1. Barry Latham Bloom High School Conceptual Physics, Hewitt, 1999.

2. 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

3. 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!

4. 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

5. 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

6. 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=Gm 1 m 2 /r 2  F=force of attraction (N)  m 1 =mass of first object (kg)  m 2 =mass of second object (kg)  r=distance separating centers of m 1 and m 2 (m)  G=gravitational constant (6.67x10 -11 Nm 2 /kg 2 )  Makes the units cancel out correctly

7. 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!

8. 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  6.37x10 6 m

9. 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”

10. Weigh the Earth (without a scale or balance)  Using F g =mg and F=Gm 1 m 2 /r 2 we can find the mass of the Earth!  mg=(m object )(g on Earth)  Gm 1 m 2 /r 2 =(G)(m object )(m Earth )/(r Earth ) 2  Set them equal to each other  (m object )(g on Earth)=(G)(m object )(m Earth )/(r Earth ) 2  Solve for (m Earth )  (r Earth ) 2 (g on Earth)/(G)=(m Earth )  Plug & Chug (scientific calculator needed!)  (r Earth ) 2 (g on Earth)/(G)/=(m Earth )  (6.4x10 6 m) 2 (9.80 m/s 2 )/(G)=(m Earth )  (m Earth )=6.02x10 24 kg  RQ 8-10

11. 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/d 2  If distance doubles, Force decreases by 1/2 2 (or 1/4)  If distance triples, Force decreases by 1/3 2 (or 1/9)

12. Inverse Square & Weight  As distance increases, F decreases  P. 176 (Transparency 20)

13. 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

14. 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