1. 3.3 Kepler’s Three Laws of Planetary Motion

2. Warm-up
What keeps earth moving the way it does?(ie, why is it moving forward in a circle)

3. Kepler’s Laws of Planetary Motions
1. Planets move in elliptical orbits with the sun at one of the foci
Vocab:
Foci – 2 points that are equidistant from center on major axis. In a circle, it is in the center
Ellipse – an oval
Perigee – closest point in orbit
Apogee – farthest point in orbit
SUN

4. 2. Law of Areas
Line from the sun to a planet sweeps with equal areas in equal time. A planet will move through equal area of space in an equal amount of time
Perihelion – closest to sun
Ahelion – farthest from sun
When a planet is in perihelion its orbital velocity increases (Moves faster)
When a planet is in aphelion its orbital velocity decreases (Moves slower)

5. Closer to the sun, faster the velocity because of the gravitational pull.
Farthest from sun
Closest to sun
Slower Velocity
Faster Velocity
Greater Gravitational Pull

6. 3. Law of Periods - The farther a planet is from the focus, the longer the period of revolution.
Ex: Earth is closer to the sun than Jupiter, therefore the Earth has a shorter period of revolution.
Vocab:
Revolution = orbit around another object
Rotation = spin on its axis

8. Gravity! Defined as the force of attraction between two objects
Does not require contact
Affected by mass and distance
NOT A ONE-WAY STREET!

11. Mass is not weight! Mass is the amount of atoms in a substance
Density is mass per volume
Weight is the measurement of the force of gravity on an object

13. Planetary orbits – why don’t’ they ‘fall in the well’?
Velocity vs gravity
When balanced it creates an orbit!

14. Not a one way street!
Two objects orbit a common point – the center of the two masses
Much of the time one object is so large, the ‘orbit’ is not noticeable (Sun and Earth)

16. Newton’s Law of Gravity
The force of attraction between any two objects depends on their masses and the distance between them.
Thus, the closer the objects, the ______________ the gravitational pull
Thus, the bigger the object the __________ the gravitational pull
greater
greater

17. Closer to the sun in the winter, farther from sun in summer

18. SIDE NOTE
The seasons are NOT caused by how close or far from the sun we are!
Caused instead by how direct the light is with Earth’s tilt

19. Check Your Understanding
Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is doubled, what is the new force of attraction between the two objects?
Answer: F = 4 units
If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (22). The new force is then 1/4 of the original 16 units.
F = (16 units ) / 4 = 4 units

20. Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is reduced in half, then what is the new force of attraction between the two objects?
Answer: F = 64 units
If the distance is decreased by a factor of 2, then force will be increased by a factor of 4 (22). The new force is then 4 times the original 16 units.
F = (16 units) • 4 = 64 units

21. Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects remained the same, then what would be the new force of attraction between the two objects?
Answer: F = 64 units
If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). The new force is then 4 times the original 16 units.
F = (16 units ) • 4 = 64 units

22. Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects?
Answer: F = 16 units
If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). But this affect is offset by the doubling of the distance. Doubling the distance would cause the force to be decreased by a factor of 4 (22); the result is that there is no net affect on force.
F = (16 units) • 4 / 4 = 16 units

23. Challenge!
Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was tripled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects?
Answer: F = 36 units
If each mass is increased by a factor of 3, then force will be increased by a factor of 9 (3*3). But this affect is partly offset by the doubling of the distance. Doubling the distance would cause the force to be decreased by a factor of 4 (22). the net affect on force is that it increased by 9/4.
F = (16 units) * 9 / 4 = 36 units

24. Challenge!
Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of object 1 was doubled, and if the distance between the objects was tripled, then what would be the new force of attraction between the two objects?
Answer: F = 3.56 units
If the mass of one object is doubled. then the force of attraction will be doubled as well. But this affect is more than offset by the tripling of the separation distance. Tripling the distance would cause the force to be decreased by a factor of 9 (32). The net affect on force is that it decreased by a factor of 2/9.
F = (16 units) • 2 / 9 = 3.56 units