Transcript Universal Gravitation

Gravity
Gravity
• Wait, what does gravity have to do with
rotational motion?
• Let’s look at some well-known physicists and
their work to find the answer.
Johannes Kepler
• 1600’s
• Kepler observed the motions of the planets
• He came up with three laws to describe their
motion, but he didn’t know WHY they moved
the way they did
Kepler’s Laws
• Orbits: All planets move in elliptical orbits
with the sun at one focus
• Areas: A line that connects a planet to the sun
sweeps out equal areas in equal times
• Periods: The square of the period of any
planet is proportional to the cube of the
semimajor axis of its orbit
And then he died
Isaac Newton
• 1600’s
• Newton did not like the lack of explanation
behind Kepler’s laws
• According to the first law, the Earth and moon
should travel in a straight line.
– So why do they deviate from this path?
Here we go again…
• So, yeah, Newton got bonked on the head by
the apple.
• He realized that what pulled the apple down is
also the same force that pulls the moon
towards the Earth.
• To determine the acceleration of the moon,
use rotational kinematics
Relationships
• So because F=ma, force is proportional to
mass
– Because we have two masses, Earth and moon,
the force is proportional to both
• And, based on the calculations we just did,
force is inversely proportional to the square of
the distance between two objects
The finale
• Put it all together and:
F= G((m1m2)/r2)
where G is a proportionality constant
G
• Newton tried to determine what G was, but
was unable to do so.
• And then he died.
Henry Cavendish
• Hundred years later.
• Cavendish figured out how to measure G
• The Cavendish Torsion Balance
G
• So the torque exerted on the wire is the force
Fg
• Therefore, G= 6.67 x 10-11 N m2/kg2
And then he died
Gravity
• So, we have a law of gravity for two objects.
• Often, it is more beneficial to find the
acceleration due to gravity between the
objects.
Orbits
• Remember, Kepler described orbits in his laws
• But, what is an orbit, truly?
Orbits
• Suppose we have a ridiculously high mountain
on Earth.
• This mountain has a cannon.
• The cannon fires a cannonball.
Orbits
• Due to gravity, the cannonball is falling
towards Earth, so it lands some distance away
from the mountain.
• But, what if we up the amount of gunpowder?
Orbits
• In theory, you can fire the cannonball with
enough force so that it never touches the
ground.
• Now, what if you hitched a ride?
Orbits
• If you rode the cannonball, odds are you’d feel
like you’re falling down.
• That’s what we call free fall. You’d find
yourself falling alongside the cannonball.
Orbits
• But again, you’d never hit the Earth.
• The cannonball hasn’t escaped Earth’s
gravitational pull, but it’s balanced out by the
speed of the cannonball.
Escape!
• Based on this, there are two ways to escape
Earth’s gravity.
– Get to a really high altitude. Practically, you want
to be less than 100 miles above the Earth; then
friction lessens
– Go fast. REALLY fast. This is called the escape
velocity: