1. Chapter 9 – Universal Gravitation

3. Caused by gravity… Things fall Moon orbits Earth
Keeps people stuck to E
Keeps Earth together
Pulls other stuff toward E
Planets in orbit around sun
Tides
Sun is “burning”
Solar systems, galaxies, moons around planets
Black holes
Everything!!

4. Universal Law of Gravitation
Inverse Square Law
Weight & Weightlessness
Ocean Tides

5. Isaac Newton Gravity extends through the universe
Newton knew inertia, and that if something changed its speed or direction a force must be responsible
Apple falling … apple changed its motion, so a force must be responsible-- Gravity
Noticed the moon, and that it was traveling in circular motion
This also requires a force
….same force was responsible for the Moon as was the apple

6. The Falling Moon- Satellite Motion
Newton realized the moon must be falling or else it would travel away in a straight line
So if it is falling, why is it never getting closer??
hypothesized that moon is just a projectile falling under the influence of gravity.
And it never falls to Earth because of its speed….

7. Newton’s Law of Universal Gravitation
Force of gravity acting between 2 objects is directly proportional to their mass and inversely proportional to the square of the distance between them
m1 and m represents the masses of the two objects involved
d - distance between the center of the two objects
G- Universal Gravitation Constant, value of
G = x Nm2/kg2
F - represents the Force of Gravity between any 2 objects
Remember that Force of Gravity is the same thing as Weight

8. Examples
What is the force of gravity between two 3 kg blocks that are placed 4 meters apart?
How much is the force of gravity from the Earth acting on a 90 Kg man? (Mass of the Earth = 6.0 x 1024 Kg ; radius of the Earth = 6400 km)

9. What this law means
Whatever factor the mass is increased by, Fg is increased by the same amount
Ex. Triple the ‘m’, Fg is also tripled
Whatever factor the ‘d’ between 2 objects is increased by, the force of gravity is multiplied by the inverse of the square of that number
Ex. Triple the distance, force of gravity is 1/9th as much

10. Examples
The force of gravity acting on you while on the surface of the Earth is 100 N.
What would be the force of gravity acting on you if the Earth’s mass was doubled?
Force Directly proportional to mass, So N
What would it be if your mass was doubled and the Earths stayed the same?
What would the force of gravity acting on you be if you were twice as far from the center of the Earth as you are now?
Force is Inversely proportional to the square of the distance, so distance is increased by 2, inverse square of 2 is 1/22 or 1/4th , so force of gravity would be 1/4th as much or N.

11. More examples….
A spaceship with a weight of 10,000 N on the surface of the Earth moves to a distance that is 3 times further away from the center of the Earth, what is the force of gravity on it now?
Distance increased by 3 x , so Fg decreases by the inverse square of this number so Fg goes down by 1/9th ,000/9 = N R
Space ship weighs N here
Space ship weighs 10,000N here

12. Why this happens?? Inverse Square Law… Surface Area of a sphere

14. Gravity… In general “How masses communicate with each other”
Force that exists between any two masses anywhere in the universe
Causes tides, shape of planets, orbits, pressure necessary for stars to burn, falling objects, projectile motion, formation of solar systems, galaxies
More mass…. More gravitational pull
Closer to something… more gravitational pull
Pulling force

15. Weight and Weightlessness
Being weightless
Can’t happen anywhere around the Earth
Would mean there is no gravity acting on you
Even astronauts are not weightless
Feeling weightless
Happens all the time
Astronauts feel weightless
Happens because of a lack of a support force

16. Weight and Weightlessness
Astronauts in orbit are in a continuous free fall
Nothing supporting them so the feel weightless
Gravity still acting though, so not actually weightless

17. Any time you are not being supported by a force equal to your Weight…
Any time you are not being supported by a force equal to your Weight…. You feel weightless
BUT…. Gravity still acts… so not actually weightless

18. Gravitational Fields g= Gm d2
The ‘field’ is the area of space affected by an objects gravity
The further an object is away… the weaker the field
‘g’ (acc of gravity) indicates the strength of a field
The field strength on the surface of the Earth is about 9.8 m/s2 or about 10 m/s2
‘g’ also changes by the inverse square rule
If you are twice as far away from the center of the Earth ‘g’ = (9.8)/4 m/s2
=2.45 m/s2
g= Gm d2

19. Gravity field inside the Earth
According to Newton, the closer you get to an object the stronger gravity is, but if you were travelling to the center of the Earth, all of the mass above you would start to cancel the gravity below you, so as you travel towards the center of earth gravity will become less and less strong
Any tunnel through E will take 42
min to travel through!

20. What if….

21. Earth Shrunk but you stayed same location…??
Force of gravity would be unchanged

22. Earth Shrunk and you stayed on its surface…
Force of gravity would increase

23. Ocean Tides From the Moon
Side of the Earth closest to the moon, has a high tide
As well as the side of earth furthest from the moon
This happens because…
Water flows
There is a large difference in gravitational strength from the moon on either side of the Earth… because of difference in distance from the moon
Gravity from the moon tugs on Earth just a bit
Gravity from moon is of course stronger when moon is close
And weaker when far away
Earth
Earth

24. http://www.youtube.com/watch?feature=fvwp& NR=1&v=u3LtEF9WPt4
k&feature=related :30
Inuit People – Mussel Gathering

26. The Sun also causes Tides
The Sun, like the Moon pulls on Earth, so the side of Earth closest to Sun, receives a high tide from Sun
Tides from the Sun are weaker than from the moon
Why is this?
Sun actually has a lot stronger pull on Earth than the moon does, so why aren’t solar tides larger??
Not that big of a difference in how far the sun is from sunny side compared to dark side
So difference in gravity strength is small
City analogy

28. Tidal Effects… spring tides, Neap Tides

29. Neap Tide – Solar & Lunar tides subtract from each other
Neap Tide – Weak Tide
Spring Tide - Solar & Lunar tides combine
Spring Tide “Super” Tide

30. Gravity is a mutual tug of war
Earth and moon orbit a common point in space
Point is center of gravity of Earth Moon system

32. Perturbations
Small irregularities in the orbit of a planet caused by a close proximity to another planet
Gravity of one planet slightly tugging on another
This is how Neptune was discovered
y/perturbations.html

33. Earth Tides and Atmosphere Tides
Tides don’t just happen with water
Occur w/ the ground
Earth is really just a thin solid crust on top of molten (liquid) rock
Ground rises and lowers small amount depending on moon’s location
and with the atmosphere
Atmosphere has much larger tides than oceans do

34. Einstein’s Theory of Gravitation & Black Holes
Next Chapter

35. Chapter 10
Projectile & Satellite Motion

36. But the ground also curves (Earth is not flat)
Launched projectiles will follow a curved path (see below) until they hit the ground
But the ground also curves (Earth is not flat)
Most projectiles have a curve that are much steeper than the curve of the Earth
BUT, if you throw a projectile fast enough, then curved path of the projectile will match the curve of the Earth
Then, the projectile will never reach the surface and forever be in an orbit
Projectile must also be above the Earth’s atmosphere, so that air resistance does not slow it down

37. Projectile being thrown a different speeds, from the top of a mountain above the atmosphere
If you could throw something as fast as you wanted and there was no air resistance could you make something orbit?/

38. Satellite Motion
Satellite - any object that orbits around another object… includes, planets, moons, man-made satellites, etc.
As discussed before, satellites are just projectiles that fall at the exact same rate that Earth (or another planet) curves away from it… and never reaches the surface

39. The Motion of Planets…
For a long time,most scientists thought all satellites travel in perfectly circular orbits
NOT TRUE
Could not make accurate predictions of their motion
Planets, moons, etc. were not where they were supposed to be!
Planets did not follow these predicted paths
Then…… along came Johannes Kepler

40. Kepler’s 3 Laws of planetary motion
First Law
1) The paths of the planets are ellipses, with the sun at one focus (the other focus is just a point in space)

41. Keppler’s 2nd Law
An Imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. This means planets move faster when they are closer to the sun and slower when they are further away

42. (Ta/Tb)2 =(ra/rb)3 Keppler’s Third Law
The square of the ratio of the periods of any two planets revolving about the sun is equal to the cube of the ratio of their average distances from the sun. Thus, if Ta and Tb are the planets periods, and ra and rb are their average distances from the sun we get
(Ta/Tb)2 =(ra/rb)3

43. Elliptical paths & Kepler
Kepler came up with Three Laws of Satellite Motion
These laws explained that planets & other satellites travel in ellipses (ovals), not circles
When tested Kepler’s laws almost perfectly predicted paths of planets and moons
This means planets are closer to the Sun at some points in their orbit, and farther from the Sun at other points

44. Orbits
Earth’s orbitVery nearly circular, but elliptical like all other planets
Elliptical path of Earth does not affect weather at all
Other planets, like Mercury, have more exaggerated elliptical orbits

45. Conservation of Energy and Satellite motion
Based on the fact that KE + PE always stays constant…..
Planets travel faster when they are closer to the Sun, and slower when they are further away
Slow
Fast

46. Escape Speed
Speed that something needs to travel in order to permanently escape an objects gravitational pull without getting pulled back
Escape speed for the Earth is roughly 7 miles per sec.

47. Einstein & Gravity
Kepler’s predictions of where objects should be were very close but still somewhat off
Albert Einstein actually defined exactly how gravity works and his Theory of General Relativity predicted perfectly the orbits of all planets
General Relativity stated mass warped Space-Time and this warping is what we feel as gravity
Has been tested many times over the past 100 years, and all tests confirm Einstein’s predictions

48. General Relativity
Many consider to be the greatest scientific discovery OF ALL TIME
Will be discussed more next chapter
In short, Gravity is not a force at all and is instead the curvature of space- time around a large mass

49. http://www.zamandayolculuk.com/cetinbal/H TMLdosya1/RelativityFile.htm

50. Black Holes Consequence of General Relativity
Again more on this next Chapter
What they are?
Remnants of a collapsed star
Shrunk to such a small size, that its gravity became infinitely strong…. So strong its escape velocity is faster than the speed of light
One of the most interesting objects in the Universe
Nothing can escape a black hole
Creates an infinitely deep hole in Space-Time,

52. Gravitational Interactions
Chapter 13
Gravitational Interactions

53. Gravity differences on Earth??
-Universal Law of Gravitation tells us if we are closer or further from Center of the Earth gravity will change
-gravity slightly weaker at the top of a tall mountain… ie you weigh less
-other inconsistencies…..
Big Earthquakes change mass distribution of Earth…
2004 Indonesia Earthquake was so big the rate at which the Earth orbits slightly changed

54. Mass of sun = 1.98 x 1030 kg Radius of the Sun = 695,500 km Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Radius (Earth=1)
0.382
0.949 1
0.532
11.209
9.44
4.007
3.883
Radius (km)
2,438
6,052
6,378
3,397
71,400
60,000
25,559
24,764
mass (Earth=1
=5.97 x 1024 kg)
0.055
0.815
0.107
318 95 15 17
mean distance from Sun (AU)
0.39
0.72
1.52
5.20
9.54
19.18
30.06
orbital period (Earth years)
0.24
0.62
1.88
11.86
29.46
84.01
164.8
orbital eccentricity
0.2056
0.0068
0.0167
0.0934
0.0483
0.0560
0.0461
0.0097
mean orbital velocity (km/sec)
47.89
35.03
29.79
24.13
13.06
9.64
6.81
5.43
rotation period (in Earth days)
58.65
-243*
1.03
0.41
0.44
-0.72*
mean temperature at surface (C)
-180 to 430
465
-89 to 58
-82 to 0
-150
-170
-200
-210
gravity at equator (Earth=1)
0.38
0.9
2.64
0.93
0.89
1.12
escape velocity (km/sec)
4.25
10.36
11.18
5.02
59.54
35.49
21.29
23.71
mean density (water=1)
5.25
5.52
3.93
1.33
0.71
1.24
1.67
number of moons 2 63 62 27 13
rings? no
yes
Mass of sun = 1.98 x 1030 kg
Radius of the Sun = 695,500 km