1. Law of Universal Gravitation
Or Is gravity responsible for people falling in love?
Content Standards:
1e the relationship between the universal law of gravitation and the force of gravity on an object at the surface of the Earth.
1m* how to solve problems involving the forces between two masses at a distance.

2. The Law of Universal Gravitation
Any two massive bodies in the universe are attracted to each other.
Force is always attractive
3rd Law still holds
Fgravity =G msource mtest / d2
This equation is always true, W=mg only true near surface of planet
Action at a distance force (influence extends beyond object)
Question: State the law of universal gravitation verbally and mathematically. In which direction is the force of gravity between two objects?
When is this formula used and when is W=mg used?
Activities:
State law verbally and then write equation on board. Define each variable.
Show pictures illustrating clumping of matter in globular cluster and galaxy arms
Point out that W=mg also gives us gravitational force on object but this is an approximation only true near the surface of a planet
Point out that gravity is an action at a distance force meaning the force extends beyond the object that is causing it. Another way to think of it is that the object changes the space around it so that all masses in that space feel a force. How this happens we don’t know.

3. Check Question 1
The Earth and Moon exert gravitational forces on one another. How do the force on and accelerations of the Moon and Earth compare?
a) The force and acceleration are greater for the Moon
b) The force is the same, the acceleration is greater for the Moon
c) The force is greater on the Moon, the acceleration is the same
d) The force and acceleration are greater for the Earth

4. Newton’s Discovery Gravity is a universal force
Showed Moon and apple fall proportional distances indicating same force is acting (1/60 x 1/60 x 5 m = m = 1.4 mm each second)
Needs to be a force on Moon because otherwise it would fly off in straight line
Same force acts between planets, stars, and galaxies
Accounts for spherical shape of planets and stars
Question: What did Newton discover about gravity? How did he discover it? How did Newton know there was a force on the Moon? In which direction is this force?
Activities:
Discuss how they knew about gravity before Newton, cavemen called it Uhhh.
Newton knew there was a force on the moon because otherwise it would travel in a straight line according to his first law of motion. State that Moon is falling below this straight line path all the time as it circles the Earth. The force must be towards the center of the Earth to account for the circular motion of the Moon and is due to the gravitational force of the Earth changing the direction of the Moon’s tangential speed. In other words, the Moon does not fall into the Earth because it has a sideways velocity.
Describe how Newton mathematically showed that an apple on Earth and the Moon fell at rates proportional to their distances from the Earth (1 earth radius and 60 earth radii respectively). Discuss how gravity should become dispersed as move away from earth.
State that now similar calculations are performed on planets, stars and galaxies and they also experience gravity. In fact spherical shape of

5. The Universal Gravitational Constant (G)
6.67 x N m2 /kg2
Stays same no matter
What planet you are on
Your altitude above the planet
If you in outer space
Difficult to measure
Cavendish’s torsion balance
Small size indicates gravity is a relatively weak force
What does G measure? What is the numerical value of the universal gravitational constant ? How is this constant different from the acceleration of gravity? How is G measured? Is gravity a relatively weak or strong force?
Activities:
1) Reveal slide line by line.
2) state that G differs from little g in that it does not vary with altitude, or the planet you’re on. Also g measures how fast you fall compared to how space-time is curved?
3) Show Physical Science laser disk Chp. 37 to demonstrate two ways to find G. Point out that masse, distances and force must be known to find G.
4) Negative 11 exponent indicates rather small numbers for the force of gravity. However its power is that it never will decease to zero with distance.
torsion balance in garage

6. The Inverse Square Law
Force varies as inverse square because force’s effect spreads out in both the vertical and horizontal directions.
Butter Gun Video and Analogy
Force never goes to zero
Other phenomenon that follow this include light brightness, and electric force
An astronaut has a weight of 400 N on the surface of the Earth. What will the astronaut weigh if she moves outward so he is twice as far from the center of the Earth? How about if she moves three times as far? If she continues to move outward, will her weight ever decrease to zero?
Activities:
1) Refer once again to formula and show inverse square relationship.
2) Ask why and go through butter gun analogy
3) Relate thickness of butter to amount gravity pulls on object. Gravity waves spread out as well.
4) Note that force never reaches zero
5) Use apple Qs. and find weight 2, 3 and 4 times the Earth’s radius.
Butter Gun Video

7. Check Question 2
Two bodies have a gravitational force between them of 10 N. What would be the new gravitational force between the bodies if both bodies were doubled in mass and the distance between them cut to 1/3 the original amount?
40 N d) 360 N
90 N e) none of these
120 N

8. Uses of the Formula: Perturbations
Perturbations are wobbles in an astronomical bodies motion due to the gravity from another body.
Resulted in discovery of
Neptune and Pluto
Charon, Hydra and Nix (New moon 2011)
extra-solar planets (1235 candidates by Kepler as of 2011)

9. Uses of the Formula: Birth and End of the Universe
Universe started with Big Bang
galaxies are moving away from us
Further galaxies are moving faster
Fate of Universe
Universes expansion is increasing with time (2011 Nobel Prize)
Universe will eventually suffer heat death
Question: What do the perturbations of the following indicate the presence?: A) Uranus B) Neptune C) Pluto D) Stars E) Galaxies? According to astronomers, how did the universe begin? What will determine how it will end?
Activities:
1) Define perturbation as a wobble in a planet’s path caused by the gravitational pull of another body.
2) Go through the listed perturbations and the discoveries they lead to
Uranus=>Neptune Neptune=>Pluto
Pluto=>Charon Stars=> Planets (over 100 known now)
Galaxies=> dark matter (more prevalent than light matter)
3) Use slides to define big bang and crunch.
4) Use balloon analogy to explain how explosion would explain observation that all bodies are moving away from us, and the further they are the greater their speed.
5) Distinguish between open and closed universe and part that gravity plays
6) Discuss new discoveries of quintesscence or dark energy and fact that universe seems to be speeding up with time
7) State we truthfully don’t know the fate of the universe.

10. Uses of the Formula: What is the Universe Made Of?
4% Normal Matter (protons, neutrons, electrons and atoms)
23% Dark Matter
Does not emit light
Produces gravity
Unknown material
73% Dark Energy
Responsible for accelerating expansion