1. G r a v i t y
Chapter 9

2. Isaac Newton ( )

3. Newton’s Universal Gravitation
Two masses separated by a distance M m d

4. Newton’s Universal Gravitation

5. Newton’s Universal Gravitation
Inverse Square Law
Separation Force
R F
2R ¼F
3R /9F
½R F
¼R F

6. Newton’s Universal Gravitation
The force of gravity cannot be made zero.
Mass causes gravity
Only one kind of mass
Contrast with the electric force
G is small
6.67 X N m2/kg2

7. Apparent Weightlessness
All objects fall at the same rate in a gravitational field.
Apparent weightlessness
Lack supporting force
Examples:
Space Shuttle
Elevator
Amusement Park Rides

8. KC-135

9. Ocean Tides
Gravity decreases with distance
Moon
Earth

10. Ocean Tides
Differences in gravity on different parts of the Earth produce tidal bulges
Low Tide
High Tide
High Tide
Low Tide

11. Ocean Tides 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

12. Ocean Tides
Spring Tide
Full or New Moon
Sun
Earth
New Moon
Full Moon

13. Ocean Tides Neap Tide First or Last Quarter Moon Sun Earth
First Quarter
Sun
Earth
Last Quarter

14. Ocean Tides Complications Bay of Fundy (Video)
Friction with ocean bottom
Irregular shape of continents
Bay of Fundy (Video)
Tides can come in very fast and exceed 15 m

15. Crustal & Atmospheric Tides
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
Measured for the moon

16. Gravitational Field Alternate view of gravitational influence
Properties of space surrounding object are changed so that another mass entering the region experiences a force.
Earth

17. Gravitational Field Objects accelerate in the direction of the arrows
Field is stronger where field lines are closer together

18. Gravitational Field
Inside the Planet
a = g
a = ½g
a = 0

19. Gravitational Field Uniform Sphere Hollow Sphere Linear inside
like Earth outside
Hollow Sphere
Zero inside g
Distance R
Distance g R

20. Distortion caused by mass
Space-Time
No mass
Distortion caused by mass

21. General Relativity Mass distorts space-time
Objects move in the straightest path they can in the distortions caused by mass

22. Advance of Mercury’s Perihelion

23. Bending of Starlight Sun Apparent position of the star
Light from star bent by the gravity of the Sun
Sun

24. Very small amount of bending
Low Gravity
Very small amount of bending

25. Light at an angle is bent noticeably
Stronger Gravity
Light at an angle is bent noticeably

26. Exit Cone and Photon Sphere

27. Near a Black Hole

28. Schwarzschild Black Hole
Event Horizon Rs
Rs = 3(Mass)
Mass Rs
3 M km
Singularity +

29. What Can We Know? Mass Charge Rotation Rate gravity Electric Fields
Co-rotation

30. Cygnus X-1

31. Edwin Hubble

32. Red Shift and Distance 24 Mpc 1200 km/s 300 Mpc 15,000 km/s 780 Mpc

33. Hubble’s Result

34. Modern Hubble’s Law

35. Raisin Cake Model 1 2 3 1 2 3

36. Raisin Cake Model Distance Distance Velocity from Home from Home
(before baking) (afterbaking)
cm cm
cm cm
cm cm
Velocity
1 cm/hr
2 cm/hr
3 cm/hr
Velocity
Distance

37. Universal Expansion Space-Time itself is expanding
Carries galaxies along with it
Conflicting cosmologies
Big Bang
Draw the expansion back in time until space-time occupies a point ( billion years ago)
Steady State
Requires continual creation of matter

38. Arno Penzias & Robert Wilson