Transcript Monday, October 5

Orbital Motion = Kepler Explained
Planet wants
to move in a
straight line
of constant
velocity
(Newton 1)
Sun’s gravitational
pull forces planet
into orbit by
changing direction
of planets velocity
“Compromise”: planet moves in curved orbit
It takes a stronger force to make a
high speed planet move in an orbit
Cannon “Thought Experiment”
• http://www.phys.virginia.edu/classes/109N/more_stuff/Appl
ets/newt/newtmtn.html
Applications
• From the distance r between two bodies and the
gravitational acceleration a of one of the bodies,
we can compute the mass M of the other
F = ma = G Mm/r2 (m cancels out)
– From the weight of objects (i.e., the force of gravity)
near the surface of the Earth, and known radius of Earth
RE = 6.4103 km, we find ME = 61024 kg
– Your weight on another planet is F = m  GM/r2
• E.g., on the Moon your weight would be 1/6 of what it is on
Earth
Applications (cont’d)
• The mass of the Sun can be deduced from the
orbital velocity of the planets: MS = rOrbitvOrbit2/G
= 21030 kg
– actually, Sun and planets orbit their common center of
mass
• Orbital mechanics. A body in an elliptical orbit
cannot escape the mass it's orbiting unless
something increases its velocity to a certain value
called the escape velocity
– Escape velocity from Earth's surface is about 25,000
mph (7 mi/sec)
From Newton to Einstein
• If we use Newton II and the law of universal
gravity, we can calculate how a celestial object
moves, i.e. figure out its acceleration, which leads
to its velocity, which leads to its position as a
function of time:
ma= F = GMm/r2
so its acceleration a= GM/r2 is independent of its mass!
• This prompted Einstein to formulate his
gravitational theory as pure geometry.
Telescopes
From Galileo to Hubble:
Telescopes use lenses and
mirrors to focus and therefore
collect light
Rain analogy: Collect light as
you collect rain
Rain/light collected is proportional
to area of umbrella/mirror, not its
diameter
Light hits Matter: Refraction
• Light travels at different speeds in vacuum, air,
and other substances
• When light hits the material at an angle, part of it
slows down while the rest continues at the original
speed – results in a change of direction
– Different colors bend different amounts – prism,
rainbow
Application for Refraction
• Lenses use refraction to focus light to a
single spot
Light hits Matter (II): Reflection
• Light that hits a mirror is
reflected at the same
angle it was incident
from
• Proper design of a mirror
(the shape of a parabola)
can focus all rays
incident on the mirror to
a single place
Application for Reflection
• Curved mirrors use reflection to focus light
to a single spot
Telescopes
• Light
collectors
• Two types:
– Reflectors
(Mirrors)
– Refractors
(Lenses)
Refracting Telescopes
Reflecting Telescope
Problems with Refractors
• Different colors (wavelengths) bent by
different amounts – chromatic aberration
• Other forms of aberration
• Deform under their own weight
• Absorption of light
• Have two surfaces that must be optically
perfect
Telescope Size
• A larger telescope gathers more light (more
collecting area)
• Angular resolution is limited by diffraction
of light waves; this also improves with
larger telescope size
Resolving Power of Telescopes
Atmospheric Limitations