1. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

2. 4.1 Describing Motion Our goals for learning:
How do we describe motion?
How is mass different from weight?

3. How do we describe motion?
Precise definitions to describe motion:
Speed: Rate at which object moves
example: speed of 10 m/s
Velocity: Speed and direction
example: 10 m/s, due east
Acceleration: Any change in velocity units of speed/time (m/s2)
Basic vocabulary of motion. Emphasize that turning, slowing, and speeding up are all examples of acceleration.

4. Free Fall
Free fall is the condition of an object that is only acted upon by gravity.
A stone dropped off the side of a cliff is in the state of free fall once it is released.
All falling objects accelerate at the same rate (not counting friction of air resistance).
Apollo 15 Demonstration

5. Uniform Acceleration
All objects in free fall experience uniform, or a constant rate of acceleration.
Near the surface of the Earth, the rate of acceleration is close to 10 m/s2 in the downward direction.
At 10 m/s2 the speed of an object would increase by 10 m/s for every second the object is in free fall. a a

6. Uniform Acceleration
How does the speed change over time when a = 10 m/s2? a
a = 10 m/s2
Time (s)
Speed (m/s)
1.0
10.0
2.0
20.0
3.0
30.0
4.0
40.0
5.0
50.0
Speed increases ≈ 10 m/s with each second of falling.

7. Uniform Acceleration How far would an object travel if a = 10 m/s2?
Time (s)
Distance (m)
1.0
5.0
2.0
20.0
3.0
45.0
4.0
80.0
125.0

8. The Acceleration of Gravity (g)
Galileo showed that g is the same for all falling objects, regardless of their mass.
When you show this video clip, be sure to point out what is going on since it is not easy to see…
Apollo 15 demonstration

9. How did Newton change our view of the universe?
Realized the same physical laws that operate on Earth also operate in the heavens
one universe
Discovered laws of motion and gravity
Much more: Experiments with light; first reflecting telescope, calculus…
Sir Isaac Newton ( )

10. The Motion of Objects
Before Newton: during the 17th Century, Galileo was the first to suggest that objects have a natural tendency to resist a change in motion.
The reason that objects do not continue to move is because of the force of friction.
Without friction, an object would continue to move in a straight line at a constant speed indefinitely.

11. What is Inertia? Galileo coined the term inertia. He said that:
All matter consists of inertia.
Inertia is a measure of an object’s resistance to change in motion.
An object’s mass is a measure of an object’s inertia: the more massive the more inertia.
More massive objects are more resistant to changes in motion.

12. Definition: The Law of Inertia
The Law of Inertia and Newton’s 1st Law of Motion are one and the same.
An object in motion will remain in motion (in a straight line at constant speed), and
An object at rest will remain at rest.
Unless acted upon by an unbalanced external force.

13. Newton’s First Law of Motion
Describe the command module’s motion in terms of Newton’s 1st Law of Motion.
The command module will continue in a straight path unless an external force acts on it.
What forces?
From the engine
Gravity from Earth or the moon
You may wish to discuss the examples in the book on p

14. How do Forces Act on Objects?
A force can cause an object to speed up (accelerate).
A force can cause an object to slow down (accelerate negatively).
A force can cause an object to change direction.

15. Thought Question#1 Is there a net force? Y/N
A car coming to a stop.
A bus speeding up.
An elevator moving at constant speed.
A bicycle going around a curve.
A moon orbiting Jupiter. Y N

16. Thought Question#2 Is a force required to keep an object in motion? No
While a force is required to put an object into motion, any additional force may cause it to speed up or slow down, or change direction.

17. Newton’s 2nd Law The Relationship Between Force and Mass
Newton determined that the acceleration of an object is directly proportional to the force applied to move it and inversely proportional to the mass of the object.
What does this mean?
As mass increases and the force is held constant, the rate of acceleration will decrease.
As the amount of force is increased while keeping the mass constant, the acceleration will increase.

18. Newton’s 2nd Law
Newton’s 2nd Law in relation to the acceleration of objects
a = F/m
Direct Relationship
Inverse Relationship
Acceleration
Force
Acceleration
Mass
Slope = mass
More Force = More Acceleration
More Mass = Less Acceleration

19. What have we learned? How do we describe motion?
Speed = distance / time
Speed & direction => velocity
Change in velocity => acceleration
Force causes change in velocity, producing acceleration

20. How is mass different from weight?
Mass – the amount of matter in an object
Weight – the force that acts upon an object due to gravity
Note: You are weightless in free-fall!

21. Thought Question #3 On the Moon:
My weight is the same, my mass is less.
My weight is less, my mass is the same.
My weight is more, my mass is the same.
My weight is more, my mass is less.

22. Why are astronauts weightless in space?
Does gravity exist in space?
Yes
Then why does an astronaut experience weightlessness?
It is because they are in a constant state of free-fall

23. What have we learned? How is mass different from weight?
Mass = quantity of matter
Weight = force acting on mass
Objects are weightless in free-fall

24. Newton’s Third Law of Motion:
For every force, there is always an equal and opposite reaction force.

25. Interaction Pairs
All forces exist in pairs (no isolated forces) that are opposite in direction and equal in magnitude (size).
When you kick a ball, you exert a force on the ball while the ball exerts a force on you.
You pull on a door to open it while the door exerts a force on you.
A hammer exerts a force on a nail while the nail exerts a force on the hammer.
When you pull on a rope, it pulls on you.

26. Do the forces cancel each other out?
No.
Since the forces act on different objects, it is not possible for them to cancel each other out.
Ff = mfaf
Fp = mpap
Force of floor on person.
Force of person on floor.

27. Newton’s 3rd Law of Motion & Acceleration
Newton’s 3rd Law of Motion says that
-F1 = F2
And Newton’s 2nd Law of Motion says that
m1a1 = m2a2
While the forces may be equal but opposite in direction, the accelerations of each object may be different. F2 F1

28. Example: Newton’s 3rd Law of Motion
A physics student is pulling on a rope, which in both cases causes the scale to read 500 Newtons. The physics student is pulling
a. with more force when the rope is attached to the wall.
b. with more force when the rope is attached to the elephant.
c. the same force in each case.

29. Thought Question #4 Is the force the Earth exerts on you larger, smaller, or the same force you exert on it?
Earth exerts a larger force on you.
I exert a larger force on Earth.
Earth and I exert equal and opposite forces on each other.

30. Thought Question #5
The Earth and moon are attracted to one another by a gravitational force. Which one attracts with a greater force? Why?
Neither. They both exert a force on each other that is equal and opposite in accordance with Newton’s 3rd Law of Motion.
Fmoon on Earth
FEarth on moon

31. Thought Question #6 A compact car and a Mack truck have a head-on collision. Are the following true or false?
The force of the car on the truck is equal and opposite to the force of the truck on the car.
The change of velocity of the car is the same as the change of velocity of the truck. T F

32. What have we learned? How did Newton change our view of the universe?
He discovered laws of motion & gravitation
He realized these same laws of physics were identical in the universe and on Earth
What are Newton’s Three Laws of Motion?
1. Object moves at constant velocity if no net force is acting.
2. Force = mass  acceleration
3. For every force there is an equal and opposite reaction force

33. 4.4 The Universal Law of Gravitation
Our goals for learning:
What determines the strength of gravity?
How does Newton’s law of gravity extend Kepler’s laws?

34. Gravity
What is it?
The force of attraction between all masses in the universe.

35. What determines the strength of gravity?
The Universal Law of Gravitation:
Every mass attracts every other mass.
Attraction is directly proportional to the product of their masses.
Attraction is inversely proportional to the square of the distance between their centers.

36. The Effects of Mass and Distance on Fg

37. The Inverse Square Relationship
As the distance between two objects increases, the gravitational force decreases by 1/r2.
If the distance between two objects is doubled, the gravitational force will decrease by 4 x.
If the distance between two objects is halved, the gravitational force will increase by 4 x.

38. The Inverse Square Relationship What it Looks Like
rE = 6380 km
Shuttle orbit
(400 km)
g = 8.65
Geosynchronous Orbit
(36,000 km)
g = 0.23

39. The Cavendish Experiment

40. How does Newton’s law of gravity extend Kepler’s laws?
Kepler’s first two laws apply to all orbiting objects, not just planets
Ellipses are not the only orbital paths. Orbits can be:
Bound (ellipses)
Not enough speed to escape
Unbound
Parabola
Just enough speed to escape
Hyperbola
More than enough speed to escape

41. Why do all objects fall at the same rate?
The gravitational acceleration of an object like a rock does not depend on its mass because Mrock in the equation for acceleration cancels Mrock in the equation for gravitational force
This “coincidence” was not understood until Einstein’s general theory of relativity.

42. Newton and Kepler’s Third Law
His laws of gravity and motion showed that the relationship between the orbital period and average orbital distance of a system tells us the total mass of the system.
Examples:
Earth’s orbital period (1 year) and average distance (1 AU) tell us the Sun’s mass.
Orbital period and distance of a satellite from Earth tell us Earth’s mass.
Orbital period and distance of a moon of Jupiter tell us Jupiter’s mass.
Emphasize that this law allows us to measure the masses of distant objects — an incredibly powerful tool.

43. Newton’s Version of Kepler’s Third Law
p = orbital period
a=average orbital distance (between centers)
(M1 + M2) = sum of object masses
Optional: use this slide if you wish to introduce the equation for Newton’s version of Kepler’s third law.

44. What have we learned? What determines the strength of gravity?
Directly proportional to the product of the masses (M x m)
Inversely proportional to the square of the separation
How does Newton’s law of gravity allow us to extend Kepler’s laws?
Applies to other objects, not just planets.
Includes unbound orbit shapes: parabola, hyperbola
Can be used to measure mass of orbiting systems.

45. 4.5 Orbits, Tides, and the Acceleration of Gravity
Our goals for learning:
How do gravity and energy together allow us to understand orbits?
How does gravity cause tides?
Why do all objects fall at the same rate?

46. How do gravity and energy together allow us to understand orbits?
More gravitational energy;
Less kinetic energy
Total orbital energy (gravitational + kinetic) stays constant if there is no external force
Orbits cannot change spontaneously.
The concept of orbital energy is important to understanding orbits.
Less gravitational energy;
More kinetic energy
Total orbital energy stays constant

47. Changing an Orbit
So what can make an object gain or lose orbital energy?
Friction or atmospheric drag
A gravitational encounter.
Examples worth mentioning:
satellites in low-Earth orbit crashing to Earth due to energy loss to friction with atmosphere
captured moons like Phobos/Deimos or many moons of Jupiter: not easy to capture, and must have happened when an extended atmosphere or gas cloud allowed enough friction for the asteroid to lose significant energy.
Gravitational encounters have affected comets like Halley’s; also used by spacecraft to boost orbits…

48. Escape Velocity
If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit)
Escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr)
Can use this to discuss how adding velocity can make a spacecraft move to a higher orbit or ultimately to escape on an unbound orbit.

49. Use this tool from the Orbits and Kepler’s laws tutorial to discuss escape velocity.

50. Escape and orbital velocities don’t depend on the mass of the cannonball

51. How do I calculate escape velocity?
What is the Earth’s escape velocity?
What is the moon’s escape velocity?
For a mass the size of Earth, what radius is required for the escape velocity to be greater than light?
Use this figure to explain the origin of the tidal bulges.
Gravitational pull decreases with (distance)2, the Moon’s pull on Earth is strongest on the side facing the Moon, weakest on the opposite side.
The Earth gets stretched along the Earth-Moon line.
The oceans rise relative to land at these points.

52. How does gravity cause tides?
Use this figure to explain the origin of the tidal bulges.
Gravitational pull decreases with (distance)2, the Moon’s pull on Earth is strongest on the side facing the Moon, weakest on the opposite side.
The Earth gets stretched along the Earth-Moon line.
The oceans rise relative to land at these points.
Moon’s gravity pulls harder on near side of Earth than on far side
Difference in Moon’s gravitational pull stretches Earth

53. Tides and Phases
Size of tides depends on phase of Moon

54. Tidal Friction
Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth).
Moon once orbited faster (or slower); tidal friction caused it to “lock” in synchronous rotation.
Optional special topic. You might wish to perform the demonstration shown in the figure…

55. What have we learned?
How do gravity and energy together allow us to understand orbits?
Change in total energy is needed to change orbit
Add enough energy (escape velocity) and object leaves
How does gravity cause tides?
Moon’s gravity stretches Earth and its oceans.
Why do all objects fall at the same rate?
Mass of object in Newton’s second law exactly cancels mass in law of gravitation.

56. 4.3 Conservation Laws in Astronomy:
Our goals for learning:
Why do objects move at constant velocity if no force acts on them?
What keeps a planet rotating and orbiting the Sun?
Where do objects get their energy?

57. Conservation of Momentum
The total momentum of interacting objects cannot change unless an external force is acting on them
Interacting objects exchange momentum through equal and opposite forces
You may wish to discuss the examples given in the text on p. 79

58. What keeps a planet rotating and orbiting the Sun?
You may wish to go over this figure in some detail to be sure the idea is clear.

59. Conservation of Angular Momentum
angular momentum = mass x velocity x radius
The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it
Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely
You may wish to discuss the examples given in the text on p. 79

60. Angular momentum conservation also explains why objects rotate faster as they shrink in radius:
Discuss astronomical analogs: disks of galaxies, disks in which planets form, accretion disks…

61. Where do objects get their energy?
Energy makes matter move.
Energy is conserved, but it can:
Transfer from one object to another
Change in form
Begin by defining energy…

62. Basic Types of Energy Kinetic (motion) Radiative (light)
Stored or potential
Energy can change type but cannot be destroyed.

63. Thermal Energy: the collective kinetic energy of many particles (for example, in a rock, in air, in water)
Thermal energy is related to temperature but it is NOT the same.
Temperature is the average kinetic energy of the many particles in a substance.
Students sometimes get confused when we’ve said there are 3 basic types of energy (kinetic, potential, radiative) and then start talking about subtypes, so be sure they understand that we are now dealing with subcategories.

64. Temperature Scales
Use this figure to review temperature scales.

65. temperature AND density Example:
Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on
temperature AND density
Example:
We’ve found this example of the oven and boiling water to be effective in explaining the difference between temperature and thermal energy. You may then wish to discuss other examples. You might also want to note that the temperature in low-Earth orbit is actually quite high, but astronauts get cold because of the low density.

66. Gravitational Potential Energy
On Earth, depends on:
object’s mass (m)
strength of gravity (g)
distance object could potentially fall
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

67. Gravitational Potential Energy
In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts.
A contracting cloud converts gravitational potential energy to thermal energy.
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.

68. E = mc2 Mass-Energy Mass itself is a form of potential energy
A small amount of mass can release a great deal of energy
Concentrated energy can spontaneously turn into particles (for example, in particle accelerators)

69. Galileo’s Experiment hi hf
Note: hi = hf
What does it mean?

70. What have we learned?
Why do objects move at constant velocity if no force acts on them?
Conservation of momentum
What keeps a planet rotating and orbiting the Sun?
Conservation of angular momentum
Where do objects get their energy?
Conservation of energy: energy cannot be created or destroyed but only transformed from one type to another.
Energy comes in three basic types: kinetic, potential, radiative.

71. Conservation of Energy
Energy can be neither created nor destroyed.
It can change form or be exchanged between objects.
The total energy content of the Universe was determined in the Big Bang and remains the same today.
You might wish to go through the example tracing the energy of a baseball back through time, as described on p. 90 of the text.

72. 4.2 Newton’s Laws of Motion
Our goals for learning:
How did Newton change our view of the universe?
What are Newton’s three laws of motion?

73. Momentum and Force Momentum = mass  velocity
A net force changes momentum, which generally means an acceleration (change in velocity)
Rotational momentum of a spinning or orbiting object is known as angular momentum

74. Center of Mass
Because of momentum conservation, orbiting objects orbit around their center of mass
We next discuss 2 subcategories of potential energy that are important in astronomy: gravitational potential energy (this and next slide) and mass-energy.