Transcript Potential Energy

Cassini Spacecraft Crosses
Saturn's Ring Plane
When Saturn's "appendages"
disappeared in 1612, Galileo did
not understand why. Later that
century, it became understood
that Saturn's unusual protrusions
were rings and that when the
Earth crosses the ring plane, the
edge-on rings will appear to
disappear. This is because
Saturn's rings are confined to a
plane many times thinner, in
proportion, than a razor blade
Several out-of-class Activities have been
posted on the class website.
Homework #4 will be posted shortly.
Ptolemy’s Geocentric Model
● Earth is at center (Geocentric)
● Sun orbits Earth
● Planets orbit on small circles (epicycles)
whose centers orbit the Earth on larger circles
(this explains apparent retrograde motion)
● Planet orbits lie in approximately the same
plane (this explains why the planets are
always near the ecliptic)
● Inferior planet epicycles are fixed to the EarthSun line (this explained why Mercury & Venus
never stray far from the Sun).
Copernicus’ Heliocentric Model
● Sun is at center of the Universe (heliocentric)
● Earth orbits the Sun like any other planet
● Earth rotates
● Circular orbits for all planets
● Inferior planet orbits are smaller
● Planets move at constant velocities in their
orbits
● Retrograde motion occurs when we “lap” Mars
& the other superior planets
Kepler's Laws
1.The Law of Orbits: All planets move in
elliptical orbits, with the sun at one focus.
2. The Law of Areas: Planets move faster in
their orbit the closer they are to the Sun.
3. The Law of Periods: Planets on larger
orbits take longer to complete an orbit than
planets smaller orbits.
a3 / P2 = constant
State of Affairs at beginning
of 17th Century -
Two models of the Universe
Geocentric
Heliocentric
Which model more accurately depicts nature?
 Both make predictions for the apparent motions of
planets and stars.
 Heliocentric model, with modifications incorporating
Kepler’s Laws, gives more accurate predictions
 But, the Geocentric model might be made more
accurate through appropriate modifications.
 Need additional predictions that clearly differentiate
between the two models.
The “Science” of Astronomy
In the broadest sense,
Science refers to any
system of knowledge
which attempts to
model objective reality.
In the broadest sense,
Science refers to any
system of knowledge
which attempts to
model objective reality.
a. Uninfluenced by emotions or personal prejudices.
b. Based on observable phenomena; presented factually
Science attempts to systemized knowledge through:
 observing
 questioning
 hypothesizing
 testing
The Nature of Science
● Science
seeks explanations for observed phenomena
that rely solely on natural
causes.
● Science progresses through the creation and testing
of models of nature that explain the observations as
simply as
possible.
●A
scientific model must make testable predictions that
could force us to revise or abandon the model.
Theory -- a model which survives repeated testing
The word “Theory” has a very
different meaning in science than
in everyday parlance
A model is only referred to as a theory
when it has successfully survived testing
to such an extent that it is generally
accepted as a valid representation of
nature.
Even then, testing continues…
Theories
 Must be Testable
 Must be continuously tested
 Should be simple
“Testable”
Separates science, nonscience & pseudoscience
 Testing separates science from nonscience:
e.g., religion is not accessible to experimental verification
 Testing invalidates pseudosciences:
e.g., astrology fails testing.
Testing of the “Two World”
Models:
Geocentric
vs
Heliocentric
Contemporary with Kepler was
Galileo Galilei (1564-1642),
the “founder of experimental science”
●
●
First person known to point a
telescope at the sky
He wanted to connect the
physics understood on earth
with objects in the heaven
His work got him in trouble with
the Church and led to his house
arrest for many years.
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
 Sunspots (sun not “perfect”)
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
 Sunspots (sun not “perfect”)
 Rotation of sun
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
 Sunspots (sun not “perfect”)
 Rotation of sun
 Moons of Jupiter (Heavenly bodies existed
which did not orbit the earth)
(Some of) Galileo’s
Observations
 Galileo saw craters and shadows cast by the
mountains on the Moon (Moon had a
landscape; it was a “place”, not a perfect
heavenly body)
 Sunspots (sun not “perfect”)
 Rotation of sun
 Moons of Jupiter (Heavenly bodies existed
which did not orbit the earth)
 Phases of Venus: the two models of the
Universe made two very different predictions.
Phases of
Venus
Galileo’s observation of the phases of Venus was the final
evidence that buried the geocentric model.
Geocentric
Heliocentric
No gibbous or full phases!
All phases are seen!
Galileo observed all phases!
With Galileo’s observations, the revolution
begun by Copernicus was nearly complete…
 The structure of the universe had been totally
changed.
 The motions of the planets were understood, at least
from a geometrical perspective.
 Earth was no longer a “special” place in the universe.
 The crowning achievement was yet to come discovering the laws of nature and that naturally led to
the newly determined structure.
Sir Isaac Newton (1642-1727)
Invented calculus
Invented the reflecting
telescope
Connected gravity and
planetary forces
Universal Law of Gravitation
Between every two objects there is an attractive force,
the magnitude of which is directly proportional to the
mass of each object and inversely proportional to the
square of the distance between the centers of the
objects.
Orbital Paths from Law of Gravitation
●
●
●
Extending Kepler’s Law #1, Newton
found that ellipses were not the only
orbital paths.
All orbits are “conic sections”
– ellipse (bound)
– parabola (unbound)
– hyperbola (unbound)
Orbital motion takes place around
the center of mass
The Center of Mass
In Kepler's Laws, the Sun is fixed at a point in space (a
focus of an ellipse) and the planet revolves around it.
Why is the Sun privileged?
Kepler had mystical ideas about the Sun, endowing it
with almost god-like qualities that justified its special
place.
Newton demonstrated that the the Sun does not occupy
a privileged postion and in the process he modified
Kepler's 3rd Law.
The center of mass is familiar to anyone who has ever played
on a see-saw. The fulcrum point at which the see-saw will
exactly balance two people sitting on either end is the center
of mass for the two persons.
m1d1 = m2d2
Newton realized that in the planet-Sun system the
planet does not orbit around a stationary Sun (a planet
exerts as much gravitational force on the Sun as the
Sun does on a planet). F = Gm m /d2
g
1
2
 Instead, Newton proposed that both the planet and
the Sun orbited around the common center of mass for
the planet-Sun system.
 This led Newton to modify Kepler's 3rd Law.
Recall Kepler’s 3rd law: P2 / a3 = constant
Newton’s Version of Kepler’s Third Law
2
2
3
P = 4 a / G (m1 + m2)
G is known as the universal gravitational constant.
If you can measure the orbital period of two objects (P)
and the distance between them (a), then you can calculate
the sum of the masses of both objects (m1 + m2).
We will return to Newton and
discuss his “Laws of Motion”
after we learn some simple
background physics
A Universe of Matter and Energy
What is matter?
What is energy?
Matter – material such as rocks,
water, air; “stuff” composed of
atoms
Energy – makes or has the
potential to make matter move!
The history of the universe, including biological
organisms, is based upon the interplay between
matter and energy.
Three Basic Types of Energy
• kinetic
– energy of motion
• potential
– stored energy; e.g., chemical,
gravitational, electrical, etc.
• radiative
– energy transported by light
(electromagetic radiation)
Conservation of
Energy
Fundamental law of
nature
Energy can be neither
created nor destroyed
It can change form or be
exchanged between objects.
K.E.
The total energy content of
the Universe was determined
in the Big Bang and remains
the same today.
P.E.
R.E.
Kinetic Energy (K.E.):
energy of motion
K.E. = 1/2 mv2
(m is mass, v is velocity)
On the microscopic level:
temperature
is a measure of the
average kinetic energy
of particles within a substance
Temperature Scales
Temperature vs. Heat
●
●
lower T
higher T
same T
Temperature is the average
kinetic energy.
Heat (thermal energy) is the
total kinetic energy.
less heat
more heat
Sound waves are a form of kinetic energy on
a microscopic level
(organized vibration of molecules)
Potential Energy:
Energy that is “stored” within an
object and that has the potential of
being released in a different form
Gravitational Potential Energy
●
gravitational potential energy is
the energy which an object stores
due to its ability to fall
g
●
It depends on:
–
–
–
m
the object’s mass (m)
the strength of gravity (g)
the distance which it can fall (d)
●
P.E. = mgd
d
●
gravitational potential energy
●
P.E. = mgd
g
Mass-Energy Potential Energy
●
●
mass-energy: energy is stored in
matter itself
this mass-energy is what would
be released if an amount of mass,
m, were converted into energy
E = mc2
[ c = 3 x 108 m/s
is the speed of light]
Chemical Potential Energy
●
Chemical potential energy:
energy stored chemical bounds
There are many additional
examples of potential energy. e.g.,
stretched springs, …
Energy, while
conserved, can be
transformed from one
type of energy to
another
Potential
Kinetic
Potential
Kinetic
Kinetic
Potential
Orbits & Energy
Uphill
Maximum
Potential
Energy
Maximum
Kinetic
Energy
Downhill