# General Relativity and Black Holes

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 General Relativity and Black Holes Lecture 19 1

2 Lecture Topics General Relativity The Principal of Equivalence Consequences of General Relativity slowing of clocks curvature of space-time Tests of GR Escape Velocity Black Holes 2

3 General Relativity A Theory of Gravity Albert Einstein 1916 Incorporates accelerated motions into Special Relativity Albert Einstein ( ) 3

4 When you re really famous 4

5 Einstein s Insight Newton s law of gravity worked very well in predicting planetary motions. But Einstein wondered how gravity could be made consistent with Special Relativity. Einstein s insight was the Principal of Equivalence He realized that a gravitational field would bend light rays. He also realized that Euclidean geometry would not apply. 5

6 Principle of Equivalence Gravity and acceleration due to a force are indistinguishable. In a small local environment (must be a small enough box ) This is the foundation of General Relativity. 6

7 Historical Background Proved a relationship between symmetries in physics and conservation principles (1915 or so). This information was used by Einstein and is used in many areas of physics. Noether was going to be a language teacher but became interested in mathematics. David Hilbert and Felix Klein fought to get her on the faculty at University of Göttingen. The battle took four years, but she was finally appointed in She remained there until 1932 when the Nazis caused her dismissal because she was Jewish. She accepted a visiting professorship at Bryn Mawr College and also lectured at the Institute for Advanced Study at Princeton. Emmy Noether ( ) 7

8 Accelerating Rocket ship Gravity Imagine yourself in a closed room. By the principle of equivalence you could not tell if you were on earth or in space in an accelerating rocket. 8

9 Falling under gravity Floating in space Now imagine yourself falling in a closed room. By the principle of equivalence you could not tell if you were falling towards earth or floating in space. 9

10 Gravity and Time Accelerating Rocket ship A B Imagine two clocks in an accelerating rocket. Clock A is in the front. Clock B is in the back. Clock A emits pulses 1 second apart. How far apart are they at Clock B? 10

11 A emits flash B receives flash Clocks in GR NO ACCELERATION A B A B d 2 d 1 A B A B Flash emitted from A To reach B it travels a distance d 1. Since the rocket is not accelerating, we have for the next flash d 2 = d 1 Flashes arrive one second apart. 11

12 A emits flash B receives flash Clocks in GR A ACCELERATING Flash emitted from A A B A d 2 B A To reach B it travels a distance d 1. Accelerating rocket rocket is traveling faster for next flash d 2 < d 1 B d 1 B Flashes arrive less than 1 second apart. 12

13 Clocks in GR Clock A runs faster than clock B. The equivalence principle states Gravity and Acceleration are the same. Therefore, the same thing happens in a gravitational field! A clock on a mountain top will run faster than a clock at sea level. 13

14 Consequences of GR GR changes our concepts of space and time (gravity and geometry are linked). Einstein no longer thought of gravity as a force but a curvature of space-time. Space is curved by massive objects causing objects to fall toward them. 14

15 Curvature of space-time Sun Empty space is flat space-time. Space with matter is curved space-time. 15

16 Bending of light Sun Near a massive object, GR predicts that light will be deflected. GR predicts 1.75 for light grazing the Sun. Measurements of stars during a solar eclipse verified this to within 1%. (Eddington ). 16

17 Time delay of light Viking At Earth Sun Near a massive object, GR predicts that light will travel a longer path due to curved space-time. Verified by timing signals from Viking spacecraft passing by the Sun. 17

18 Binary Pulsar Two neutron stars orbiting one another Work done at Arecibo Observatory Orbit period = 8 hr, Orbit speed = 0.1c!! Serves as a test of General Relativity Precession (movement of orbit) on sky. Decay of orbit due to Gravitational Radiation. (New type of radiation!!) General relativity has been proven over and over to be correct. 18

19 Gravitational Redshift Light from the surface of a massive object will be redshifted. The more massive and/or more compact an object, the greater the redshift. ~ 0.01 A for the Sun. ~ 1 A for a white dwarf. Gravitational redshift verified to 0.01% by hydrogen masers (one in space, the other on the ground). 19

20 Escape velocity Escape velocity is the speed an object would need to escape from a celestial body. Gravity is low on an asteroid. You could throw a ball off it, or jump off it. The escape velocity depends on mass & radius 20

21 Escape velocity Escape velocity is the speed an object would need to escape from a celestial body. The escape velocity depends on mass. Examples: Earth: Moon: 1 km asteroid: Sun: 11.2 km/sec (25,000 mph) 2.4 km/sec 1.3 m/sec (you could jump off it!) 618 km/sec White Dwarf: 6000 km/sec!! How high can the escape velocity get? 21

22 Dark Stars Rev. John Mitchell An object more massive than the Sun could have an escape velocity greater than the speed of light! Today we call this object a black hole. An object from which no light can escape. 22

23 Making a Dark Star Suppose the escape velocity of an object was equal to the speed of light. R s = Schwarzchild radius Putting in numbers: Rs = 3M R s in km M in solar masses 23

24 Warped Space Time

25 How big are black holes? Object Mass (M sun ) R s Star km Star 3 9 km Sun 1 3 km Earth 3 x mm 25

26 The Event Horizon The event horizon is located at R s. Anything inside the event horizon is gone from sight forever (nothing can escape). R s 26

27 Event Horizon

### Manifestations of General Relativity. Relativity and Astrophysics Lecture 32 Terry Herter

Manifestations of General elativity elativity and Astrophysics Lecture 32 Terry Herter Outline Consequences of General elativity Tests of G Escape Velocity => Black holes Black holes Size, Event Horizon,

### Mr Green sees the shorter, straight, green path and Mr. Red sees the longer, curved, red path.

Mr Green sees the shorter, straight, green path and Mr. Red sees the longer, curved, red path. In an accelerated frame, time runs slow compared to a non-accelerated frame. The Equivalence Principle tells

### Black Holes. Over the top? Black Holes. Gravity s Final Victory. Einstein s Gravity. Near Black holes escape speed is greater than the speed of light

Black Holes Over the top? What if the remnant core is very massive? M core > 2-3 M sun (original star had M > 18 M sun ) Neutron degeneracy pressure fails. Nothing can stop gravitational collapse. Collapses

### 11/1/16. Important Stuff (Section 001: 9:45 am) Important Stuff (Section 002, 1:00 pm) 14.1 White Dwarfs. Chapter 14: The Bizarre Stellar Graveyard

Important Stuff (Section 001: 9:45 am) The Second Midterm is Thursday, November 10 The Second Midterm will be given in a different room: Willey 175 Bring 2 pencils and a photo-id. In accordance with the

### 11/1/17. Important Stuff (Section 001: 9:45 am) Important Stuff (Section 002, 1:00 pm) 14.1 White Dwarfs. Chapter 14: The Bizarre Stellar Graveyard

11/1/17 Important Stuff (Section 001: 9:45 am) The Second Midterm is Thursday, November 9 The Second Midterm will be given in a different room: Willey 175 Bring 2 pencils and a photo-id. In accordance

### Test #3 Next Tuesday, Nov. 8 Bring your UNM ID! Bring two number 2 pencils. Announcements. Review for test on Monday, Nov 7 at 3:25pm

Test #3 Next Tuesday, Nov. 8 Bring your UNM ID! Bring two number 2 pencils Announcements Review for test on Monday, Nov 7 at 3:25pm Neutron Star - Black Hole merger Review for Test #3 Nov 8 Topics: Stars

### A100 Exploring the Universe: Black holes. Martin D. Weinberg UMass Astronomy

A100 Exploring the Universe: Black holes Martin D. Weinberg UMass Astronomy weinberg@astro.umass.edu October 30, 2014 Read: S2, S3, Chap 18 10/30/14 slide 1 Sizes of s The solar neighborhood visualized!

### 7/5. Consequences of the principle of equivalence (#3) 1. Gravity is a manifestation of the curvature of space.

7/5 Consequences of the principle of equivalence (#3) 1. Gravity is a manifestation of the curvature of space. Follow the path of a light pulse in an elevator accelerating in gravityfree space. The dashed

### The interpretation is that gravity bends spacetime and that light follows the curvature of space.

7/8 General Theory of Relativity GR Two Postulates of the General Theory of Relativity: 1. The laws of physics are the same in all frames of reference. 2. The principle of equivalence. Three statements

### Lecture 10: General Relativity I

Lecture 10: General Relativity I Einstein Tower Experiment Gravitational redshifting Strong Equivalence Principal Sidney Harris 10/2/13 1 O: RECAP OF SPECIAL RELATIVITY Einstein s postulates Laws of physics

### Lecture 18 : Black holes. Astronomy 111

Lecture 18 : Black holes Astronomy 111 Gravity's final victory A star more massive than about 18 M sun would leave behind a post-supernova core this is larger than 2-3 M sun :Neutron degeneracy pressure

### Einstein s Relativity and Black Holes

Einstein s Relativity and Black Holes Guiding Questions 1. What are the two central ideas behind Einstein s special theory of relativity? 2. How do astronomers search for black holes? 3. In what sense

### ASTR 200 : Lecture 21. Stellar mass Black Holes

1 ASTR 200 : Lecture 21 Stellar mass Black Holes High-mass core collapse Just as there is an upper limit to the mass of a white dwarf (the Chandrasekhar limit), there is an upper limit to the mass of a

### 18.3 Black Holes: Gravity's Ultimate Victory

18.3 Black Holes: Gravity's Ultimate Victory Our goals for learning: What is a black hole? What would it be like to visit a black hole? Do black holes really exist? What is a black hole? Gravity, Newton,

### Stellar remnants II. Neutron Stars 10/18/2010. (progenitor star 1.4 < M< 3 Msun) Stars, Galaxies & the Universe Announcements

Stars, Galaxies & the Universe Announcements Exam #2 on Wednesday Review sheet and study guide posted by Thursday Use office hours and Astronomy Tutorial hours Covers material since Exam #1 (plus background

### Lecture Outlines. Chapter 22. Astronomy Today 8th Edition Chaisson/McMillan Pearson Education, Inc.

Lecture Outlines Chapter 22 Astronomy Today 8th Edition Chaisson/McMillan Chapter 22 Neutron Stars and Black Holes Units of Chapter 22 22.1 Neutron Stars 22.2 Pulsars 22.3 Neutron-Star Binaries 22.4 Gamma-Ray

### Einstein s Gravity. Understanding space-time and the gravitational effects of mass

Einstein s Gravity Understanding space-time and the gravitational effects of mass Albert Einstein (1879-1955) One of the iconic figures of the 20 th century, Einstein revolutionized our understanding of

### Chapter 14: The Bizarre Stellar Graveyard

Lecture Outline Chapter 14: The Bizarre Stellar Graveyard 14.1 White Dwarfs Our goals for learning: What is a white dwarf? What can happen to a white dwarf in a close binary system? What is a white dwarf?

### Relativity. Astronomy 101

Lecture 29: Special & General Relativity Astronomy 101 Common Sense & Relativity Common Sense is the collection of prejudices acquired by the age of 18. Albert Einstein It will seem difficult at first,

### Chapter 13: The Stellar Graveyard

Chapter 13: The Stellar Graveyard Habbal Astro110 http://chandra.harvard.edu/photo/2001/1227/index.html Chapter 13 Lecture 26 1 Low mass star High mass (>8 M sun ) star Ends as a white dwarf. Ends in a

### GENERAL RELATIVITY. The presence of matter affects 4-space.

GENERAL RELATIVITY Whereas Special Relativity is the study of constant velocity motion, General Relativity is associated with situations in which accelerations exist. As gravitation produces acceleration,

### Lecture 21: General Relativity Readings: Section 24-2

Lecture 21: General Relativity Readings: Section 24-2 Key Ideas: Postulates: Gravitational mass=inertial mass (aka Galileo was right) Laws of physics are the same for all observers Consequences: Matter

### Class 6 : General Relativity. ASTR398B Black Holes (Fall 2015) Prof. Chris Reynolds

Class 6 : General Relativity ASTR398B Black Holes (Fall 2015) Prof. Chris Reynolds RECAP! Einstein s postulates " Laws of physics look the same in any inertial frame of reference. " The speed of light

### Black Holes, or the Monster at the Center of the Galaxy

Black Holes, or the Monster at the Center of the Galaxy Learning Objectives! How do black holes with masses a few times that of our Sun form? How can we observe such black holes?! Where and how might you

### Black Holes -Chapter 21

Black Holes -Chapter 21 The most massive stellar cores If the core is massive enough (~3 M ; total initial mass of star > 25 M or so), even neutron degeneracy pressure can be overwhelmed by gravity. A

### Lecture 10: General Relativity I

Lecture 10: General Relativity I! Recap: Special Relativity and the need for a more general theory! The strong equivalence principle! Gravitational time dilation! Curved space-time & Einstein s theory

### Neutron Stars. Chapter 14: Neutron Stars and Black Holes. Neutron Stars. What s holding it up? The Lighthouse Model of Pulsars

Neutron Stars Form from a 8-20 M Sun star Chapter 14: Neutron Stars and Black Holes Leftover 1.4-3 M Sun core after supernova Neutron Stars consist entirely of neutrons (no protons) Neutron Star (tennis

### Chapter 18 Lecture. The Cosmic Perspective Seventh Edition. The Bizarre Stellar Graveyard Pearson Education, Inc.

Chapter 18 Lecture The Cosmic Perspective Seventh Edition The Bizarre Stellar Graveyard The Bizarre Stellar Graveyard 18.1 White Dwarfs Our goals for learning: What is a white dwarf? What can happen to

### Lecture 23: Black Holes Readings: Sections 24-3, 24-5 through 24-8

Lecture 23: Black Holes Readings: Sections 24-3, 24-5 through 24-8 Key Ideas Black Holes are totally collapsed objects Gravity so strong not even light can escape Predicted by General Relativity Schwarzschild

### Space and Time Before Einstein. The Problem with Light. Admin. 11/2/17. Key Concepts: Lecture 28: Relativity

Admin. 11/2/17 1. Class website http://www.astro.ufl.edu/~jt/teaching/ast1002/ 2. Optional Discussion sections: Tue. ~11.30am (period 5), Bryant 3; Thur. ~12.30pm (end of period 5 and period 6), start

### Astronomy 1 Fall 2016

Astronomy 1 Fall 2016 Lecture 14; November 10, 2016 Previously on Astro 1 Late evolution and death of intermediate-mass stars (about 0.4 M to about 4 M ): red giant when shell hydrogen fusion begins, a

### A100H Exploring the Universe: Black holes. Martin D. Weinberg UMass Astronomy

A100H Exploring the Universe: Black holes Martin D. Weinberg UMass Astronomy astron100h-mdw@courses.umass.edu March 22, 2016 Read: S2, S3, Chap 18 03/22/16 slide 1 Exam #2: March 29 One week from today!

### White dwarfs are the remaining cores of dead stars. Electron degeneracy pressure supports them against the crush of gravity. The White Dwarf Limit

The Bizarre Stellar Graveyard Chapter 18 Lecture The Cosmic Perspective 18.1 White Dwarfs Our goals for learning: What is a white dwarf? What can happen to a white dwarf in a close binary system? Seventh

### Relativity and Black Holes

Relativity and Black Holes Post-MS Evolution of Very High Mass (>15 M Θ ) Stars similar to high mass except more rapid lives end in Type II supernova explosions main difference: mass of iron core at end

### Physics. Special Relativity

Physics Special Relativity 1 Albert Einstein, the high school dropout and patent office clerk published his ideas on Special Relativity in 1905. 2 Special vs. General Relativity Special Relativity deals

### Chapter 26. Relativity

Chapter 26 Relativity Time Dilation The vehicle is moving to the right with speed v A mirror is fixed to the ceiling of the vehicle An observer, O, at rest in this system holds a laser a distance d below

### Cracking the Mysteries of the Universe. Dr Janie K. Hoormann University of Queensland

Cracking the Mysteries of the Universe Dr Janie K. Hoormann University of Queensland Timeline of Cosmological Discoveries 16c BCE: flat earth 5-11c CE: Sun at the centre 1837: Bessel et al. measure distance

### Chapter 18 The Bizarre Stellar Graveyard

Chapter 18 The Bizarre Stellar Graveyard 18.1 White Dwarfs Our goals for learning What is a white dwarf? What can happen to a white dwarf in a close binary system? What is a white dwarf? White Dwarfs White

### Outline. General Relativity. Black Holes as a consequence of GR. Gravitational redshift/blueshift and time dilation Curvature Gravitational Lensing

Outline General Relativity Gravitational redshift/blueshift and time dilation Curvature Gravitational Lensing Black Holes as a consequence of GR Waste Disposal It is decided that Earth will get rid of

### General Relativity. on the frame of reference!

General Relativity Problems with special relativity What makes inertial frames special? How do you determine whether a frame is inertial? Inertial to what? Problems with gravity: In equation F = GM 1M

### GR and Spacetime 3/20/14. Joys of Black Holes. Compact Companions in Binary Systems. What do we mean by the event horizon of a black hole?

ASTR 1040: Stars & Galaxies Prof. Juri Toomre TA: Ryan Orvedahl Lecture 20 Thur 20 Mar 2014 zeus.colorado.edu/astr1040-toomre Tycho Brahe SNR (1572) Joys of Black Holes Black holes, their general properties,

### 10/25/2010. Stars, Galaxies & the Universe Announcements. Stars, Galaxies & the Universe Lecture Outline. Reading Quiz #9 Wednesday (10/27)

Stars, Galaxies & the Universe Announcements Reading Quiz #9 Wednesday (10/27) HW#8 in ICON due Friday (10/29) by 5 pm - available Wednesday 1 Stars, Galaxies & the Universe Lecture Outline 1. Black Holes

### Neutron Stars. are as small as a city (~10 km) But as massive as the Sun!

Neutron Stars are as small as a city (~10 km) But as massive as the Sun! Extra-Terrestrial Mystery...! In 1967, graduate student Jocelyn Bell helped build a radio telescope in England.! She found a source

### Announcements. Lecture 6. General Relativity. From before. Space/Time - Energy/Momentum

Announcements 2402 Lab will be started next week Lab manual will be posted on the course web today Lab Scheduling is almost done!! HW: Chapter.2 70, 75, 76, 87, 92, 97*, 99, 104, 111 1 st Quiz: 9/18 (Ch.2)

### RELATIVITY. The End of Physics? A. Special Relativity. 3. Einstein. 2. Michelson-Morley Experiment 5

1 The End of Physics? RELATIVITY Updated 01Aug30 Dr. Bill Pezzaglia The following statement made by a Nobel prize winning physicist: The most important fundamental laws and facts of physical science have

### Chapter 18 The Bizarre Stellar Graveyard. White Dwarfs. What is a white dwarf? Size of a White Dwarf White Dwarfs

Chapter 18 The Bizarre Stellar Graveyard 18.1 White Dwarfs Our goals for learning What is a white dwarf? What can happen to a white dwarf in a close binary system? What is a white dwarf? White Dwarfs White

### Astronomy 182: Origin and Evolution of the Universe

Astronomy 182: Origin and Evolution of the Universe Prof. Josh Frieman Lecture 6 Oct. 28, 2015 Today Wrap up of Einstein s General Relativity Curved Spacetime Gravitational Waves Black Holes Relativistic

### Chapter S3 Spacetime and Gravity. Agenda. Distinguishing Crackpots

Chapter S3 Spacetime and Gravity Agenda Announce: Online Quizzes Observations Extra Credit Lecture Distinguishing Crackpot/Genuine Science Review of Special Relativity General Relativity Distinguishing

### Review Special Relativity. February 3, Absolutes of Relativity. Key Ideas of Special Relativity. Path of Ball in a Moving Train

February 3, 2009 Review Special Relativity General Relativity Key Ideas of Special Relativity No material object can travel faster than light If you observe something moving near light speed: Its time

### Astronomy 122 Outline

Astronomy 122 Outline This Class (Lecture 19): Black Holes Next Class: The Milkyway Last Nightlab tonight! HW7 due on Friday. Mar Lecture report due in discussion class on April 5 th th. Nightlab report

### ASTR 200 : Lecture 31. More Gravity: Tides, GR, and Gravitational Waves

ASTR 200 : Lecture 31 More Gravity: Tides, GR, and Gravitational Waves 1 Topic One : Tides Differential tidal forces on the Earth. 2 How do tides work???? Think about 3 billiard balls sitting in space

### Syllabus and Schedule for ASTRO 210 (Black Holes)

Black Holes Syllabus and Schedule for ASTRO 210 (Black Holes) The syllabus and schedule for this class are located at: http://chartasg.people.cofc.edu/chartas/teaching.html Gravity is Universal Gravity

### 240,000 mi. It takes light just over one second to travel from the moon to the earth

240,000 mi It takes light just over one second to travel from the moon to the earth The simplest atom is hydrogen. Its nucleus is a single proton. And one distant electron moves around it An atom

### 22. Black Holes. Relativistic Length Contraction. Relativistic Time Dilation

22. Black Holes Einstein s Special Theory of Relativity Einstein s General Theory of Relativity Black holes exist in some binary star systems Supermassive black holes at of galaxy centers Two properties

### Limitations of Newtonian Physics

Limitations of Newtonian Physics 18 th and 19 th Centuries Newtonian Physics was accepted as an ultimate truth Science is never absolute Hundreds of experiments can t prove my theory right but only one

Wallace Hall Academy CfE Higher Physics Unit 1 - Universe Notes Name 1 Newton and Gravity Newton s Thought Experiment Satellite s orbit as an Application of Projectiles Isaac Newton, as well as giving

### ASTR 200 : Lecture 30. More Gravity: Tides, GR, and Gravitational Waves

ASTR 200 : Lecture 30 More Gravity: Tides, GR, and Gravitational Waves 1 Topic One : Tides Differential tidal forces on the Earth. 2 How do tides work???? Think about 3 billiard balls sitting in space

### General Relativity and Gravity. Exam 2 Results. Equivalence principle. The Equivalence Principle. Experiment: throw a ball. Now throw some light

General Relativity and Gravity Special Relativity deals with inertial reference frames, frames moving with a constant relative velocity. It has some rather unusual predictions Time dilation Length contraction

### Chapter 18 Reading Quiz Clickers. The Cosmic Perspective Seventh Edition. The Bizarre Stellar Graveyard Pearson Education, Inc.

Reading Quiz Clickers The Cosmic Perspective Seventh Edition The Bizarre Stellar Graveyard 18.1 White Dwarfs What is a white dwarf? What can happen to a white dwarf in a close binary system? What supports

### Chapter 13 2/19/2014. Lecture Outline Neutron Stars. Neutron Stars and Black Holes Neutron Stars. Units of Chapter

13.1 Neutron Stars Lecture Outline Chapter 13 Neutron Stars and After a Type I supernova, little or nothing remains of the original star. After a Type II supernova, part of the core may survive. It is

### ASTR Midterm 2 Phil Armitage, Bruce Ferguson

ASTR 1120-001 Midterm 2 Phil Armitage, Bruce Ferguson SECOND MID-TERM EXAM MARCH 21 st 2006: Closed books and notes, 1 hour. Please PRINT your name and student ID on the places provided on the scan sheet.

### Relativity. Physics April 2002 Lecture 8. Einstein at 112 Mercer St. 11 Apr 02 Physics 102 Lecture 8 1

Relativity Physics 102 11 April 2002 Lecture 8 Einstein at 112 Mercer St. 11 Apr 02 Physics 102 Lecture 8 1 Physics around 1900 Newtonian Mechanics Kinetic theory and thermodynamics Maxwell s equations

### Protostars on the HR Diagram. Lifetimes of Stars. Lifetimes of Stars: Example. Pressure-Temperature Thermostat. Hydrostatic Equilibrium

Protostars on the HR Diagram Once a protostar is hot enough to start, it can blow away the surrounding gas Then it is visible: crosses the on the HR diagram The more the cloud, the it will form stars Lifetimes

### Black Holes in Terms of Escape Velocity. Agenda for Ast 309N, Nov. 27. How Big is the Event Horizon? The Anatomy of a (Simple) Black Hole

Agenda for Ast 309N, Nov. 27 Black Holes in Terms of Escape Velocity Optional HW 3 - due now; Quiz 8 Thursday Next week: repeat survey (Tues), Exam 3 (Thurs) Feedback on black hole index cards Black hole

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

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

### Lecture Outline Chapter 29. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 29 Physics, 4 th Edition James S. Walker Chapter 29 Relativity Units of Chapter 29 The Postulates of Special Relativity The Relativity of Time and Time Dilation The Relativity of

### Stellar Remnants. White Dwarfs Neutron Stars Black Holes

Stellar Remnants White Dwarfs Neutron Stars Black Holes 1 Announcements q Homework # 5 is due today. q Homework # 6 starts today, Nov 15th. Due on Tuesday, Nov 22nd. 2 Assigned Reading Chapters: 64.4,

### Astronomy Hour Exam 2 March 10, 2011 QUESTION 1: The half-life of Ra 226 (radium) is 1600 years. If you started with a sample of 100 Ra 226

Astronomy 101.003 Hour Exam 2 March 10, 2011 QUESTION 1: The half-life of Ra 226 (radium) is 1600 years. If you started with a sample of 100 Ra 226 atoms, approximately how many Ra 226 atoms would be left

### Lecture 18 Vacuum, General Relativity

The Nature of the Physical World Lecture 18 Vacuum, General Relativity Arán García-Bellido 1 Standard Model recap Fundamental particles Fundamental Forces Quarks (u, d, c, s, t, b) fractional electric

### 1. (15.1) What are the approximate mass and radius of a white dwarf compared with those of the Sun?

SUMMARY White dwarfs, neutron stars, and black holes are the remnants of dead stars. A white dwarf forms when a low mass star expels its outer layers to form a planetary nebula shell and leaves its hot

### Lecture 10: General Relativity I

Lecture 10: General Relativity I! Einstein Tower Experiment! Gravitational redshifting! Strong Equivalence Principal! Read Chapter 8! Due to snow and confusion the mid-term is delayed to Thursday March

### Today: Start Ch. 18: Cosmology. Homework # 5 due next Wed. (HW #6 is online)

Today: Start Ch. 18: Cosmology Homework # 5 due next Wed. (HW #6 is online) Dark Matter! A rotation curve is a graph of how fast a something is rotating, as a function of distance from the center.! We

### CURVED SPACE. 6 mon line of latitude. But you can get there in 3,605 miles if you fly

CURVED SPACE - J7 - ing your compass for 3,707 miles almost straight east, along their com 6 mon line of latitude. But you can get there in 3,605 miles if you fly CURVED SPACE along a great circle, heading

### Chapter 23 Lecture. The Cosmic Perspective Seventh Edition. Dark Matter, Dark Energy, and the Fate of the Universe Pearson Education, Inc.

Chapter 23 Lecture The Cosmic Perspective Seventh Edition Dark Matter, Dark Energy, and the Fate of the Universe Curvature of the Universe The Density Parameter of the Universe Ω 0 is defined as the ratio

### Evolution of High Mass stars

Evolution of High Mass stars Neutron Stars A supernova explosion of a M > 8 M Sun star blows away its outer layers. The central core will collapse into a compact object of ~ a few M Sun. Pressure becomes

### One of the factors that misled Herschel into concluding that we are at the Universe's center was

Homework 11! This is a preview of the draft version of the quiz Started: Apr 14 at 9:17am Quiz Instruc!ons Question 1 One of the factors that misled Herschel into concluding that we are at the Universe's

### Black Holes. Introduction: Stable stars which balance pressure due to gravity by quantum pressure(qp) are:

Black Holes Introduction: Stable stars which balance pressure due to gravity by quantum pressure(qp) are: 1. White Dwarfs (WD) : QP = electron degeneracy pressure. Mass < 1.4 M_sun This upper limit is

### Neutron Stars. Properties of Neutron Stars. Formation of Neutron Stars. Chapter 14. Neutron Stars and Black Holes. Topics for Today s Class

Foundations of Astronomy 13e Seeds Phys1403 Introductory Astronomy Instructor: Dr. Goderya Chapter 14 Neutron Stars and Black Holes Cengage Learning 2016 Topics for Today s Class Neutron Stars What is

### Black Holes and Curved Space-time. Paths of Light and Matter. The Principle of Equivalence. Implications of Gravity Bending Light

Black Holes and Curved Space-time When a massive star collapses at the end of its life, it can become a black hole A black is an object that is so massive that light cannot escape from it The theory that

### Centers of Galaxies. = Black Holes and Quasars

Centers of Galaxies = Black Holes and Quasars Models of Nature: Kepler Newton Einstein (Special Relativity) Einstein (General Relativity) Motions under influence of gravity [23] Kepler The planets move

### Black Holes. Class 17 Prof J. Kenney June 19, 2018

Black Holes Class 17 Prof J. Kenney June 19, 2018 basic structure of (non-rotating) black hole basic structure of (non-rotating) black hole SINGULARITY: all the mass of the black hole is crushed to incredibly

### Chapter 5 Newton s Universe

Chapter 5 Newton s Universe Lecture notes about gravitation Dr. Armen Kocharian Units of Chapter 5 The Idea of Gravity: The Apple and the Moon The Law of Gravity: Moving the Farthest Star Gravitational

### Astronomy 1141 Life in the Universe 10/24/12

Friday, October 19 Newton vs. Einstein 1) Newton: Gravity is a force acting between massive objects in static, Euclidean space. Guest lecturer: Barbara Ryden 2) Einstein: Gravity is the result of the curvature

### Monday, April 2, 2012 Reading: Chapter 9: all except 9.6.3, Astronomy in the news?

Monday, April 2, 2012 Reading: Chapter 9: all except 9.6.3, 9.6.4 Astronomy in the news? News: Goal: To understand how time works in curved space and near black holes. Specifically for Black Holes Photons

### 6 General Relativity. Today, we are going to talk about gravity as described by Einstein s general theory of relativity.

6 General Relativity Today, we are going to talk about gravity as described by Einstein s general theory of relativity. We start with a simple question: Why do objects with di erent masses fall at the

### PHSC 1053: Astronomy Relativity

PHSC 1053: Astronomy Relativity Postulates of Special Relativity The speed of light is constant in a vacuum and will be the same for ALL observers, independent of their motion relative to the each other

### Astronomy 421. Lecture 24: Black Holes

Astronomy 421 Lecture 24: Black Holes 1 Outline General Relativity Equivalence Principle and its Consequences The Schwarzschild Metric The Kerr Metric for rotating black holes Black holes Black hole candidates

### Chapter 23 Lecture. The Cosmic Perspective Seventh Edition. Dark Matter, Dark Energy, and the Fate of the Universe Pearson Education, Inc.

Chapter 23 Lecture The Cosmic Perspective Seventh Edition Dark Matter, Dark Energy, and the Fate of the Universe Curvature of the Universe The Density Parameter of the Universe Ω 0 is defined as the ratio

### Chapter 14. Outline. Neutron Stars and Black Holes. Note that the following lectures include. animations and PowerPoint effects such as

Note that the following lectures include animations and PowerPoint effects such as fly ins and transitions that require you to be in PowerPoint's Slide Show mode (presentation mode). Chapter 14 Neutron

### Testing Genaral Relativity 05/14/2008. Lecture 16 1

There is a big difference between the Newtonian and the Relativistic frameworks: Newtonian: Rigid flat geometry, universal clocks Gravitational force between objects Magic dependence on mass Relativistic:

### Survey of Astrophysics A110

Black Holes Goals: Understand Special Relativity General Relativity How do we observe black holes. Black Holes A consequence of gravity Massive neutron (>3M ) cannot be supported by degenerate neutron

### ASTR 101 General Astronomy: Stars & Galaxies. NEXT Tuesday 4/4 MIDTERM #2

ASTR 101 General Astronomy: Stars & Galaxies NEXT Tuesday 4/4 MIDTERM #2 The Stellar Graveyard What s In The Stellar Graveyard? Lower mass stars (M< 8M sun ) à white dwarfs Gravity vs. electron degeneracy

### Today HW#4 pushed back to 8:00 am Thursday Exam #1 is on Thursday Feb. 11

Today HW#4 pushed back to 8:00 am Thursday Exam #1 is on Thursday Feb. 11 Bring a calculator and a #2 pencil Allowed 1 page notes (front and back) E=mc 2, General Relativity, and exam review ISP209s10

### Gravity Waves and Black Holes

Gravity Waves and Black Holes Mike Whybray Orwell Astronomical Society (Ipswich) 14 th March 2016 Overview Introduction to Special and General Relativity The nature of Black Holes What to expect when Black

### Objectives. HR Diagram

Objectives HR Diagram Questions from Yesterday Centripetal Force perpendicular to the rotation axis Acts to slow down collapse Strongest 90 deg from rotation axis Particles with an angle < 90 feel the

### Pic of the day: Halloween aurora

Friday, October 28, 2011 No Office Hours Today Reading: Chapter 9, Sections 9.5.1, 9.5.2, 9.6.1, 9.6.2. 9.7, 9.8 Astronomy in the news? Lisa Randall on the Daily Show http://www.thedailyshow.com/watch/wed-october-26-2011/lisa-randall

### Relativity. Class 16 Prof J. Kenney June 18, boss

Relativity Class 16 Prof J. Kenney June 18, 2018 boss Length contraction (moving sticks are shorter) A measuring stick at rest has a length Lo. When it is propelled at velocity v, it has a shorter length