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