plane and one quarter of the other planes (either the half of the upper or lower half sphere). However, the results for the middle plane have to be multiplied with two and the results for the other planes have to be multiplied with four. Figure 3 illustrates the single planes of a sphere. The three values (A, B, and C) are used to determine the distance between the mass points and measuring point. The formulas used to calculate the gravitational forces need adjustments for every mass point. The mass of each of the 10 planes is predetermined and also symmetrical. The EXCEL spread sheet is similar to Figure 3, and even includes the cancellation of gravitational forces for each of the mass points. Before determining the gravitational forces within a non-ideal hollow sphere and a nonhomogenous sphere, it is preferable to think about the characteristics of these two types of spheres. The non-ideal hollow sphere To make things a little easier, a symbiosis between full and hollow sphere a nearly hollow sphere - shall be examined first. Because formulas for the calculation of gravitational forces in such a sphere are missing in mathematical books, the only possible way to determine the gravitational forces is to test the discrete model with a symbiosis. It is possible to enter every possible mass variation into the EXCEL model, which will deliver the according gravitational forces and other parameter. Ideal spheres have identical declining forces on their outside, therefore, the mixed sphere should have similar forces on the outside. As the forces in ideal spheres are either zero or linear

4 Gravitational Forces in a Non-Ideal Sphere 4 increasing, a positive, which means a force directed toward the center, is to be expected on the inside of the sphere. The following figure illustrates the result. Figure 4 non-ideal hollow sphere F turns <0 F declines exponentially The forces on the inside and outside of the hollow sphere with an uneven distribution of mass, the inside of the sphere is almost empty (1000:1) F of the mid plane for example, a plane-like sphere On the outside of the sphere, gravitational forces decline as expected. On the inside, however, the gravitational forces are negative. Let us revise: the forces in an ideal hollow sphere are zero, but the middle plane of such a hollow sphere has negative gravitational forces (Krause, 2005). So how does a hollow sphere need to be constructed to facilitate these negative gravitational forces? The answer is easy. The sphere should be a mixture of plane, hollow sphere, and sphere: a planelike sphere, for example a rotation ellipsoid. The reason for this is probably the grid lining of the model, which keeps the sphere from being completely round. Hence, the model does not equal a completely hollow sphere. This slight variation causes an error big enough to let any mass on inside of the sphere appear to accelerate toward the outer edge. The sphere in the model has a small amount of mass, which influences the gravitational forces toward the edge. The ideal hollow sphere does not allow any masses on its edge like a non-ideal hollow sphere.

5 Gravitational Forces in a Non-Ideal Sphere 5 Consequently, to further examine the non-ideal hollow sphere, the discrete model is equipped with a few more mass points at the edge. The modification of the model according to the new guidelines confirms the expected results. The model illustrates how easily the gravitational forces are altered. It only takes a few mass points at the outer edge. With the help of the non-ideal sphere or the errors in the ideal hollow sphere model, an unexpected solution has been found. Figures 5a and 5b show the internal gravitational forces toward the edge of the hollow sphere. (the center is on the left, the edge on the right side) If the sphere is slightly altered (plane-like), the curve changes dramatically. Gravity within a non-ideal hollow sphere Gravity within a non-ideal hollow sphere With the according mass distribution in the sphere, it is possible to influence the curve to the point that, it in fact, declines linearly(!) to the edge. The mass at the edge of the sphere is not taken into consideration, but the gravitational forces are positive toward the inside of the sphere. Conclusion for the calculation of the gravitational forces of a non-ideal sphere If the masses of a non-ideal sphere concentrate at the edge, the gravitational forces will pull them further toward the edge of the sphere. Once they reach the edge; however, the gravitational forces reverse and direct toward the center of the sphere. Hence, the masses at the edge of the sphere are trapped close to the edge, where they have the highest amount of kinetic energy and the smallest amount of potential energy. From the center of the sphere, the gravitational forces are negative and pull masses toward the edge. From the edge of the sphere, gravitational forces are positive and accelerate masses toward the edge. The gravitational forces in a sphere model do not oppose each other (they are not a new form of force either). The well-known gravity pulls masses toward the edge. The ratio of gravity within and around the sphere is approximately 1:1000. This ratio dwindles as the sphere flattens,

6 Gravitational Forces in a Non-Ideal Sphere 6 for example, if 75% of the combined mass of the sphere concentrates close to the edge, the ratio is 1:100 (for the single mass points). In a round plane and a non-ideal sphere the gravitational forces on the inside are negative, which means directed towards the edge, as long as they are filled with a relative small number of masses. What are the consequences for the cosmic standard model? If the results of the previous examination of gravitational forces in non-ideal hollow spheres are applied to the entire cosmos, one can expect the following scenario: The universe is static and stable; it does not expand or shrink. Albert Einstein favored this cosmic view; however, without an alternative explanation for the movement of galaxies, he could not explain the galactic red shift. Nevertheless, after evaluating the gravitational forces in and around a hollow sphere, it becomes clear why galaxies are drawn toward the edge of the cosmos (based on a central point of view). The universe is slightly flattened; it is a non-ideal sphere, similar to the Kerr metric of rotating black holes (Mueller, 2004). Each mass in the cosmos has a torque, starting with the smallest unit, all the way to the largest galaxies. If this logical fact is extended, the whole cosmos has a torque, comparable to the movement of stars assembled in the shape of a sphere. Because of the non-ideal sphere shape of the universe, the gravitational forces on the inside are negative. Therefore, all masses (galaxies) fall and are accelerated toward the edge of the universe, where they reach their peak speed of near the speed of light. Once galaxies reach the edge of the cosmos, the direction of their movement changes permanently, and they begin to orbit around the center of the cosmos close to its edge. The galaxies close to the edge of the universe move at almost the speed of light. Their high amount of kinetic energy means a great increase in relative mass. Consequently, the masses at the edge of the cosmos have a steadily growing value compared to the masses closer to the center. Their ratio may even be 1:1000. The relativistic ɣ-factor that ensures the correct ratio between the masses close to the edge and close to the center of the universe in addition to the background radiation with its temperature is This is calculated with the formula discussed in the paper about cosmic background radiation. The mass distribution within the universe is currently even. Within the next billion years, however, the majority of galaxies will have moved toward the edge. The universe is

7 Gravitational Forces in a Non-Ideal Sphere 7 slowly differentiating. This process cannot be reversed because an even distribution of masses in the universe is the first step in the life of this universe. If we assumed that the cosmos is millions or even billions of years, it would be nearly empty today. The majority of galaxies, visible from the center only as dimly red glimmering stars, would be orbiting at the edge of the cosmos. The light emitted by the galaxies orbiting at the edge of the universe reaches us as isotropic cosmic background radiation. (The direction of their movement is irrelevant.) The galaxies have to orbit at a speed of % of the speed of light around the center of the universe, to facilitate the temperature and red shift of the current background radiation. The universe is similar to a black hole, as it has an event horizon, and therefore, a solid, unmovable frontier. In short, we are living inside a gigantic, cosmic black hole. Due to the immense speed of galaxies, time almost comes to a stand-still at the edge of the cosmos. It passes 2638 times slower than on Earth. Beyond our cosmos is eternity, as time seizes to pass, which implies that we are living in a type of time-bubble. This theory explains the increasing and accelerating red shift of galaxies towards the edge of the universe, and, at the same time, allows the cosmos to be spatially consistent. Hence, the continuous expansion of the universe is rendered obsolete, just as Albert Einstein, a genius in his own right, already suspected and he was right! This, and all the other papers in this forum, illustrate that our current understanding of the cosmos is faulty. Scientists have taken a wrong turn in their theories and are scrambling to explain facts with fiction. Dark energy and maybe even dark matter highlight the weaknesses of the model [of the Big Bang Theory]. Though the Big Bang is an easy explanation and does indeed reflect our observations, it contains two ingredients of our imagination - similar to the antique astronomers, who invented Epicycles to explain the movement of planets. This part of the model will fail, because physicists are generally on the wrong path if they have to invent pieces of the puzzle (Spergel, 2004). Cosmologist Spergel s statement is correct: Physicists are wrong with their invention of dark matter and dark energy. However, this does not mean that a new field of physics had to be invented to explain the cosmos. Instead, the calculation errors of gravitational forces within spheres have to be eliminated. According to modern physicists, only 4% of the universe is visible, while the remaining 96% consist of dark matter or dark energy. This paper, clearly illustrates that these two inventions are completely fictional, illogical, and unnecessary. Hence, every model, such as the standard big bang model based on or supported with dark energy or matter is questionable.

8 Gravitational Forces in a Non-Ideal Sphere 8 References EXCEL Modelldatei KOKUG10 Krause, M. (2005). Die Berechnung der Gravitation in einem kugelförmigen Körper und in einer runden Fläche Mueller, A. (2004). Wirbel der Raumzeit. Sterne und Weltraum 2004(10), 24ff. Spergel, D. (2004). In diesen sechs Zahlen steckt eine neue Physik. Sterne und Weltraum, 2004(11), 28.

### Calculation of gravitational forces of a sphere and a plane

Sphere and plane 1 Calculation of gravitational forces of a sphere and a plane A paper by: Dipl. Ing. Matthias Krause, (CID) Cosmological Independent Department, Germany, 2007 Objective The purpose of

### What Are Stars? continued. What Are Stars? How are stars formed? Stars are powered by nuclear fusion reactions.

What Are Stars? How are stars formed? Stars are formed from clouds of dust and gas, or nebulas, and go through different stages as they age. star: a large celestial body that is composed of gas and emits

### What Energy Drives the Universe? Andrei Linde

What Energy Drives the Universe? Andrei Linde Two major cosmological discoveries:! The new-born universe experienced rapid acceleration (inflation)! A new (slow) stage of acceleration started 5 billion

### Astro 102 Test 5 Review Spring 2016. See Old Test 4 #16-23, Test 5 #1-3, Old Final #1-14

Astro 102 Test 5 Review Spring 2016 See Old Test 4 #16-23, Test 5 #1-3, Old Final #1-14 Sec 14.5 Expanding Universe Know: Doppler shift, redshift, Hubble s Law, cosmic distance ladder, standard candles,

### 4/27/ Unseen Influences in the Cosmos. Chapter 18: Dark Matter, Dark Energy, and the Fate of the Universe.

Lecture Outline 18.1 Unseen Influences in the Cosmos Chapter 18: Dark Matter, Dark Energy, and the Fate of the Universe Our goals for learning: What do we mean by dark matter and dark energy? What do we

### Lecture 2 - The current state of fundamental physics

Lecture 2 - The current state of fundamental physics 1) Einstein & General Relativity Gravity as Spacetime Curvature Gravitational Radiation, LIGO & LISA Cosmology & the Expanding Universe Dark Energy

### Measuring the mass of galaxies Luminous matter in a galaxy: stars (of different masses) gas (mostly hydrogen) Can detect these directly using optical

Measuring the mass of galaxies Luminous matter in a galaxy: stars (of different masses) gas (mostly hydrogen) Can detect these directly using optical and radio telescopes - get an estimate of how much

### Federation of Galaxy Explorers Space Science

Federation of Galaxy Explorers Space Science Once Upon A Big Bang Learning Objectives: 1. Explain how the universe was created using the Big Bang theory. 2. Understand how the existence of Cosmic Background

### Lecture Outlines. Chapter 26. Astronomy Today 7th Edition Chaisson/McMillan Pearson Education, Inc.

Lecture Outlines Chapter 26 Astronomy Today 7th Edition Chaisson/McMillan Chapter 26 Cosmology Units of Chapter 26 26.1 The Universe on the Largest Scales 26.2 The Expanding Universe 26.3 The Fate of the

### Science Standard 4 Earth in Space Grade Level Expectations

Science Standard 4 Earth in Space Grade Level Expectations Science Standard 4 Earth in Space Our Solar System is a collection of gravitationally interacting bodies that include Earth and the Moon. Universal

### The Expanding Universe. Prof Jim Dunlop University of Edinburgh

The Expanding Universe Prof Jim Dunlop University of Edinburgh Cosmology: The Study of Structure & Evolution of the Universe Small & Hot Big & Cold Observational Evidence for the Expansion of the Universe

### 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

### 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

### PART 3 Galaxies. Stars in the Milky Way

PART 3 Galaxies Stars in the Milky Way A galaxy is a large collection of billions of stars The galaxy in which the Sun is located is called the Milky Way From our vantage point inside the galaxy, the Milky

### The Big Bang Theory: How the Universe Began

The Big Bang Theory: How the Universe Began The Big Bang Theory is the most widely accepted theory of how the universe began. It states that the universe started when all matter was contained in a small,

### The Fundamental Forces of Nature

Gravity The Fundamental Forces of Nature There exist only four fundamental forces Electromagnetism Strong force Weak force Gravity Gravity 2 The Hierarchy Problem Gravity is far weaker than any of the

### Big bang, red shift and doppler effect

Big bang, red shift and doppler effect 73 minutes 73 marks Page of 26 Q. (a) Scientists have observed that the wavelengths of the light from galaxies moving away from the Earth are longer than expected.

### Dark Energy and the Accelerating Universe. Dragan Huterer Kavli Institute for Cosmological Physics University of Chicago

Dark Energy and the Accelerating Universe Dragan Huterer Kavli Institute for Cosmological Physics University of Chicago The universe today presents us with a grand puzzle: what is 95% of it made of!? Shockingly,

### WHAT EMERGED FROM THE BIG BANG?

2 WHAT EMERGED FROM THE BIG BANG? David Christian explains how the Big Bang theory developed during the 20th century. This three-part lecture focuses on how the evidence for the expansion of the Universe

### The Milky Way is a spiral galaxy.

The Big Bang Logistics Final Exam: Monday May 6, 1530-1730 We will *not* have normal office hours next week, but if you need to meet, email Will cover *all* material this semester (including todays class)

### Data Provided: A formula sheet and table of physical constants is attached to this paper. DARK MATTER AND THE UNIVERSE

Data Provided: A formula sheet and table of physical constants is attached to this paper. DEPARTMENT OF PHYSICS AND ASTRONOMY Autumn Semester (2014-2015) DARK MATTER AND THE UNIVERSE 2 HOURS Answer question

### The Cosmic Perspective Seventh Edition. Dark Matter, Dark Energy, and the Fate of the Universe. Chapter 23 Review Clickers

Review Clickers The Cosmic Perspective Seventh Edition Dark Matter, Dark Energy, and the Fate of the Universe Doppler shifts can be measured with a) visible light. b) radio waves. c) microwaves. d) all

### OBSERVING THE UNIVERSE

OBSERVING THE UNIVERSE Overview: Galaxies are classified by their morphology. Objectives: The student will: classify 15 images of distant galaxies using a galaxy classification table; sketch, classify

### The Expanding Universe

Stars, Galaxies, Guided Reading and Study This section explains how astronomers think the universe and the solar system formed. Use Target Reading Skills As you read about the evidence that supports the

### 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

### 13 Universal Gravitation. Everything pulls on everything else.

Everything pulls on everything else. Gravity was not discovered by Isaac Newton. What Newton discovered, prompted by a falling apple, was that gravity is a universal force that it is not unique to Earth,

### What was before the Big Bang?

1 / 68 Std. What was before the Big Bang? of the Very Robert Brandenberger McGill University February 21, 2013 2 / 68 Outline Std. 1 What is? 2 Standard Big Bang 3 ary 4 String 5 3 / 68 Plan Std. 1 What

### 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

### Beginning of the Universe Classwork 6 th Grade PSI Science

Beginning of the Universe Classwork Name: 6 th Grade PSI Science 1 4 2 5 6 3 7 Down: 1. Edwin discovered that galaxies are spreading apart. 2. This theory explains how the Universe was flattened. 3. All

### Einstein s theory of relativity

Department of Mathematics, Institute of Origins, December 5, 2008 Overview UCL Institute of Origins Origins UCL has established the Institute of Origins to promote world leading research in topics related

### 165 points. Name Date Period. Column B a. Cepheid variables b. luminosity c. RR Lyrae variables d. Sagittarius e. variable stars

Name Date Period 30 GALAXIES AND THE UNIVERSE SECTION 30.1 The Milky Way Galaxy In your textbook, read about discovering the Milky Way. (20 points) For each item in Column A, write the letter of the matching

### World of Particles Big Bang Thomas Gajdosik. Big Bang (model)

Big Bang (model) What can be seen / measured? basically only light (and a few particles: e ±, p, p, ν x ) in different wave lengths: microwave to γ-rays in different intensities (measured in magnitudes)

### Concept Review. Physics 1

Concept Review Physics 1 Speed and Velocity Speed is a measure of how much distance is covered divided by the time it takes. Sometimes it is referred to as the rate of motion. Common units for speed or

### Lecture 15 Fundamentals of Physics Phys 120, Fall 2015 Cosmology

Lecture 15 Fundamentals of Physics Phys 120, Fall 2015 Cosmology A. J. Wagner North Dakota State University, Fargo, ND 58108 Fargo, October 20, 2015 Overview A history of our view of the universe The Big

### 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

### Chapter 15 Cosmology: Will the universe end?

Cosmology: Will the universe end? 1. Who first showed that the Milky Way is not the only galaxy in the universe? a. Kepler b. Copernicus c. Newton d. Hubble e. Galileo Ans: d 2. The big bang theory and

### Gravity slows down the expansion

Key Concepts: Lecture 33: The Big Bang! Age of the Universe and distances from H 0 Gravity slows down the expansion Closed, Flat and Open Universes Evidence for the Big Bang (Galactic Evolution; Microwave

### Where is Fundamental Physics Heading? Nathan Seiberg IAS Apr. 30, 2014

Where is Fundamental Physics Heading? Nathan Seiberg IAS Apr. 30, 2014 Disclaimer We do not know what will be discovered. This is the reason we perform experiments. This is the reason scientific research

### Today. Course Evaluations Open. Modern Cosmology. The Hot Big Bang. Age & Fate. Density and Geometry. Microwave Background

Today Modern Cosmology The Hot Big Bang Age & Fate Density and Geometry Microwave Background Course Evaluations Open 1 Distances between faraway galaxies change while light travels. distance? 2 2007 Pearson

### 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

### Shenandoah Community School District Astronomy Grade - 11

Shenandoah Community School District Astronomy Grade - 11 11.1 (SCSD) Earth and Space Astronomy 11.1.1 (SCSD) Understand and explain the tools used by astronomers to study electromagnetic radiation to

### Chapter S3 Spacetime and Gravity

Chapter S3 Spacetime and Gravity What are the major ideas of special relativity? Spacetime Special relativity showed that space and time are not absolute Instead they are inextricably linked in a four-dimensional

### Lecture 17: Dark Energy & The Big Bang

Lecture 17: Dark Energy & The Big Bang As with all course material (including homework, exams), these lecture notes are not be reproduced, redistributed, or sold in any form. Solution? ~1998 astronomers

### Origins of the Cosmos Summer 2016. Pre-course assessment

Origins of the Cosmos Summer 2016 Pre-course assessment In order to grant two graduate credits for the workshop, we do require you to spend some hours before arriving at Penn State. We encourage all of

### A Space-Time Map of the Universe

Chapter 35 A Space-Time Map of the Universe John A. Gowan Introduction In an age of giant telescopes, deep space observations to early eras of our universe are becoming commonplace. A map of the whole

### The Birth of Our Universe Today s Lecture:

The Birth of Our Universe Today s Lecture: (Chapter 19, pages 454-481) Cosmic Microwave Background (CMB) The first few minutes of the Universe Inflation! Cosmic Microwave Background (CMB) A. Penzias and

### GENERAL RELATIVITY & the UNIVERSE

GENERAL RELATIVITY & the UNIVERSE PCES 3.32 It was realised almost immediately after Einstein published his theory that it possessed solutions for the configuration of spacetime, in the presence of a homogeneous

### The Origin and Evolution of the Universe

The Origin and Evolution of the Universe 9.7 People have been wondering about the Universe for a long time. They have asked questions such as Where did the Universe come from? How big is it? What will

### 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

### Transcript 22 - Universe

Transcript 22 - Universe A few introductory words of explanation about this transcript: This transcript includes the words sent to the narrator for inclusion in the latest version of the associated video.

### Patterns in the Solar System. Patterns in the Solar System. ASTR 105 The Solar System

ASTR 105 The Solar System 1. Orderly motions 2.Two kinds of planets 3.Two kinds of small bodies 4.Exceptions to the rules Today: Group Lab at the end of class Next THURSDAY 03/10: First Group Project Orderly

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

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

### A new formula for the rotation velocity and density distribution of a galaxy

IOSR Journal of Applied Physics (IOSR-JAP) e-issn: 2278-4861. Volume 3, Issue 4 (Mar. - Apr. 2013), PP 44-51 A new formula for the rotation velocity and density distribution of a galaxy Tony Barrera, Bo

### Domain walls may form in the early universe during a phase transition involving the spontaneous breaking of a discrete symmetry. If the mass density (

UTPT-93-18 hep-ph/9307359 July 1993 Cosmic Balloons B. Holdom 1 Department of Physics University of Toronto Toronto, Ontario Canada M5S 1A7 ABSTRACT Cosmic balloons, consisting of relativistic particles

### The Cosmic Perspective Seventh Edition. Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Chapter 4 Lecture

Chapter 4 Lecture The Cosmic Perspective Seventh Edition Making Sense of the Universe: Understanding Motion, Energy, and Gravity Making Sense of the Universe: Understanding Motion, Energy, and Gravity

### A. Answer all of the following multiple choice questions (50%):

Core 30.01 - Cosmology Fall 2006 Prof. Micha Tomkiewicz Final Exam: My Name A. Answer all of the following multiple choice questions (50%): 1. The universe became matter dominated approximately after the

### Chapter 22 Review Clickers. The Cosmic Perspective Seventh Edition. The Birth of the Universe Pearson Education, Inc.

Review Clickers The Cosmic Perspective Seventh Edition The Birth of the Universe What do we know about the beginning of the universe? a) It was about 6000 years ago. b) It was billions of years ago. c)

### An Introduction to Astronomy and Cosmology. 1) Astronomy - an Observational Science

An Introduction to Astronomy and Cosmology 1) Astronomy - an Observational Science Why study Astronomy 1 A fascinating subject in its own right. The origin and Evolution of the universe The Big Bang formation

### Energy by Einstein. - Big Bang and Dark Energy are not Required. - Hideaki Yanagisawa

Relation between Constant Dark Energy and Ignored Energy 1 Relation between Constant Dark Energy Pattern and Ignored Energy by Einstein - Big Bang and Dark Energy are not Required. - Hideaki Yanagisawa

### 4 Formation of the Universe

CHAPTER 2 4 Formation of the Universe SECTION Stars, Galaxies, and the Universe BEFORE YOU READ After you read this section, you should be able to answer these questions: What is the big bang theory? How

### 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

### Unit 1: Cosmology and Earth s Place in Space

Unit 1: Cosmology and Earth s Place in Space Objectives: E5.1b - Describe how the Big Bang theory accounts for the formation of the universe. E5.1c - Explain how observations of the cosmic background radiation

### 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

### The Milky Way Galaxy. Studying Its Structure Mass and Motion of the Galaxy Metal Abundance and Stellar Populations Spiral Structure and Star Formation

The Milky Way Galaxy Studying Its Structure Mass and Motion of the Galaxy Metal Abundance and Stellar Populations Spiral Structure and Star Formation The Milky Way Almost everything we see in the night

### The Early Universe. Lecture 27-1

The Early Universe Lecture 27-1 Back to the Big Bang The total energy of the universe consists of both radiation and matter. As the Universe cooled, it went from being radiation dominated to being matter

### Lecture Outlines. Chapter 27. Astronomy Today 7th Edition Chaisson/McMillan. 2011 Pearson Education, Inc.

Lecture Outlines Chapter 27 Astronomy Today 7th Edition Chaisson/McMillan Chapter 27 The Early Universe Units of Chapter 27 27.1 Back to the Big Bang 27.2 The Evolution of the Universe More on Fundamental

### REALIZING EINSTEIN S DREAM Exploring Our Mysterious Universe

REALIZING EINSTEIN S DREAM Exploring Our Mysterious Universe The End of Physics Albert A. Michelson, at the dedication of Ryerson Physics Lab, U. of Chicago, 1894 The Miracle Year - 1905 Relativity Quantum

### Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves sp e e d = d ista

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

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

### 1 A Solar System Is Born

CHAPTER 3 1 A Solar System Is Born SECTION Formation of the Solar System BEFORE YOU READ After you read this section, you should be able to answer these questions: What is a nebula? How did our solar system

### Pillars of Standard Model. Homogeneity and Isotropy Night Sky is Dark

Pillars of Standard Model Homogeneity and Isotropy Night Sky is Dark Linear Expansion Light Element Abundances Microwave Background Radiation [+other large scale structures] Wilkinson Microwave Anisotropy

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

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

### Where did the idea for the Big Bang come from anyway? Strategy

The Big Bang Where did the idea for the Big Bang come from anyway? Strategy 1. Document present state of the Universe via observations 2. Find an explanation that fits all observations Observation 1a:

### Cosmology - The Story of our Universe. Raghu Rangarajan Physical Research Laboratory Ahmedabad

Cosmology - The Story of our Universe Raghu Rangarajan Physical Research Laboratory Ahmedabad What is Cosmology? Study of our Universe today galaxies, clusters, superclusters Understanding the past history

### PSS 27.2 The Electric Field of a Continuous Distribution of Charge

Chapter 27 Solutions PSS 27.2 The Electric Field of a Continuous Distribution of Charge Description: Knight Problem-Solving Strategy 27.2 The Electric Field of a Continuous Distribution of Charge is illustrated.

### Lecture 19 Big Bang Cosmology

The Nature of the Physical World Lecture 19 Big Bang Cosmology Arán García-Bellido 1 News Exam 2: you can do better! Presentations April 14: Great Physicist life, Controlled fusion April 19: Nuclear power,

### 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

### First Discoveries. Asteroids

First Discoveries The Sloan Digital Sky Survey began operating on June 8, 1998. Since that time, SDSS scientists have been hard at work analyzing data and drawing conclusions. This page describes seven

### LAB 8: Electron Charge-to-Mass Ratio

Name Date Partner(s) OBJECTIVES LAB 8: Electron Charge-to-Mass Ratio To understand how electric and magnetic fields impact an electron beam To experimentally determine the electron charge-to-mass ratio.

### Lecture 7: Light Waves. Newton s Laws of Motion (1666) Newton s First Law of Motion

Lecture 7: Light Waves Isaac Newton (1643-1727) was born in the year Galileo died He discovered the Law of Gravitation in 1665 He developed the Laws of Mechanics that govern all motions In order to solve

### Gasses at High Temperatures

Gasses at High Temperatures The Maxwell Speed Distribution for Relativistic Speeds Marcel Haas, 333 Summary In this article we consider the Maxwell Speed Distribution (MSD) for gasses at very high temperatures.

### The Origin, Evolution, and Fate of the Universe

The Origin, Evolution, and Fate of the Universe Announcements n Homework # 8 is available as of this morning in OWL. Due date for is Friday Dec 9th n Exam # 3 will take place on Tuesday, December 6 th

### The Crafoord Prize 2005

I N F O R M A T I O N F O R T H E P U B L I C The Royal Swedish Academy of Sciences has decided to award the Crafoord Prize in Astronomy 2005 to James Gunn, Princeton University, USA, James Peebles, Princeton

### University Physics 226N/231N Old Dominion University. Chapter 13: Gravity (and then some)

University Physics 226N/231N Old Dominion University Chapter 13: Gravity (and then some) Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2016-odu Monday, November 28,

### How do we describe motion?

Lecture 3: The Laws of Motion and Universal Gravitation Astronomy 2020, Prof. Tom Megeath To be ignorant of motion is to be ignorant of nature -Aristotle Overview of Today s Lecture 1. Newton s three laws

### 10. Our violent origin Cosmology and the nuclear processes in the Big Bang

10. Our violent origin Cosmology and the nuclear processes in the Big Bang Our Universe is getting larger. The space between the galaxies is expanding so that we see distant galaxies in all directions

### California Standards Grades 9 12 Boardworks 2009 Science Contents Standards Mapping

California Standards Grades 912 Boardworks 2009 Science Contents Standards Mapping Earth Sciences Earth s Place in the Universe 1. Astronomy and planetary exploration reveal the solar system s structure,

### 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.

### Modeling Galaxy Formation

Galaxy Evolution is the study of how galaxies form and how they change over time. As was the case with we can not observe an individual galaxy evolve but we can observe different galaxies at various stages

### Ay 20 - Fall Lecture 16. Our Galaxy, The Milky Way

Ay 20 - Fall 2004 - Lecture 16 Our Galaxy, The Milky Way Our Galaxy - The Milky Way Overall structure and major components The concept of stellar populations Stellar kinematics Galactic rotation and the

### 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

### CHAPTER 9: STARS AND GALAXIES

CHAPTER 9: STARS AND GALAXIES Characteristics of the Sun 1. The Sun is located about 150 million kilometres from the Earth. 2. The Sun is made up of hot gases, mostly hydrogen and helium. 3. The size of

### Our UNIVERSE: where it all came from.

Our UNIVERSE: where it all came from. QUESTIONS OF THE DAY. How did the Universe start? How did the Universe evolve up to the present day? What is the fate of our Universe? The theory of general relativity

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

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

Answering Gauguin s Questions with the Large Hadron Collider John ELLIS King s College London (& The world s biggest scientific laboratory Where do we come from? What are we? Where are we going? The aim

### 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!

### Today. Laws of Motion Conservation Laws Gravity tides. What is the phase of the moon?

Today Laws of Motion Conservation Laws Gravity tides What is the phase of the moon? How is mass different from weight? Mass the amount of matter in an object Weight the force that acts upon an object You