1. Chapter 9
Gravity
The
Earth
Sucks

2. 1. THE UNIVERSAL LAW OF GRAVITY
From Law 3 of Kepler, Newton deduced the inverse square law of attraction.
Newton compared the fall of the moon to the falling of an apple.
Moon's fall from straight line is (0.05 in/s).

3. Newton's Law of Universal Gravitationm1 m2 r

4. 2. The Universal Gravitational Constant, G

5. 3. Gravity and Distance: The Inverse-Square Law
Gravity is the most dominant force in nature.
Yet it is the weakest.

6. Let’s look at the inverse-square nature for the force of gravity.
4 units
1 unit
3 units
2 units
Let’s look at the inverse-square nature for the force of gravity.

7. 4. WEIGHT AND WEIGHTLESSNESS
W = mg (the gravitational force acting on m)
Weighing on an elevator and
Weighing in outer space or in orbit
We define the weight of something as the force it exerts against the supporting floor or the weighing scale. (Remember the elevator video.)

8. 5. OCEAN TIDES demo - Earth-moon system
Force of gravity decreases with distance from moon.
Moon
Earth

9. Differences in gravity on different parts of the Earth produce tidal bulges.
North Pole
High Tides

10. Should expect two high tides, two low tides per day.
Moon moves in its orbit so that it returns to the same place in your sky every 24h 50 m.
Sun has one-half the influence of the moon
The gravitational force is greater but tides depend on the gravitation difference on opposite sides of the Earth.

11. Sun
Moon
SFA

12. Spring Tides
First Quarter
Sun
Earth
Full Moon
New Moon
SFA

13. Neap Tides
First Quarter
Sun
Earth
Last Quarter
SFA

14. Complications Bay of Fundi Friction with ocean bottom
Irregular shape of continents
Bay of Fundi
Tides can come in very fast and exceed 15 m.
SFA

15. Tides in the Earth and Atmosphere
Tides in ionosphere produce electric currents and alter the magnetic field.
Affects penetration of cosmic rays
Can have effects on living things
Tides in the crust mean that volcanoes and earthquakes are more common at new or full moon.
SFA

16. Tides on the Moon
Just as the earth has “land tides” the moon has moon tides.
Because the moon always keeps the same face toward the earth, the moon tides are always in the same place.
SFA

17. 6. GRAVITATIONAL FIELDS Alternate view of gravitational influence
Properties of space surrounding object are changed so that another mass entering the region experiences a force.
Earth
SFA

18. Objects accelerate in the direction of the arrows.
Earth
Objects accelerate in the direction of the arrows.
Field is stronger where lines are closer together.
SFA

19. The Gravitational Field Inside a Planet
Inside the Planet
a = g
a = ½g
a = 0
a = ½g
a = g
SFA

20. Gravitational Field Uniform Sphere Hollow Sphere
Linear inside - like Earth outside
Hollow Sphere
Zero inside - like Earth outside
SFA

21. 7. EINSTEIN'S THEORY OF GRAVITATION
Warped Space
SFA

22. Bending of Starlight Sun Eye SFA
Apparent position of star in this direction
Light from star bent by the gravity of the Sun
Sun
Eye
SFA

23. 8. BLACK HOLES
Let’s observe a star that is shrinking but whose mass is remaining the same.
What happens to the force acting on an indestructible mass at the surface of the star?
What effect is there on the escape velocity?
SFA

24. which means the force is 64 times larger
Remember that the force between
the two masses is given by R2 F R R2 F R R R R2 F
SFA
which means the force is 64 times larger

25. Particles entering it would suffer disintegration.
If a massive star shrinks enough so that the escape velocity is equal to or greater than the speed of light, then it has become a black hole.
Particles entering it would suffer disintegration.
How are black holes detected?
SFA

26. 9. UNIVERSAL GRAVITATION
Earth is a "sphere" because of gravitation.
The universal law of gravitation was a great accomplishment.
Its accuracy is phenomenal.
Perturbations in planet's orbits
Examples:
Neptune was discovered because of Uranus's wobble.
Pluto was discovered in a similar way.
Oscillating universe. Wow!

27. Chapter 9 Review Questions

28. If somehow the moon were moved to a distance twice as far away from the earth as it is now, the force that the earth has for the moon would
(a) be twice what it is now
(b) be one half of what it is now
(c) be four times greater than it is now
(d) be one fourth as much as it is now
(d) be one fourth as much as it is now

29. What must be the phase of the moon if neap tides are occurring?
(a) first quarter
(a) first quarter
(b) full
(c) lunar eclipse
(d) new

30. Newton said that the path of a planet curves because a force acts on it. Why does a planet's path curve according to Einstein?
(a) because a force acts on it
(b) because it is spinning
(c) because it is in a geometric warp of space and time
(c) because it is in a geometric warp of space and time