Transcript Chapter 05

Chapter 5
Newton, Einstein, and Gravity
Guidepost
Astronomers are gravity experts. All of the heavenly motions
described in the preceding chapters are dominated by
gravitation. Isaac Newton gets the credit for discovering
gravity, but even Newton couldn’t explain what gravity was.
Einstein proposed that gravity is a curvature of space, but
that only pushes the mystery further away. “What is
curvature?” we might ask.
This chapter shows how scientists build theories to explain
and unify observations. Theories can give us entirely new
ways to understand nature, but no theory is an end in itself.
Astronomers continue to study Einstein’s theory, and they
wonder if there is an even better way to understand the
motions of the heavens.
The principles we discuss in this chapter will be companions
through the remaining chapters. Gravity is universal.
Outline
I. Galileo and Newton
A. Galileo and Motion
B. Newton and the Laws of Motion
C. Mutual Gravitation
II. Orbital Motion
A. Orbits
B. Orbital Velocity
C. Calculating Escape Velocity
D. Kepler's Laws Re-examined
E. Newton's Version of Kepler's Third Law
F. Astronomy After Newton
III. Einstein and Relativity
A. Special Relativity
B. The General Theory of Relativity
C. Confirmation of the Curvature of Space-Time
A New Era of Science
Mathematics as a tool for
understanding physics
Galileo and Inertia
Forefather of modern science: conducts
experiments using scientific method.
Used inclined planes and tried to
eliminate friction to study motion.
Determined that objects (without friction)
naturally maintain motion-they have inertia
Galileo and Gravity
Acceleration of gravity
is independent of the
mass (weight) of the
falling object.
Iron ball
Wood ball
Friction interferes with
falling bodies so they
fall differently.
Without friction, all
bodies fall at same
rate near Earth’s
surface.
Isaac Newton (1643 - 1727)
• Builds on the results of Galileo and Kepler
• Adds physics to the mathematical descriptions of
astronomy by Copernicus, Galileo and Kepler
• “If I have seen farther than others, it has been
by standing on the shoulders of giants.”
Major achievements:
1. Invented Calculus as a necessary tool to solve
mathematical problems related to motion
2. Discovered the three laws of motion
3. Discovered the universal law of mutual gravitation
Newton’s Laws of Inertia
1st Law: A body continues at
rest or in uniform motion in a
straight line unless acted
upon by some net force.
Example: A spacecraft moving
in space will continue to travel
forever in a straight line unless
some external force acts on it.
Newton’s Laws of Acceleration
2nd Law: The acceleration a of a
body is inversely proportional to
its mass m, directly proportional
to the net force F, and in the
same direction as the net force.
a = F/m  F = m a
Acceleration is the rate at which
velocity changes: a race car goes
from 0 to 200 mph in a few seconds!
Aristotle’s “natural” and “violent”
motion are rejected. Newton
says that constant speed in a
straight line is natural, and any
accelerated motion is forced.
Newton’s Laws of Action/Reaction
3rd Law: To every action,
there is an equal and
opposite reaction.
A rifle pushes on a bullet and
the bullet pushes on the rifle
The same force that is
accelerating the boy
forward, is accelerating
the skateboard backward.
A rocket is pushed up by
forcing exhaust out of engine.
The Universal Law of Gravity
• Newton assumed the laws of the universe apply
to terrestrial (Earth) objects and celestial (above
Earth) objects alike. He compared a falling apple
(downward acceleration) with the orbiting moon
(circular acceleration).
• Newton found that any two bodies
attract each other through gravitation,
with a force equal to the product of
their masses divided by the square of
their distance. There’s a constant too.
F G
m1m 2
r
For astronomy, a body of mass m
orbits another body of mass M.
2
Gravity & Inverse Square Law
Understanding Orbital Motion
The universal law of gravity allows us to
understand orbital motion of planets and moons:
Example:
• Earth and moon attract each other through gravitation.
• Since Earth is much more massive
than the moon, the moon’s effect
on Earth is small (tides!).
• Earth’s gravitational force
constantly accelerates the
moon towards Earth (not
• straight).
This acceleration is constantly
changing the moon’s direction
of motion, keeping it on an
almost circular orbit.
v
v
moon
F
Earth
Center of Mass
(SLIDESHOW MODE ONLY)
Orbital Motion (2)
In order to stay on a
closed orbit, an object
has to be within a certain
range of velocities:
Too slow  object falls
back down to Earth
Too fast  object
escapes Earth’s gravity
Satellite projection animation
Newton’s Cannon
(SLIDESHOW MODE ONLY)
Orbital Motion (3)
Geosynchronous
Orbits
Geosynchronous Orbit
(SLIDESHOW MODE ONLY)
Kepler’s Laws Explained by Newton
1st Law: The orbits of the planets are
ellipses with the sun at one focus.
2nd Law: A line from a planet to the sun
sweeps over equal areas in equal
intervals of time.
3rd Law: A planet’s orbital period (P)
squared is proportional to its average
distance from the sun (a) cubed.
Py2 = aAU3
All laws of planetary motion are proved using law of gravitation!
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Platonic Solid
Inside the Octahedron
Octahedron
Icosahedron
Dodecahedron
Tetrahedron
Cube
Kepler
Newton
Einstein and Relativity
Albert Einstein (1879 – 1955)
showed that Newton’s laws of motion
are approximate. For low velocities
they work well, but not for high
velocities (near the speed of light.)
Einstein developed two theories:
Theory of Special Relativity
- for constant velocities
- revised ideas of space and time
Theory of General Relativity
- for acceleration
- revises concept of gravitation
Two Postulates Leading to Special
Relativity (1)
1. Observers can
never detect their
uniform motion,
except relative to
other objects.
This is equivalent to:
The laws of physics are the same for all
observers, no matter what their motion, as
long as they are not accelerated.
Two Postulates Leading to Special
Relativity (2)
2. The velocity of
light, c, is
constant and
will be the
same for all
observers,
independent of
their motion
relative to the
light source.
Basics of Special Relativity
Time Dilation
- Time is not absolute! It is “relative”.
Depends on motion of an observer.
Examples
Light clock animation
- Atomic clocks keep precise time. When a clock is
flown on an airplane, it slows down compared with
another atomic clock that remained at rest.
- Global Positioning Satellites (GPS)
require relativity for exact results.
Basics of Special Relativity
Length Contraction
- Length is not absolute! It’s
“relative” - depends on
motion of on observer.
Length contraction animation
Energy/Mass Equivalence
- Mass is not absolute – it’s relative too!
2
E  mc
- Objects that move have kinetic energy.
But so do objects at rest - they have “rest energy”
- Nuclear energy utilizes
the conversion of
mass to energy with
radioactive elements.
Basics of Special Relativity
speed
beta (β)
Object
v
v/c
fast car
62 m/s
0.00000021
1.000000000
sound
333 m/s
0.00000111
1.000000000
Apollo 10
1.11 x 104 m/s
0.0000037
1.000000001
Earth
2.96 x 104 m/s
0.000099
1.000000005
electrons in TV
9.0 x 107 m/s
0.3
1.05
0.9994
28.87
0.9999999997
4 x 104
Muons at CERN 2.996 x 108 m/s
Electrons at
SLAC
2.998 x 108 m/s
gamma (γ)
General Relativity
A new description of gravity
Equivalence Principle:
“Observers can not tell
the difference between
acceleration and
gravitational forces.”
Which also means:
“Mass tells space-time
how to curve, and the
curvature of space-time
(gravity) tells mass how
to accelerate.”
Another Thought Experiment
Imagine a light source on board a rapidly
accelerated space ship:
Time
Light
source
Time
a
a
a
a
g
As seen by a
“stationary” observer
As seen by an observer
on board the space ship
Thought Experiment (2)
For the accelerated observer, the light
ray appears to bend downward!
Now, we can’t distinguish between
this inertial effect and the effect of
gravitational forces
Thus, a gravitational force
equivalent to the inertial force
must also be able to bend light!
Thought Experiment (Conclusion)
This bending of light by the gravitation of massive
bodies has indeed been observed:
During total solar
eclipses:
The positions of
stars apparently
close to the sun
are shifted away
from the position
of the sun.

New description of gravity as
curvature of space-time!
Another manifestation of bending of light:
Gravitational lenses
A massive galaxy cluster is bending and
focusing the light from a background object.
Other Effects of General Relativity
• Perihelion advance
(in particular, of
Mercury)
• Gravitational red shift: Light from sources
near massive bodies seems shifted towards
longer wavelengths (red).
New Terms
natural motion
violent motion
acceleration of gravity
momentum
mass
acceleration
velocity
inverse square law
field
circular velocity
geosynchronous satellite
center of mass
closed orbit
escape velocity
open orbit
angular momentum
energy
joule (J)
special relativity
general theory of relativity
Discussion Questions
1. How did Galileo idealize his inclines to conclude that
an object in motion stays in motion until it is acted on by
some force?
2. Give an example from everyday life to illustrate each
of Newton’s laws.