Ch 12: Universal Gravitation
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Transcript Ch 12: Universal Gravitation
Barry Latham
Bloom High School
Conceptual Physics, Hewitt, 1999.
CH 12: UNIVERSAL
GRAVITATION
12.1: The Falling Apple
Newton is credited with the idea of the falling apple
to prove gravity.
Probably never happened.
If no outside forces are present, an object continues
on a straight line path forever.
Inertia!
What keeps the Moon in orbit then?
RQ 1-2
12.2: The Falling Moon
The Moon really is falling
toward the Earth!
We just keep getting out of the
way!
If we fire a cannonball from
Earth, we get the same results.
Image: Fire a cannonball with
faster and faster velocities.
Faster velocities mean that the
cannonball will farther and farther.
Eventually it will go all the way
around!
Tangential Velocity
Tangent- “perpendicular to”
Gravity tries to pull the Moon toward the Earth, the
tangential velocity keeps it from crashing into us
The only difference that matters for the apple vs. Moon
is the distance from the Earth.
If the Moon is 60 times further away than an apple at
1s… (Transparency 19, p. 170)
The apple will fall 4.9m in the first second
The Moon will only fall 1.4mm
RQ 3-6
12.3: The Falling Earth
The Moon is “falling” toward the Earth
The Earth is then “falling” toward the Sun
Why don’t we crash into the Sun?
RQ 7
12.4: Newton’s Law of Universal
Gravitation
Universal Gravitation: Everything is gravitationally
attracted to everything else!
F=ma
Only for local objects or those in an independent frame of
reference
F=Gm1m2/r2
F=force of attraction (N)
m1=mass of first object (kg)
m2=mass of second object (kg)
r=distance separating centers of m1 and m2 (m)
G=gravitational constant (6.67x10-11 Nm2/kg2)
Makes the units cancel out correctly
Measurement of G
“G” was measured by
Cavendish 150 years
AFTER Newton
“discovered” gravity
Device measured a
small twist in a quartz
wire due to attraction
between two Pb
spheres
A small value of G
means that gravity is
very weak!
Scientific Notation Review
Scientific notation is needed when working with F
because the numbers are SO big!
6.67x10-11 is way easier to write than
0.0000000000667 every single time.
The equatorial radius of the Earth is 6,370,000 m
Keep dividing by 10 until you get to the one’s place
Use the number of 10’s as your exponent
6.37x106 m
One billion examples
Meters: Earth-Moon distance
Kilograms: mass of Earth’s oceans
Seconds: 31.7 years (Mr. Latham in 09/2008)
Minutes: 1903 years
Years ago: no Humans on Earth
People: Population of China
Atoms: enough to make the dot on a printed “i”
Weigh the Earth
(without a scale or balance)
Using Fg=mg and F=Gm1m2/r2 we can find the mass of the Earth!
mg=(mobject)(g on Earth)
Gm1m2/r2 =(G)(mobject)(mEarth)/(rEarth)2
Set them equal to each other
(mobject)(g on Earth)=(G)(mobject)(mEarth)/(rEarth)2
Solve for (mEarth)
(rEarth)2(g on Earth)/(G)=(mEarth)
Plug & Chug (scientific calculator needed!)
(rEarth)2(g on Earth)/(G)/=(mEarth)
(6.4x106 m)2(9.80 m/s2)/(G)=(mEarth)
(mEarth)=6.02x1024 kg
RQ 8-10
12.5: Gravity & Distance:
The Inverse Square Law
The quantity varies as the inverse square of the
distance, keeping masses constant (p. 175)
F≈1/d2
If distance doubles, Force decreases by 1/22 (or 1/4)
If distance triples, Force decreases by 1/32 (or 1/9)
Inverse Square & Weight
As distance increases, F decreases
P. 176 (Transparency 20)
CD 12-1 worksheet
Inverse Square Law
1. Complete the areas and thicknesses
2. Complete the areas
3. How does depth perception help us? Mislead us?
RQ 11-12
12.6: Universal Gravitation
Applications
Most celestial objects are a sphere because gravity
pulls equally in all direction.
Because all objects also pull on each other, the
planets change their orbits when they come close
enough to each other
Perturbation
Uranus displayed perturbations
Neptune was calculated to exist before it was seen
Pluto was also calculated to exist before it was seen
RQ 13-14