1. Instructions for PowerPoint
Copy into your notebook (or if you don’t have that with you on a separate sheet of paper)
the stuff in BLUE

2. Universal Gravitation
Circular Motion
Universal Gravitation

3. What we know… What is uniform circular motion?
How do you define centripetal acceleration?
What is the difference between a centripetal and centrifugal force

4. What we want to know… What is Newton’s Law of Universal Gravitation?
How does distance affect gravitational force between two objects?
What is weight and how can something appear weightless?
What are Kepler’s Laws of Planetary Motion?

5. Gravity
The force that causes an apple to fall to the ground is the same force that holds the planets in orbit.

6. Projectile Motion Gravity causes an object to fall
Orbit occurs when velocity is such that the projectile’s path is parallel to the surface
This is true when centripetal force equals the force of gravity…
 However, the force of gravity is not the same everywhere

7. Tides Gravity from moon cause high and low tides.
Pull of moon’s gravity stronger.
Water pools. High tide.
Water pulled away. Low tide M
Earth A B
Pull of Earth’s gravity stronger.
Water pools. High tide.
Flow of water
Water pulled away. Low tide

8. Tides
High Tide
Low Tide
Around a 10 m difference

9. Newton’s Law of Universal Gravitation
Gravitational Force
depends on the distance between two masses
depends on the mass of the objects
Mathematically… d M1 m2
G= the gravitational constant
= 6.67 x Nm2/kg2
r = distance between the
center of each mass.

10. Gravity All objects that have mass have gravity.
Small dense objects can have as much or more gravity than larger hollow objects.
*Black holes can have a size 4 times the size of our sun but a pull of gravity millions times stronger

11. Gravity has no range limit- copy down graph to the left
Gravity follows the inverse square law..
Force of gravity is inversely related to the square of the distance
Gravity has no range limit- copy down graph to the left

12. Weight Weight is the measure of the force of gravity. Apparent Weight
Weight = mass x acceleration of gravity
Weight varies depending on location
Apparent Weight
Depending on the forces acting on an object, the perceived weight of the object may change.
“How heavy an object appears to be”

13. G force People have experienced various levels of “g-forces”.
1 g is normal weight. 3 g’s means a person feels they weigh 3 times their normal weight.
46.2 g’s by John Stapp on a rocket sled. (for science)
180 g’s involuntarily by a formula one racer who crashed into a wall (173 km/hr to 0 in 66 cm)

14. Fun Facts (around town)
Desperado (at Buffalo Bill’s- near CA state line) reaches 4 Gs
El Loco (at Circus Circus) reaches a 1.5 Gs
Canyon Blaster (at Adventure Dome) reaches 3.5 Gs
Astronauts feel 3.5 Gs in space during take-off
Most people pass out above 5 Gs!

15. Planetary Motion
Originally believed that the Earth was the center of the Universe. Everything including the planets and sun revolved around us.
Copernicus ( ): proposed that the Earth and other planets revolved around the Sun in perfect circles (heliocentric)
Did not match up with the new precise observations made by Tycho Brahe ( ).

16. Kepler’s Laws of Planetary Motion
Johannes Kepler ( ): reconciled the Copernican model with Brahe’s observations. Developed 3 laws of planetary motion.

17. Kepler’s 1st Law
Planets travel in an elliptical orbit around the sun, and the sun is at one of the focal points.
Sun

18. Kepler’s 2nd Law
An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals.
Planets travel faster when they are closer to the sun.
Δt1
Sun A1 A2
Δt2

19. Practice worksheet

20. Try this…in your notebook
Given G = 6.67 x Nm2/kg2, the mass of the earth is 5.98 x 1024 kg, and the radius of the earth is 6.37 x 106 m, what is the force of gravity between the Earth and a 9 kg apple?
Remember… the gravitational force is actually the object’s weight.
Fg= Weight = mg
“g” only equals 9.81 on Earth
_____
Fg = G
M1m2 r²

21. Gravity on the Moon M1m2 _____ mag = G r² ag = gmoon M1 ___ ag = G r²
What is the acceleration of gravity on the moon, given the Moon’s mass is 7.35 x 1022 kg and the radius of the moon is 1.74 x 106 m?
_____
mag = G
M1m2 r²
ag = gmoon
___
ag = G M1 r²

22. Kepler’s 3rd Law T² is proportional to r³ 4π² T² = r³ Gm
The square of a planet’s orbital period is proportional to the cube of the average distance between the planet and the sun.
T² is proportional to r³
T² = r³
4π² Gm

23. Try it (in your notebook) Gravity on Mars
Lance Fortnight has a total mass of 140 kg when he lands on Mars. Mars has a mass of 6.42x1023 kg, and a mean radius of 3.40x106 m.
Find Mars’ acceleration of gravity. (gM)
Find the force of gravity between Lance and Mars. (Fg)
3.7 m/s2
518 N

24. Try it…in your notebook
Lance Fortnight has a total mass of 140 kg when he lands on Mars. Mars has a mass of 6.42x1023 kg, and a mean radius of 3.40x106 m.
Find Mars’ acceleration of gravity. (gM)
Find the force of gravity between Lance and Mars. (Fg)
Buzz Miles has a mass of 140 kg too, but an apparent weight of 480 N. How far from Mars’ center is he?
3.7 m/s2
518 N
m away