Transcript Ch4 Gravity - UCF Physics

The Road to a Sun-Centered
Solar System
• Ptolemy (90-168)
- Almagest published ~150
• Copernicus (1473-1543)
- Published in 1544
• Tycho Brahe (1546-1601)
- Never published
• Johannes Kepler (1571-1630)
- Published his Laws of Motion
starting in 1609
• Galileo (1564-1642)
- Published “Dialogue of the Two
Chief World Systems” in 1632
The Acceleration of Gravity (g)
• Galileo showed
that g is the same
for all falling
objects,
regardless of
their mass.
• Newton was born about a
year after Galileo died
• He nailed the foundation
of the physics of our
ordinary reality. He
dominated Physics until
Einstein.
• He was a bit of a
misanthrope.
‒ Did poorly in school.
Reports described him as
'idle' and 'inattentive'.
‒ He went to college at
Cambridge when he was 18.
‒ Even then he was thought of
as an average student.
Newton
• But at 20 (1663) math caught
his fancy
- In two years he ran through all of
humankind’s mathematical
knowledge and then proceeded to
significantly advance it….
• The plague closed the
University between 1665-1667,
sending Newton back home to
a bit of enforced reflection.
• It was during this period that
he puzzled-out most of his
major contributions
-
Invention of calculus
Theory of gravity
The Laws of Motion
The inverse square law
Newton
• At 27 he became the Lucasian
Professor of Mathematics at
Cambridge
• In later life he held a number of
major positions
-
Member of Parliament
Master of the Mint
President of the Royal Society
The first scientist to be knighted
• He was still very much a
misanthrope
- His response to any criticism was
a bit extreme
- He suffered two nervous
breakdowns
• He could be a pretty nasty guy.
- Take his dispute with Leibniz
- His time as Master of the Mint….!
Newton
Gravity
• Take a look around you….in our everyday
experience we see gravity acting on all
objects.
• Newton made some simple observations
based on his understanding of motion.
- “A body remains stationary or moves in a
straight line unless a force acts on it”
- If a pen drops out of your hand, there HAS TO
BE a force acting on that pen.
• Newton watched the Moon
orbiting the Earth.
- It is in orbit
- it is moving in (essentially) a
circle
- Therefore…. force HAS TO BE
acting on it to deflect it from a
straight line.
• If you know the force HAS
TO EXIST, then you can
calculate what its strength
has to be….
- About 1/3600 of the force of
gravity on the Earth’s surface.
- Other fact: Moon was about
60 times farther from the
CENTER OF THE EARTH than
the Earth’s surface
• So the force on the Moon
was 1/3600 as strong as
the force acting on you at
the surface of the
Earth…..
- He concluded that the force
of the Earth’s gravity
decreases by 1/r2. The
inverse square of distance
- That is how gravity (and
other fundamental forces)
work, their intensity
decreases by the inverse
square of distance.
• This is called the
INVERSE SQUARE LAW
• ALL matter produces a
gravitation force!
• Why???
• The force changes by 1/r2
• The inverse square law
applies to ALL
Forces….gravity,
magnetism, electrical
fields, light….!
How does this
work?
Gravity
Light
• What is the difference in terms of
gravity between these pictures?
Gravity
• Remember gravity is
measured from the
center of an object
- We are 6378 km from
the center of the Earth
- Space shuttle
astronauts in space are
only 200 km farther
away…..
- In inverse square terms
that is 1.03 times
Gravity
• Work it out
- If the distance is
1.03 times the
distance at the
Earth’s surface….
- R2 = 1.06
- 1/R2 x G = 9.2 m/s2
- The force of gravity
is only 6% less in
low Earth orbit
• The reason astronauts are
“weightless” in orbit is because
they are in FREEFALL!
Remember: We live on a sphere
• When you drop
something it
heads toward the
center of the
Earth
• IF you put a bit of
horizontal
velocity on that
something….
Newton’s three laws of motion
Newton’s first law of motion: An object moves
at constant velocity unless a net force acts to
change its speed or direction.
Newton’s second law of motion:
Force = mass  acceleration
Newton’s third law of
motion:
For every force, there is
always an equal and
opposite reaction force.
How do gravity and energy
together explain orbits?
• Orbits cannot change spontaneously.
• An object’s orbit can only change if it
somehow gains or loses orbital energy =
kinetic energy + gravitational potential energy
(due to orbit).
 So what can
make an object
gain or lose
orbital energy?
• Friction or
atmospheric
drag
• A gravitational
encounter.
• Rockets….
Center of mass
• Objects attracted
by gravity orbit
around their center
of mass
Why Does Gravity Work?
• Einstein’s Relativity
• Quantum Gravity (String theory, Loop quantum
gravity, Causal Dynamical Triangulation……and
many more)
• Brans–Dicke theory of gravity
• Induced gravity
• In the modified Newtonian dynamics (MOND)
• The self-creation cosmology theory of gravity
• Nonsymmetric gravitational theory (NGT)
• Tensor–vector–scalar gravity (TeVeS)
• Gravity as an entropic force
• Superfluid vacuum theory
Why are there Tides?
• Take the Bay of Fundy in Nova
Scotia
- Tides there can range 50 feet
between high and low
• High (and low) tides happen
basically twice a day
Tidal Bores in the Severn Estuary
Tides
 Gravitational force decreases with (distance)2
 The Moon’s pull on Earth is strongest on the side facing the
Moon, and weakest on the opposite side.
 The Earth gets stretched along the Earth-Moon line.
 The oceans rise relative to land at these points.
Tides
• Every place on Earth passes
through high tides twice per
day as the Earth rotates.
• High tides occur every 12
hours 25 minutes
• remember, the Moon moves!
• The Sun’s tidal effect on
Earth is not as strong.
Remember the inverse
square law….the Sun is a
long way away.
Tides
Spring and Neap
Tides
• Tides are strongest when the
Sun & Moon pull in the same
direction (new & full phases)
– high tide is higher than usual
(spring)
• Weakest when the Sun & Moon
pull at right angles (first & last
quarter phases)
– high tide is lower than usual (neap)
Tidal Friction
• This fight between Moon’s
pull & Earth’s rotation
causes friction.
• Earth’s rotation slows down
(1 sec every 50,000 yrs.)
• Conservation of angular
momentum causes the Moon
to move farther away from
Earth.
- The Moon is moving away from
Earth at of 38 mm per year!
Tidal Friction
- It adds up! 4 billion years
ago 1 day may have only
been 5 or 6 hours long.
- The moon may have been
1/10 the distance: 22 Earth
radii away instead of 221
- How big would the tides be
if the Moon was 110 Earth
radii away?