Science 3210 001 : Introduction to Astronomy Lecture 9 : Stellar Structure Robert Fisher.
Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience...
Transcript of Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience...
![Page 1: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/1.jpg)
Science 3210 001 : Introduction to Astronomy
Lecture 10 : Relativity, Black Holes
Robert Fisher
![Page 2: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/2.jpg)
Items
! Homework and first observational project due next week.
! Second midterm will be on April 11th. Covers the material in
between the last midterm and the end of the next lecture.
! We plan to have a guest speaker sometime shortly after the
second midterm. Lunch in the loop (on me) with the guest
speaker following the lecture at Frontera Fresco for anyone who
wants to join us.
! Short proposals (1 paragraph) for final projects will be due on
April 18th. We will have a peer review session of the proposals
that day.
! Final projects due on the last day of class, along with a short (5
minute) presentation that day.
![Page 3: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/3.jpg)
Final Project
! Your final project is to construct a creative interpretation a scientifictheme we encountered during the class. You will present your work in afive minute presentation in front of the entire class on May 11.
! The project must have both a scientific component and a creative one.
! For instance, a Jackson Pollock-lookalike painting would fly, but ONLY ifyou said that it was your interpretation of the big bang cosmologicalmodel AND you could also demonstrate mastery of the basicastrophysics of the big bang while presenting your work.
! Be prepared to be grilled!
! Ideas :
! Mount your camera on a tripod and shoot star trails.
! Create a “harmony of the worlds” soundtrack for the Upsilon Andromedasystem.
! Paint the night sky as viewed from an observer about to fall behind thehorizon of a black hole.
! Write a short science fiction story about the discovery of intelligent life in theuniverse.
![Page 4: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/4.jpg)
Review of Three Weeks Ago
! Extrasolar planets
! 51b Peg
! HD209458b
![Page 5: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/5.jpg)
Review of Two Weeks Ago
! Interstellar Medium and Star Formation
! Binary Stars
! Star Clusters
! HR (Hertzsprung-Russell) Diagram of Stars
![Page 6: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/6.jpg)
Review of Last Week
! Stellar Structure
! Stellar Evolution
! Evolution of a low-mass star
! Evolution of a high-mass star
! Supernovae
![Page 7: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/7.jpg)
Today -- Relativity and Black Holes
! Special Relativity
! Michelson-Morley Experiment
! Introduction to Spacetime Physics
! Relativity of Simultaneity
! General Relativity
! Black Holes
![Page 8: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/8.jpg)
The Aether
! Late 19th century scientists attempting to make sense of the wavelikebehavior of light argued that light must be a wave like other wavesknown at that time -- water waves, sound waves, seismic waves, and soon.
! The common opinion developed was that waves are the result of amechanical disturbance in a physical medium -- for instance, waterwaves oscillate once a rock is dropped in a pond.
! By analogy, light must be the result of a disturbance in an undetectedmedium known as the aether (sometimes ether or luminiferous aether).
! If the aether did exist, it must carry physical properties like mass andmomentum, just like a pond. If it has physical properties, it must bedetectable.
! If that is all true, then where was all of the evidence for the existence ofthe aether ??
![Page 9: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/9.jpg)
Michelson-Morley Experiment
! In 1887, physicists Michelson and Morley devised a brilliant
method to detect the aether.
! To understand how their experiment worked, consider Alexis,
who is standing on the shore watching Bettie, moving on a boat
moving at a fixed speed through a river.
! When Bettie is moving downstream, the boat moves with a speed
relative to Alexis which is the sum of the boat speed and the
water speed.
Bettie
![Page 10: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/10.jpg)
Michelson-Morley Experiment
! When Bettie is moving upstream, the boat moves with a speed
relative to Alexis which is the difference of the boat speed and the
water speed.
! Even if Alexis observed only the motion of the boat in both
directions, she could easily infer both the direction and speed of
the water current.
! By analogy, Michelson and Morley hoped to measure the
difference in the speed of light as it moved relative to the aether,
and from that knowledge, both establish the existence of the
aether and also its direction of motion and speed.
Bettie
![Page 11: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/11.jpg)
Michelson-Morley Experiment
! Believing that the speed of light relative to the Earth must vary as
the Earth moves through the aether, physicists Michelson and
Morley planned a highly-sensitive experiment to measure this
effect.
Lig
ht M
oves F
aste
r
Lig
ht M
oves S
low
er
![Page 12: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/12.jpg)
Michelson-Morley Video
![Page 13: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/13.jpg)
Classical Space and Classical Time
! Classical physics prior to Einstein considered motion taking place
upon a fixed space and a universal time.
! Space is the stage where all action takes place. Everyone always
agrees upon distances measured on the stage -- it is absolute
and unchanging.
! Time is a universal concept as well. Everyone’s clock always
precisely agrees with everyone else’s clock.
![Page 14: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/14.jpg)
Spacetime
! One of the key ideas in relativity theory is that space and time aredramatically different from the classical viewpoint.
! The concepts which Einstein hit upon are radically different thanboth the classical point of view, and our own everydayexperience.
! Because relativity is so radically different from our everydayexperience, Einstein had proceed using razor-sharp logic, startingfrom basic axioms.
! This reasoning was often applied to extraordinary situationsknown as thought experiments (sometimes gedankenexperimentfrom the German).
![Page 15: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/15.jpg)
A Short Note on Historical Attributions
! The popular conception is that the
theory of relativity was nearly single-
handedly created by Einstein. While
largely true, it is far from the entire
story.
! Early ideas remarkably similar to
Einstein’s were espoused by Karl
Friedrich Gauss and Behrnard
Riemann.
! Key contributions to the theory were
made by several other scientists,
including George Francis Fitzgerald,
Hendrik Lorentz, and Henre
Poincare.
Einstein & Lorentz
![Page 16: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/16.jpg)
A Short Note on Historical Attributions
! “Whoever speaks of absolute space usesa word devoid of meaning. This is a truththat has been long proclaimed by all whohave reflected on the question, but onewhich we are too often inclined to forget…have shown elsewhere what are theconsequences of these facts from thepoint of view of the idea that we shouldconstruct non-Euclidean and other
analogous geometries.” -- HenriPoincare, Science and Method, 1897
! Recently more controversialsuggestions have been made thatEinstein’s first wife Mileva Mariccontributed substantially to therelativity, and even that otherscientists came upon E = m c2
independently.
! What remains true is that the wholeof relativity theory owes more to onesingle individual more than anyother major theory in modernphysics.
Henri Poincare
![Page 17: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/17.jpg)
Einstein
! A large part of the Einstein myth
are the circumstances in which
his first papers were published.
! In 1905, while publishing his
“miracle year” papers on
relativity and other subjects,
Einstein was employed as a
clerk (third class) at the Swiss
patent office in Zurich.
! He remained a clerk in the office
well afterwards -- until he was
appointed “Extraordinary
Professor of Physics” at the
University of Zurich -- in 1909.
![Page 18: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/18.jpg)
Spacetime Preliminaries
! In building a conception of how space and time work, it is first
crucial to define what we mean by such basic concepts as
‘space’, ‘time’, ‘event’, and ‘simultaneity’.
! The elementary building block in this framework is the event.
! An event defines a single point in space and time.
! For our thought experiments, we can imagine that events are
defined by flashes of light which move spherically outwards from
their sources -- for instance, as set off by an electronic light
source.
![Page 19: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/19.jpg)
The Building Block of Spacetime -- The Event
! An event has no duration or spatial extent -- it is a single point in
space and in time.
! A distant observer will note the event when the light from the
event first reaches him or her.
! It is important to note that the light flash itself at the source and
the event of detection are two distinct events.
![Page 20: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/20.jpg)
Spacetime Preliminaries -- Measuring Time
! Fundamental to this picture is that spacetime is filled with
hypothetical observers who can conduct observations and
measurements on their own.
! Each observer carries with him or her a clock (which we will
describe in detail later) to measure elapsed time.
! Using the pulses of light from events, and his or her clock, each
observer can measure time intervals between events.
![Page 21: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/21.jpg)
Spacetime Preliminaries -- Measuring Distance
! Using events, light pulses, and clocks, observers can also
measure distances between spacetime events.
! Consider, for instance, measuring the distance between yourself
and the wall of a room. You send a light pulse out, which defines
event A. A mirror hanging on the wall reflects the light pulse,
which returns to you at event B.
! The distance between you and the wall is easily determined from
d = c t -- the speed of light times the elapsed time, divided by two
(to account for there and back again).
A
B
Mirror
![Page 22: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/22.jpg)
An Important Word of Caution About Spacetime
Misconceptions
! Most students have common hangups when first learning relativity.
! In one hangup, some students do not see any immediate flaw in thelogic, and so accept the basic logic and conclusions of the theory.
! However, the conclusions are simply too “weird” to fully accept, so theycome to believe that because the conclusions are based onmeasurements made by observers, relativity is actually an illusionarytrick played on their instruments. The “real world” behaves differently.
! This misses one of the key logical premises of the theory -- that we knowof space and time only through our measurements. Any presumed “realworld” outside of our measurements cannot be verified by anyexperiment and so does not exist.
! This viewpoint is further refuted by the fact that relativity has real,observable consequences -- sometimes startling. We will discuss someof these later.
![Page 23: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/23.jpg)
Spacetime Diagram
! A key tool used to understand how spacetime works is the
spacetime diagram.
! In this diagram, only one spatial dimension is plotted along one
axis. The other two spatial dimensions are suppressed.
! Along the second axis, time is plotted.
time
space
![Page 24: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/24.jpg)
Question
! Which of the following figures represents the spacetime motion of
a body (shown in red) at rest?
time
space
time
space
![Page 25: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/25.jpg)
Question
! Which of the following figures represents the spacetime motion of
a body (shown in red) moving at constant speed?
time
space
time
space
![Page 26: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/26.jpg)
Spacetime Diagram of a Pulse of Light
! Imagine that an observer sets off a pulse of light at the origin of
our spacetime diagram, O. This defines an event.
time
spaceO
![Page 27: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/27.jpg)
Spacetime Diagram of a Pulse of Light
! Light, traveling at a constant speed, moves outward from the
origin.
! On the spacetime diagram, this is represented by the two rays
shown below.
time
spaceO
![Page 28: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/28.jpg)
Spacetime Diagram of a Pulse of Light
! Note that in the full three dimensions of space, the region
encompassed by the expanding pulse is of course, spherical, like
the rings on the surface when a rock is dropped into a pond.
time
spaceO
From Above Spacetime Diagram
![Page 29: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/29.jpg)
Spacetime Diagram of a Pulse of Light
! The region encompassed by the expanding light front is known as
the future light cone.
! Because nothing can travel faster than light, only those events
lying in the future light cone of an event are in causal contact with
it.
time
spaceO
Light cone
![Page 30: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/30.jpg)
Question
! Which of the events shown below are out of causal contact with
event O?
time
spaceO
Light cone
A CB
![Page 31: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/31.jpg)
Inertial Observers
! Imagine Albert and Heindrik, aboard two rocket ships gliding pastone another at constant speed in distant interstellar space, faraway from any other objects.
! From Albert’s viewpoint, he is at rest, and Heindrik is movingrelative to him.
! From Heindrik’s viewpoint, he is at rest, and it is Albert who ismoving relative to him.
A
H
Albert’s Frame of
Reference
![Page 32: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/32.jpg)
Question
! How might we be able to settle the debate as to who is moving --Heindrik or Albert?
A
H
Albert’s Frame of
Reference
A
H
Heindrik’s Frame of
Reference
![Page 33: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/33.jpg)
The Axioms of Special Relativity Theory
! In a famous paper written in 1905, “On the Electrodynamics of
Moving Bodies,” Einstein posited the following two basic
assumptions :
! The speed of light is constant for every observer.
! The laws of physics are identical for every inertial observer -- every
observer moving at a constant speed.
![Page 34: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/34.jpg)
The Relativity of Simultaneity
! These two seemingly straightforward assumptions turn out to
have profound implications for physics, and for the structure of
spacetime itself.
! Consider two inertial observers, Hendrik and Albert, moving
relative to one another on identical moving trains. Suppose that
each train has marked off an identical, fixed distance, with two
fixed two stationary light detectors there.
H
A
Albert’s Frame of
Reference
![Page 35: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/35.jpg)
The Relativity of Simultaneity
! Each observer is stationary in his own frame of reference, and
sees the other observer moving toward him.
! So far, without the introduction of light, there is nothing new here -
- this understanding of the relative properties of motion was
known all the way back to Galileo.
H
A
Heindrik’s Frame of
Reference
![Page 36: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/36.jpg)
Relativity of Simultaneity
! The critical new ingredient in relativity is the introduction of light,
which is presumed to move at the same speed to all inertial
observers.
! Consider what happens when an observer sets off a flash of light
from the center of the train, halfway between the two light
detectors.
! The speed of light is constant in every frame, so both detectors
are set off simultaneously.
A
Albert’s Frame of
Reference
![Page 37: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/37.jpg)
The Relativity of Simultaneity
! Now, imagine that at the instantaneous event when Heindrik and
Albert pass one another, a light flash is set off at their precise
location.
! Each observer sees himself as the center of the expanding front
of light.
H
A
Albert’s Frame of
Reference
![Page 38: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/38.jpg)
The Relativity of Simultaneity
! This poses an immediate paradox -- how can two different inertial
observers at two different spatial locations both be at the center
of the same sphere -- the one determined by the expanding flash
of light??
H
A
Albert’s Frame of
Reference
![Page 39: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/39.jpg)
The Relativity of Simultaneity
! This poses an immediate paradox -- how can two different inertial
observers at two different spatial locations both be at the center
of the same sphere -- the one determined by the expanding flash
of light??
H
A
Heindrik’s Frame of
Reference
![Page 40: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/40.jpg)
The Relativity of Simultaneity
! According to Albert, the light pulse reaches both of his detectors
simultaneously -- at the same time. However, he sees the pulse
reach Heindrik’s detectors at two distinct times.
! Heindrik, of course, observes precisely the opposite -- the light
pulse reaches both of his detectors simultaneously, but Albert’s
detectors at two distinct times.
! How can these two evidently contradictory conclusions be
resolved?
H
A
Albert’s Frame of
Reference
![Page 41: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/41.jpg)
Resolution of Relativity of Simultaneity --
Gott im Himmel !
! Einstein’s solution to this paradox was bold and radical. Rather
than suggesting a modification to the two basic axioms laid out,
he proposed that our understanding of space and time itself
had to be modified.
! In the case of Heindrik and Albert, it is clear that we must reject
the notion that two events which are viewed as simultaneous by
one inertial observer must also be simultaneous for all other
inertial observers.
! The very concept of simultaneity itself only makes sense
when we also specify WHO is making the measurement.
![Page 42: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/42.jpg)
Relativity of Simultaneity
! Einstein’s resolution to the paradox also clarifies that indeed, both
observers are correct to state that they are the center of the
expanding sphere of light.
! The conflict arises when we inject our prior notions of a fixed
absolute space and a fixed absolute time, independent of all
observers, into the picture.
! Therefore, there can be no such absolute space, and no such
absolute time.
! Einstein’s theory elegantly describes how space and time can be
unified and understood as a single entity -- spacetime.
![Page 43: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/43.jpg)
Relativity of Simultaneity Video
![Page 44: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/44.jpg)
Relativity of Time
! Einstein also analyzed the flow of time. Consider Heindrik and
Albert again, and let us assume both carries a light clock.
! The light clock consists of two mirrors, which light bounces in
between.
! When viewed at rest, in the frame of reference of the clock, the
distance between the two mirrors is fixed, and the speed of light
is constant, so each cycle of the clock has a fixed time.
![Page 45: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/45.jpg)
Relativity of Time
! Consider how Albert sees Heindrik’s moving clock.
Albert’s Frame of
Reference
H H
![Page 46: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/46.jpg)
Relativity of Time
! Albert measures that the light ray in Heindrik’s clock moves for a
further distance than Heindrik.
Albert’s Frame of
Reference
Heindrik’s Frame of
Reference
Heindrik’s Clock
![Page 47: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/47.jpg)
Relativity of Time
! Since the speed of light is the same in all reference frames, and
because Albert sees Heindrik’s light rays move further, Albert
measures the time between cycles on Heindrik’s clock as longer
than Albert’s.
! Consequently, according to Albert, Heindrik’s clock is slow
relative to Albert’s.
Albert’s Frame of
Reference
Heindrik’s Frame of
Reference
Heindrik’s Clock
![Page 48: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/48.jpg)
Relativity of Time
! Framing the same issues from the standpoint of Heindrik instead
of Albert, it is clear that Heindrik also sees Albert’s clock move
more slowly relative to his own.
! This relativistic effect -- that an inertial observer measures a
moving clock as progressing more slowly than his own -- is
referred to as “time dilation”.
![Page 49: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/49.jpg)
Discussion
! Albert sees Heindrik’s clock move slowly relative to his own.
Heindrik sees Albert’s clock move slowly relative to his own.
! Who do you think is correct? Albert or Heindrik? Why?
![Page 50: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/50.jpg)
Putting Relativity to the Test --
Decaying Muons
! At first glance, the predictions of the theory of relativity may seem
so bizarre that they cannot possibly be true.
! The theory has been tested numerous times to extraordinary
accuracy, and each time, the experiments have proven to be in
complete agreement with the theory.
! One of the most amazing experimental tests of relativity makes
use of an exotic, more massive cousin of the electron -- the
muon. It has 207 times the mass of the electron.
! The muon is identical to the electron in all respects apart from its
mass and lifetime. It is essentially the fat cousin of the electron,
with a lifetime of about 2 microseconds.
![Page 51: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/51.jpg)
Decay of Muons
! Muons are created in the upper atmosphere of the Earth during
bombardment by cosmic rays, and stream downwards towards
the surface of the Earth.
! In 1941, physicists measured found that the number of muons
present at 2 km altitude at the peak of a mountain was about 1.4
times that at its base, implying that the majority of muons made
the descent without decaying.
2 km
Muons
![Page 52: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/52.jpg)
Decaying Muons
! Multiplying the speed of light by the lifetime of the muon, we
would infer that the muons could travel only about 0.6 km on
average before decaying into other particles. If this were true,
fewer than 1 in 10 particles could traverse 2 km.
! The resolution to this paradox is quite simple -- according to the
observer on the Earth, the muon’s clock is running more slowly
than the Earthbound clock.
! Consequently, fewer muons decay than one would have
expected based on on the elapsed interval on the Earth.
! Once the time dilation effect of the muons is taken into account,
relativity accounts for just the muon fluxes we observe.
![Page 53: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/53.jpg)
Einstein’s General Theory of Relativity
! From 1905 to 1915, Einstein struggled with the problem of fitting gravityinto his work.
! From the time of Newton, the origin of gravity appeared to be a completemystery. How could it seem to act instantaneously over vast distances ofspace with nothing in between??
! “I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I donot feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; andhypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place inexperimental philosophy. In this philosophy particular propositions are inferred from the phenomena, andafterwards rendered general by induction.” -- Sir Isaac Newton
! Einstein’s vision was to create a theory of gravity which accounted forthis “action at a distance” mystery, while also limiting to his previous workon relativity as a “special” case. Hence, “Special Relativity” and “GeneralRelativity”.
![Page 54: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/54.jpg)
The Principle of Equivalence
! The tremendous challenge to Einstein was to explain the effects
of gravity as a curvature in spacetime. The motion of falling
bodies provided a starting place.
! The special theory of relativity asserted as an axiom that the laws
of physics are the same for any uniformly-moving observer.
! Einstein had a flash of intuition when he realized that there is no
experiment that could distinguish between a stational laboratory
in the gravitational field of the Earth, and a rocket ship
accelerating at exactly 1 g in distant space.
![Page 55: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/55.jpg)
The Principle of Equivalence
! The general theory begins with the assertion that the laws of physics are
the same for any freely-falling observer.
! This principle became known as the principle of equivalence.
! Because the motion of the rocket ship can be understood as a bending
of the trajectory of an inertial observer, it suggested to Einstein that our
understanding of gravity can be framed as a purely geometric problem.
Earth Rocket
gravity
Acceleration of rocket
![Page 56: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/56.jpg)
Greene Video
![Page 57: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/57.jpg)
General Theory of Relativity Summary
! The whole picture of the General Theory can be summarized by a
simple viewpoint.
! Matter tells spacetime how to curve.
! Curved spacetime tells matter how to move.
! The mathematics of computing how spacetime becomes curved,
and determining how a body moves in the curved spacetime is
quite complex, but the basic idea remains simple.
![Page 58: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/58.jpg)
Predictions of The General Theory --
Bending of Starlight
! If the Special Theory of Relativity seems strange at first, the
General Theory may seem downright impossible.
! The first truly new prediction of the theory to be confirmed (during
the eclipse of 1919 by Eddington) was the bending of starlight.
![Page 59: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/59.jpg)
Gravitational Lensing Due to A Cluster of
Galaxies
! Spectacular instances of extragalactic gravitational lensing have
been observed over the last 20 years.
![Page 60: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/60.jpg)
Prediction of Relativity Theory -- Gravitational
Redshift
! Imagine that we send a laser
light beam inside the
accelerating rocket ship.
! A detector placed at the top of
the rocket ship will be moving
away from the source, and so
there will be a Doppler shift of
the light beam toward the red.
! By the equivalence principle, an
identical laer light ray sent
upwards in the laboratory in a
gravitational field will experience
a redshift -- a gravitational
redshift.
Rocketlaser
laser Lab
![Page 61: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/61.jpg)
Gravitational Redshift and
Gravitational Time Dilation
! Earlier we discussed one method of constructing a clock based
on two mirrors and a light beam.
! A second clock can be constructed by simply measuring the
frequency of a laser beam of light. Blue light has a higher
frequency than red light, and so oscillates more times per second.
! From the existence of a gravitational redshift effect, it follows that
for two observers at two altitudes in a gravitational field like that of
the Earth, the clock at a lower altitude moves more slowly
than that of an observer at a higher altitude.
![Page 62: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/62.jpg)
Pound-Rebka Experiment
! This prediction of General Relativitymay seem astonishing, though it isimportant to realize that for relativelyweak gravitational fields like theEarth’s, the effect is incredibly tiny --though still measurable.
! In 1959, Pound and Rebkaconstructed an nuclear experiment inthe physics building at Harvard usinga radioactive source (57Fe) in thebasement, and a moveable detector22 meters above it.
! Their measurements confirmed thatthe gamma rays emitted by the ironwere indeed redshifted, andconsistent with the gravitationalredshift effect predicted by Einstein.
![Page 63: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/63.jpg)
Relativity and GPS
! GPS satellites require extraordinarily precise timing -- to withinnanoseconds per day -- in order to obtain accurate measurements oflocations on the Earth.
! The time dilation effect of Special Relativity due to the moving satellite,AND the gravitational redshift effect of General Relativity are absolutelycritical to the GPS system.
! In fact, taking into account both the gravitational redshift effect and thetime dilational effect predicts clocks on the ground are slower than on thesatellite, by about 40 microseconds per day.
! 40 microseconds per day may not seem like a large effect, but withoutrelativity, it would amount to an error of nearly 10 km per day -- whichwould make the GPS system completely useless.
![Page 64: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/64.jpg)
Black Holes
! If the gravitational field of a body becomes sufficiently strong, not
even light can escape from it.
! This body is known as a black hole. The boundary beyond which
there is no escape is known as the horizon.
![Page 65: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/65.jpg)
Cygnus X-1
! The first strong case for the detection of a black hole was made in
the Cygnus X-1 x-ray emitting system in the 1970s.
![Page 66: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/66.jpg)
Black Hole Physics
! Imagine what it might be like to make a trip to a black hole.
! Alexis uses a rocket ship to move close to a huge black hole, thesize of a galaxy. Bettie stays nearby and sends a radio messageto her. Alexis radios a message back to her.
! As Alexis nears the horizon, Bettie sees her signal become moreand more redshifted. Alexis’s clock slows down further and furtheras she approaches the horizon.
! Conversely, Alexis sees Bettie’s signal become more and moreblueshifted -- until it is not a radio wave at all, but infrared,visible… eventually become high-frequency gamma radiation.Alexis sees Bettie’s clock move faster and faster, and indeed theentire universe moves in fast forward.
![Page 67: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/67.jpg)
Black Hole Physics
! In addition, as she nears the horizon, only those photons fromAlexis moving nearly vertically have a chance to escape; the onesmoving horizontally begin to fall into the black hole.
! This means that Bettie sees the signal from Alexis become moreand more highly-beamed as she moves further in.
! Alexis, on the other hand, sees the sky overhead begin to darkento absolute black apart from a narrow cone above her.
Radio waves
![Page 68: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/68.jpg)
Beyond the Horizon
! While Bettie will never see Alexis move behind the horizon, Alexisactually falls behind the horizon in a finite time.
! What happens behind the horizon, and in particular whathappens as one approaches the center of the black hole is amatter of intense speculation, but is not understood in the currentframework of physics.
! According to General Relativity, all of the mass of the black holeis concentrated in a single point of infinite density -- thesingularity. This is in fact a breakdown of the theory itself, and soGeneral Relativity cannot be used to understand what goes on atthe location of the singularity.
![Page 69: Robert Fisher - University of Chicagoflash.uchicago.edu/~rfisher/saic/saic_spring08_09.pdfScience 3210 001 : Introduction to Astronomy Lecture 10 : Relativity, Black Holes Robert Fisher](https://reader031.fdocuments.in/reader031/viewer/2022030722/5b07562e7f8b9a58148e2564/html5/thumbnails/69.jpg)
Next Week : More Black Holes and Galaxies
! What would happen if two regions of spacetime were tied
together in a “wormhole”?
! What do we think happens at the very smallest scales in which
gravity and quantum effects both become important?
! And is there a black hole at the center of the Milky Way?