• Gravitational Potential Energy for the surface of
the Earth is:
mgr (where r is the radius of the Earth)
F = ma
= mg
= GMEm/r2 = m (GME /r2)
so:
and:
g = GME /r2
mgr = m(GME /r2) r
So, Gravitational Potential Energy = m(GME /r)
Escape Velocity
set: ½ m v2 = GmME /r
for a mass m to escape from the Earth (of mass ME)
½ v2 = GME /r
vesc =
2GME /r
Orbital Paths
• Extending Kepler’s
Law #1, Newton
found that ellipses
were not the only
orbital paths.
• possible orbital
paths
– ellipse (bound)
– parabola (unbound)
– hyperbola (unbound)
Changing Orbits
orbital energy = kinetic energy +
gravitational potential energy
conservation of energy implies:
orbits can’t change spontaneously
An object can’t crash into a planet
unless its orbit takes it there.
An orbit can only change if it
gains/loses energy from another
object, such as a gravitational
encounter:
If an object gains enough energy so that its new orbit is unbound,
we say that it has reached escape velocity.
What is light?
Four Ways in Which Light can Interact
with Matter
emission
absorption
transmission
reflection
But, what is light?
• In the 17th Century, Isaac Newton argued
that light was composed of little particles
while Christian Huygens suggested that light
travels in the form of waves.
• In the 19th Century, Thomas Young
demonstrated that light bends slightly around
corners and acts like interfering waves.
Light
A vibration in an electromagnetic field
through which energy is transported.
Light as a wave
f=c
Light as a particle
E=
a hf
f
photon
Planck’s constant h = 6.6 x 10-34 J s
Scottish physicist James Clerk Maxwell showed
mathematically in the 1860s that light must be
a combination of electric and magnetic fields.
Anatomy of a Wave
Light as a Wave
• For a wave, its speed:
v =  f [distance/time]
• But the speed of light is
a constant
c = 3 x 108 m/s
• For light:  f = c and
f=c/
• The higher f is, the
smaller  is, and vice
versa.
• Our eyes recognize f (or
) as color!
Light as a Particle
• Light can also be treated as photons –
packets of energy.
• The energy carried by each photon depends
on its frequency (color)
E = hf = hc /  (h = 6.6 x 10-34 J s)
• Bluer light carries more energy per photon.
Interaction of Light with Matter
Hydrogen
• Remember that each electron is
only allowed to have certain
energies in an atom.
• Electrons can absorb light and
gain energy or emit light when
they lose energy.
• It is easiest to think of light as a photon when discussing its
interaction with matter.
• Only photons whose energies (colors) match the “jump” in electron
energy levels can be emitted or absorbed.
Light as Information Bearer
We can separate light into its different wavelengths (spectrum).
By studying the spectrum of an object, we can learn its:
1 Composition
2 Temperature
3 Velocity