1. Making Sense of the Universe Understanding Gravity and Motion

2. Astronomical Motion Planets move along curved (elliptical) orbits
Speed & direction are constantly changing
Is a force present?
Yes!

3. Gravity is that force!

4. Gravity gives Universe its structure
Universal attractive force that causes all objects to pull on all other objects everywhere
Holds Moon in orbit around Earth
Holds Earth in orbit around Sun
Sun in orbit around Milky Way
Milky Way in path within Local Group of galaxies

5. Sir Isaac Newton Invented reflecting telescope Invented calculus
Connected gravity & planetary forces
Philosophiae naturalis principia mathematica

6. Universal Laws of Motion
“If I have seen farther than others, it is because I have stood on the shoulders of giants.”
Sir Isaac Newton (1642 – 1727)
Physicist

8. How do we describe motion?
Speed: Rate at which object moves
speed of 10 meters/second = 10 m/s
speed of 22 miles/hour = 22 mph
Velocity: Speed and direction
10 m/s, due east
22 mph down Hesperian Blvd.
Basic vocabulary of motion. Emphasize that turning, slowing, and speeding up are all examples of acceleration.

9. How do we describe motion?
Velocity: Speed and direction
10 m/s, due east
Acceleration: Any change in velocity; either in direction, magnitude, or both
Basic vocabulary of motion. Emphasize that turning, slowing, and speeding up are all examples of acceleration.

10. The Acceleration of Gravity
As objects fall, they move faster & faster.
They accelerate.

11. The Acceleration of Gravity
Acceleration from gravity is constant near Earth’s surface
Falling speed increases by 10 meters/second each second

12. The Acceleration of Gravity
g = ~10 meters/sec/sec
g = ~22 miles/hour/sec

13. The Acceleration of Gravity
Falling from rest…
after 1 second, moving 10 m/s (about 22 mph)
after 2 seconds, moving 20 m/s (about 44 mph)

14. The Acceleration of Gravity
Acceleration from gravity is constant FOR ALL OBJECTS near Earth’s surface
Why don’t heavier things fall faster than lighter ones???

15. Acceleration of Gravity (g)
Galileo demonstrated g same for all objects, regardless of mass!
Heavier objects (with more mass) must be pulled more to accelerate at same rate.
And Gravity indeed pulls more on heavier objects!

16. How is mass different from weight?
Mass = amount of matter in an object (protons, neutrons, electrons)
Weight = force from gravity that acts upon an object from another mass

17. Question: On the Moon….? your weight is the same, your mass is less.
your weight is less, your mass is the same.
your weight is more, your mass is the same.
your weight is more, your mass is less.

18. Question: On the Moon…. your weight is the same, your mass is less.
your weight is less, your mass is the same.
your weight is more, your mass is the same.
your weight is more, your mass is less.

19. Newton’s Laws of Motion1
A body at rest or in motion at a constant speed
along a straight line
remains in that state of rest or motion
unless acted upon by an outside force.

20. Newton’s 1st Law
Planets orbit stars stay in motion, but are continually being pulled in their orbit by the star.
Rockets heading to the moon or Mars, once launched, can coast along a straight line.

21. Newton’s 2nd Law of Motion

22. Newton’s 2nd Law
The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it, but is inversely proportional to the body’s mass.
F = m a
Launch a rocket – as fuel is used up, mass decreases, and rocket accelerates even faster!
“Staging” rockets is even smarter!

23. Thought Question Is there a net force for each of the following?
A car coming to a stop.
A bus speeding up.
An elevator moving up at constant speed.
A bicycle going around a curve.
A moon orbiting Jupiter.
Use to check if students can figure out where a net force is acting. For bonus questions, ask if they can identify the forces.

24. Thought Question Is there a net force for each of the following?
A car coming to a stop. Yes
A bus speeding up. Yes
An elevator moving up at constant speed. No
A bicycle going around a curve. Yes
A moon orbiting Jupiter. Yes
Use to check if students can figure out where a net force is acting. For bonus questions, ask if they can identify the forces.

25. Newton’s 3rd Law of Motion

26. Newton’s 3rd Law
For every applied force, a force of equal size but opposite direction arises.
As rocket exhaust pushes backwards, the rocket itself moves forwards
As Earth pulls on the Moon, the Moon pulls on Earth

27. Universal Law of Gravitation
Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

28. Universal Law of Gravitation
Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

29. Law of Gravity
Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.
Gravity is ONLY attractive!
There is no “anti-gravity”

30. Gravity
Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.
What kind of Mass?
It doesn’t matter !
What shape, size, temperature, state?
It doesn’t matter!!

31. Why are astronauts weightless in space?
There is no gravity in space.
The force of gravity is much less.
The moon is pulling astronauts in the other direction.
The Earth’s magnetic field holds them up.
They are massless.

32. Why are astronauts weightless in space?
There is no gravity in space.
The force of gravity is much less.
The moon is pulling astronauts in the other direction.
The Earth’s magnetic field holds them up.
They are massless.

33. Why are astronauts weightless in space?
There is no gravity in space.
The force of gravity is much less.
The moon is pulling astronauts in the other direction.
The Earth’s magnetic field holds them up.
They are massless.
Gravity IS pulling them towards Earth.
They ARE falling!

34. Why are astronauts weightless in space?
There is gravity in space!
Gravity is always attractive!
They *have* to be coming towards Earth!
Weightlessness is due to a constant state of free-fall.

35. How can they ORBIT?

36. How can they ORBIT? As spacecraft fall, they also move sideways fast
At 350+ miles above Earth:
Falling towards Earth continuously, but…
Moving SIDEWAYS at 17,000 miles per hour
Orbits are continuous falling “around” Earth!

37. Illustrating Gravity with Tides
Why are there two high tides each day?
Why are tides on Earth caused primarily by the Moon rather than by the Sun?
Why is Earth’s rotation gradually slowing down?
Why does the Moon always show the same face to Earth?

38. Tides
Gravitational force decreases with (distance)2,

39. Tides
Since gravitational force decreases with (distance)2, the Moon’s attractive pull on Earth is strongest on the side closer to the Moon & weakest on the opposite side.

40. Tides

41. Tides Earth gets stretched along the Earth-Moon line.
Oceans rise relative to land at these points.

42. Tides - Observations
Every place on Earth passes through these points, called high tides, twice per day as the Earth rotates.
SF Bay Tide Tables

43. Tides - Observations High tides occur every 12 hours… plus!
Average difference between high tides = 12 hours and 25 minutes
Why not exactly 12 hours?
The Moon moves!

44. Tides - Observations
Tides are tied to the phases of the moon

45. Tides - Observations High tides occur every 12 hours 25minutes
the Moon moves!
The Sun’s tidal effect on Earth is not as strong
About ½ as large as the Moon
But when BOTH stretch in the same direction, even larger tides!

46. Tides - Observations
Tides are tied to the phases of the moon

47. “Spring” Tides
When Sun & Moon pull in the same direction (new & full phases)
high tide is HIGHER than usual

48. “KING” Tides
When Sun & Moon pull in the same direction (new & full phases)
AND…
Earth is closest to the Sun (January!)
high tide is HIGHER than usual

49. Spring Tides in Miami

50. Spring Tides in California

51. Spring Tides in California

52. “Neap” Tides
When Sun & Moon pull at right angles (first & last quarter phases)
high tide is LOWER than usual

53. Tidal Friction Reaction between Moon’s pull & Earth’s rotation.
Earth’s rotation slows down (1 sec every 50,000 yrs.)
Moon moves farther away from Earth.

54. Where’s the PROOF? Stromatolites!
Earth’s rotation slows down

55. Synchronous Rotation
When rotation period of a moon, planet, or star equals its orbital period about another object.
Tidal friction on the Moon (caused by Earth) has slowed its rotation down to 1 month.
The Moon now rotates synchronously.
We always see the same side of the Moon.

56. Orbital Paths
Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths.
possible orbital paths
ellipse (bound)
parabola (unbound)
hyperbola (unbound)

57. Newton’s Version of Kepler’s Third Law
Using calculus, Newton was able to derive Kepler’s Third Law from his own Law of Gravity.
In its most general form:
P2 = 42 a3 / G (m1 + m2)
If you can measure the orbital period of two objects (P) and the distance between them (a), then you can calculate the sum of the masses of both objects (m1 + m2).

58. Changing Orbits
orbital energy = kinetic energy + gravitational potential energy
conservation of energy implies orbits can’t change spontaneously
An object can’t crash into a planet unless its orbit takes it there.

59. Changing Orbits
An orbit can only change if it gains/loses energy from another object, such as a gravitational encounter
If an object gains enough energy so that its new orbit is “unbound” it has reached escape velocity.

60. Changing Orbits
We can use the gravitational pull of planets to “slingshot” spacecraft to other parts of the solar system!
“Gravitational Assist” cuts travel time to outer solar system by years!