READING
Unit 8, Unit 19, Unit 20, Unit 21, Unit 22, Unit 23
Potential Energy
• You can think of potential
energy as stored energy,
energy ready to be converted
into another form
• Gravitational potential energy
is the energy stored as a result
of an object being lifted
upwards against the pull of
gravity
• Potential energy is released
when the object is put into
motion, or allowed to fall.
Conversion of Potential Energy
• Example:
– A bowling ball is lifted from the floor
onto a table
• Converts chemical energy in your
muscles into potential energy of the ball
– The ball is allowed to roll off the table
• As the ball accelerates downward
toward the floor, gravitational potential
energy is converted to kinetic energy
– When the ball hits the floor, it makes a
sound, and the floor trembles
• Kinetic energy of the ball is converted
into sound energy in the air and floor, as
well as some heat energy as the atoms
in the floor and ball get knocked around
by the impact
Definition of Angular Momentum
• Angular momentum is the rotational equivalent of
inertia
• Can be expressed mathematically as the product of the
objects mass, rotational velocity, and radius
• If no external forces are acting on an object, then its
angular momentum is conserved, or a constant:
L  m V  r  constant
Conservation of Angular Momentum
• Since angular momentum is
conserved, if either the mass,
size or speed of a spinning
object changes, the other
values must change to
maintain the same value of
momentum
– As a spinning figure skater
pulls her arms inward, she
changes her value of r in
angular momentum.
– Mass cannot increase, so her
rotational speed must increase
to maintain a constant angular
momentum
• Works for stars, planets
orbiting the Sun, and satellites
orbiting the Earth, too!
The Origin of Tides
• The Moon exerts a
gravitational force
on the Earth,
stretching it!
– Water responds to
this pull by
flowing towards
the source of the
force, creating
tidal bulges both
beneath the Moon
and on the
opposite side of
the Earth
Solar Eclipses
• At New Moon, the Moon is between
the Earth and the Sun. Sometimes, the
alignment is just right, allowing the
Moon to block the light from the Sun,
creating an eclipse
Solar Eclipse – the Shadow of the Moon
A solar eclipse seen
from space
•
•
•
In a solar eclipse, the Moon casts
a shadow on the surface of the
Earth. People within the shadow
see the eclipse, and those outside
the shadow do not.
The Moon’s umbra is the darkest
part of the shadow, directly
behind the body of the Moon.
Within the umbra, the Sun
appears completely eclipsed (total
eclipse).
The penumbra of the Moon (not
shown in figure) is the part of the
shadow where the light from the
Sun is only partially blocked
(partial eclipse).
Lunar Eclipses
•
•
As the Moon passes behind the Earth, the Earth can cast
a shadow on the surface of the Moon, creating a lunar
eclipse
The reddish glow of a fully eclipsed Moon is light that
has been refracted through the Earth’s atmosphere and
bounced back to Earth – it is, in essence, the light of
every sunrise and sunset on Earth reflected off the Moon!
Lunar Eclipse – the Shadow of the Earth
•
•
•
In a lunar eclipse, the Earth
casts a shadow on the surface
of the Moon. In its orbit, the
Moon passes through the
penumbra and umbra of the
Earth
The penumbra of the Earth is
the part of the shadow where
the light from the Sun is only
partially blocked. The Moon
dims a little as it passes into
the penumbra.
The Earth’s umbra is the
darkest part of the shadow,
directly behind the body of
the Earth. After the Moon
moves into the umbra, its
surface becomes very dark.
This is a total lunar eclipse.
Why don’t eclipses happen all the time?
•
•
In order for an eclipse to occur, the Moon
must lie directly between the Earth and
the Sun (solar eclipse), or the Earth must
lie directly between the Moon and the
Sun (lunar eclipse).
The orbit of the Moon around the earth is
inclined slightly to the plane of the
ecliptic (the plane in which the Earth’s
orbit lies).
Most of the time, the Moon’s
shadow misses the Earth, or the
Earth’s shadow misses the Moon!
Everything Must be Just Right
• For an eclipse to occur, the Moon must be crossing the
ecliptic at the same time it passes either in front of (solar
eclipse) or behind (lunar eclipse) the Earth (B&D).
• Otherwise, no eclipses are possible (A&C).
The Nature of Light
• Light is radiant energy.
• Travels very fast –
300,000 km/sec!
• Can be described either
as a wave or as a
particle traveling
through space.
•
•
As a wave…
– A small disturbance in an electric field creates
a small magnetic field, which in turn creates a
small electric field, and so on…
• Light propagates itself “by its bootstraps!”
– Light waves can interfere with other light
waves, canceling or amplifying them!
– The color of light is determined by its
wavelength.
As a particle…
– Particles of light (photons) travel
through space.
– These photons have very specific
energies. that is, light is quantized.
– Photons strike your eye (or other
sensors) like a very small bullet, and
are detected.
The Effect of Distance on Light
• Light from distant objects
seems very dim
– Why? Is it because the photons
are losing energy?
– No – the light is simply
spreading out as it travels from
its source to its destination
– The farther from the source you
are, the dimmer the light seems
– We say that the object’s
brightness, or amount of light
received from a source, is
decreasing
Brightness 
Total Light Output
4d 2
This is an inverse-square law –
the brightness decreases as the
square of the distance (d) from
the source
The Nature of Matter
• The atom has a nucleus at
its center containing protons
and neutrons
• Outside of the nucleus,
electrons whiz around in
clouds called orbitals
– Electrons can also be
described using wave or
particle models
– Electron orbitals are quantized
– that is, they exist only at
very particular energies
•
– The lowest energy orbital is
called the ground state, one
electron wave long
•
To move an electron from one orbital to the next higher
one, a specific amount of energy must be added.
Likewise, a specific amount of energy must be released
for an electron to move to a lower orbital
These are called electronic transitions
The Chemical Elements
• The number of protons (atomic number) in a nucleus
determines what element a substance is.
• Each element has a number of electrons equal to the
number of protons
• The electron orbitals are different for each element,
and the energy differences between the orbitals are
unique as well.
• This means that if we can detect the energy emitted or
absorbed by an atom during an electronic transition,
we can tell what element the atom belongs to, even
from millions of light years away!
Periodic Table
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D. Mendeleev
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Absorption
•
If a photon of exactly the
right energy (corresponding
to the energy difference
between orbitals) strikes an
electron, that electron will
absorb the photon and move
into the next higher orbital
– The atom is now in an
excited state
•
If the photon is of higher or
lower energies, it will not be
absorbed – it will pass
through as if the atom were
not there.
•
•
This process is called absorption
If the electron gains enough energy to leave the
atom entirely, we say the atom is now ionized, or
is an ion.
Emission
• If an atom drops
from one orbital
to the next lower
one, it must first
emit a photon
with the same
amount of energy
as the orbital
energy
difference.
• This is called
emission.
Seeing Spectra
• Seeing the Sun’s
spectrum requires a few
special tools, but it is
not difficult
– A narrow slit only lets a
little light into the
experiment
– Either a grating or a
prism splits the light
into its component
colors
– If we look closely at the
spectrum, we can see
lines, corresponding to
wavelengths of light
that were absorbed.
Emission Spectra
•
Imagine that we have a hot
hydrogen gas.
–
–
–
–
Collisions among the hydrogen
atoms cause electrons to jump
up to higher orbitals, or energy
levels
Collisions can also cause the
electrons to jump back to lower
levels, and emit a photon of
energy hc/
If the electron falls from orbital
3 to orbital 2, the emitted
photon will have a wavelength
of 656 nm
If the electron falls from orbital
3 to orbital 2, the emitted
photon will have a wavelength
of 486 nm
• We can monitor the gas, and count how many
photons of each wavelength we see. If we
graph this data, we’ll see an emission
spectrum!
Wavelength
•
•
•
•
The colors we see are determined by the
wavelength of light.
Wavelength is the distance between
successive crests (or troughs) in an
electromagnetic wave.
This is very similar in concept to the
distance between the crests in ocean
waves!
We denote the wavelength of light by the
symbol .
• Wavelengths of visible light are very
small!
– Red light has a wavelength of 710-7
meters, or 700 nanometers (nm)
– Violet light has a wavelength of
410-7 meters, or 400 nm
– Colors in between red and violet
(remember ROY G BIV?) have
intermediate wavelengths
Frequency
•
•
•
•
Sometimes it is more convenient to
talk about light in terms of
frequency, or how fast successive
crests pass by a given point
You can think of frequency as a
measure of how fast you bob up and
down as the waves pass.
Frequency has units of Hz (Hertz),
and is denoted by the symbol 
Long wavelength light has a low
frequency, and short wavelength
light has a high frequency
•
Frequency and wavelength are related by:
   c
‘c’ is the speed of light.
White Light
• Light from the Sun
arrives with all
wavelengths, and we
perceive this mixture of
colors as white
• Newton demonstrated
that white light could be
split into its component
colors with a prism, and
then recombined into
white light with a lens
Measuring Temperature
•
It is useful to think of temperature
in a slightly different way than we
are accustomed to
– Temperature is a measure of the
motion of atoms in an object
– Objects with low temperatures have
atoms that are not moving much
– Objects with high temperatures have
atoms that are moving around very
rapidly
•
The Kelvin temperature scale was
designed to reflect this
– 0  K is absolute zero –the atoms in
an object are not moving at all!
Results of More Collisions
• Additional collisions mean
that more photons are
emitted, so the object gets
brighter
• Additional hard collisions
means that more photons of
higher energy are emitted, so
the object appears to shift in
color from red, to orange, to
yellow, and so on.
• Of course we have a Law to
describe this…
Wien’s Law and the Stefan-Boltzmann Law
• Wien’s Law:
– Hotter bodies emit more
strongly at shorter
wavelengths
• SB Law:
– The luminosity of a hot
body rises rapidly with
temperature
Taking the Temperature of Astronomical Objects
• Wien’s Law lets us estimate
the temperatures of stars
easily and fairly accurately
• We just need to measure the
wavelength (max) at which
the star emits the most
photons
• Then,
T
2.9 106 K  nm
max
The Stefan-Boltzmann Law
• If we know an object’s
temperature (T), we can
calculate how much energy
the object is emitting using
the SB law
L  T
4
•  is the Stefan-Boltzmann
constant, and is equal to
5.6710-8 Watts/m2/K4
• The Sun puts out 64 million
watts per square meter – lots
of energy!