1. For Wednesday, Feb. 18 Reading: Section 4.1 (including Math Tools 4.1)
Assignments: Homework #2 (due today)
Homework #3 (due Wed. Feb 23)

2. The “Asteroid Tugboat”
spacecraft lands and fires rocket to push asteroid
what direction will the asteroid go?
what if the asteroid is spinning?
how far in advance of a collision do we need to start?
discussion about why the deflection helps? how long? (about a year); talk about _turning_ asteroid
Strongman plane pull:

3. Thought Question: Which of the following is an example of
constant velocity?
a car speeding up on a straight road
a car slowing down on a straight road
a car maintaining a steady speed on a straight road
a car speeding up on a curved road
a car slowing down on a curved road
a car maintaining a steady speed on a curved road
Answer: C.

4. Newton’s Laws of Motion
speed: how fast an object’s position changes
measured by speedometers, radar guns
velocity: speed and direction of travel
measured by weather vanes
First Law: An object will maintain a constant velocity if there is no net force acting on it.
EMPHASIZE are trying to get to understanding of orbits; WENT TOO LONG FOR ONE CLASS
VELOCITY

5. Newton’s Laws of Motion
acceleration: how fast velocity changes
3 ways to accelerate a car:
 GAS PEDAL (change speed)
 BRAKE PEDAL
 STEERING WHEEL (change direction)
Mass resists acceleration

6. Newton’s Laws of Motion
force: strength and direction of a push or pull
any effort that can cause acceleration
Second Law: For an unbalanced force,
a: acceleration (units: )
m: mass (units: kg)
F: force (units: Newton = )
MASS REDUCES ACCELERATION
discuss meaning of the equation; EMPHASIZE UNITS; SHOW how units work out right; force to hold up a hamburger patty against gravity
Mass resists acceleration

7. Explosion…Bad! trying to blow up a BIG asteroid is not a great idea…
… even a big explosion wouldn’t accelerate it much  Newton’s Second Law
… fragments would keep moving in mostly the same direction  Newton’s First Law
mention “Deep Impact”, “Armageddon”; asteroid has much momentum
Move something the size of Texas? What does an A bomb do to Texas?

8. Thought Question:
A ball is attached to a string and swung in a circular path above my head. At the point shown below, I suddenly release the string. If this is viewed from directly above, which of the paths below would the ball most closely follow when released? D E C B
Answer: B. (100%) A
VIEW FROM ABOVE:

9. Orbits are Curved Paths
Newton’s First Law says: If object travels on a curved path, there MUST BE an unbalanced force.
FORCE
TOP VIEW:
(friction between tires and road)
VELOCITY
VELOCITY
FORCE
(gravity)
PATH
PATH
example: ball on string WITHOUT initial speed… just comes toward me
Luposlipaphobia?
Speed skating wipeouts
ALSO standing on a rotating planet
Newton’s Second Law says: object accelerates (turns) in direction of unbalanced force
 force is NOT pushing planet forward
 force IS pulling toward inside of orbit (toward Sun)
Video

10. Thought Question:
The picture below shows the velocity of a planet at different times in its orbit (larger arrow means larger speed). 2
Draw the direction of the force on the planet at the different positions shown. 1
For position #3, which combination of these describes the direction the force is acting:
To the right of the velocity arrow
To the left of the velocity arrow
Forward (with the velocity arrow)
Back (against the velocity arrow)
Enter all that apply.
Answer: AD; see next slide (33%) 3

11. Ellipse Orbit: PLANET’S VELOCITY (ALWAYS TANGENT TO ORBIT)
SUN’S FORCE TURNS AND SPEEDS PLANET
SUN’S FORCE JUST TURNS PLANET
SUN’S FORCE TURNS AND SLOWS PLANET
By changing net force on object, we can change its orbit
PLANET’S VELOCITY
THE FORCE POINTS TOWARD THE SUN!

12. Newton’s Laws of Motion
Third Law: When one object exerts a force on a second object, second object exerts an equal and opposite force back on the first.
EXAMPLES:
GAS FORCE ON ROCKET
ROCKET’S FORCE ON GAS
USA
(water propelled car)
(video with CO2 cannister)
Person on skateboard/person on rolling chair?
SKATER FORCES ON EACH OTHER
ICE

13. Measuring New Planets
Newton’s Third Law: star moves slightly as planet orbits
“wobble” of star depends on star and planet masses, and size of planet orbit
PLANET’S FORCE ON STAR
STAR’S FORCE ON PLANET
include some extrasolar planet diagrams?

14. Thought Questions:
A compact car and a large truck collide head-on and stick together.
Which one feels the largest force during the collision?
Which one receives the largest acceleration?
(Enter both letters of your answers, then hit “Enter”.)
The car.
The truck.
Both experience the same amount.
You can’t tell without knowing how fast they were moving before the collision.
Answer: 1) C. 2) A. (#1 high %; #2 split with D; just do #1?)

15. Forces have equal strength, but accelerations may differ:
Newton’s Third Law
Forces have equal strength, but accelerations may differ:
MAN’S FORCE ON BOAT
BOAT’S FORCE ON MAN
FORCE
MORE MASS, LESS ACCELERATION
stand on skateboard/push on wall

16. For Friday, Feb. 20
Reading: Section 4.2 (including Math Tools 4.2), Appendix 7
Assignments: Homework #3 (due Mon. Feb. 23)

17. Asteroid Ida (and Dactyl)
54 km
Ida and Dactyl
Dactyl about 1km across (first discovered to orbit another asteroid)

18. The “Gravity Tractor” satellite uses rocket to hover near asteroid
What direction will the satellite pull the asteroid?
How long would it take to deflect the asteroid enough?
discussion about why the deflection helps? how long? (about a year)
Less effort required if done further in advance

19. Thought Question
A hypothetical planet system has planets in equally-spaced circular orbits. The planet masses are given in terms of the mass of the innermost planet. Which of the planets exerts the greatest gravitational force on the star? A. B. C. D.
16 M
4 AU
10 M
3 AU
3 M
2 AU
1 M
1 AU
Answer: B (%)

20. Universal Gravitation
Fg: force
m1, m2: masses
d: distance between centers of objects
G: universal gravitational constant
attractive force: always pulls masses together
equal strength forces pull on both masses
EMPHASIZE UNITS, give examples of sizes of forces

21. Thought Question:
At which positions does a rocket feel a greater gravitational force from Earth than from the Moon? Earth is about 80 times more massive than the Moon. (There may be more than one answer.) A B C
USA
Answer: AB (low on first trial)

22. Weight on Planets  
(radius of planet)
strength of force is same as if WHOLE mass is distance d = Rplanet away
More mass to exert force/farther from more of the weight
do Mars as an example?
planet’s gravity is made up of pulls from every bit of its mass…
The bigger the planet, the farther you are from most of the mass

23. Thought Question:
An astronaut goes on the first mission to Mars. Mars has a mass that is only about 1/10th the mass of Earth, and it is ½ the size. How will the astronaut’s weight on Mars compare to their weight on Earth?
The same as on Earth
1/2 (50%) the weight on Earth
2/5ths (40%) the weight on Earth
1/4th (25%) the weight on Earth
1/5th (20%) the weight on Earth
1/10th (10%) the weight on Earth
Your weight will be:
or 40% what it is on Earth
Answer: C.

24. Mass in Astronomy Moon: 7  1022 kg 1/80th Earth Earth: 6  1024 kg
Jupiter: 2  1027 kg
300 Earth
Sun: 2  1030 kg
1000 Jupiter
300,000 Earth .
Emphasize having a feeling for mass scale
Hid Moon under black rectangle

25. Center of Mass center of mass
examples: extrasolar planets, interplanetary travel, parent swinging kid in circle
Center-of-mass is actually at focus of ellipse orbits - not necessarily other star

26. Center of Mass “balance point” is closer to more massive object:

27. For Monday, Feb. 23 Reading: Review Section 4.2 (and Math Tools 4.3)
Assignments: Homework #3 (due Mon. Feb. 23)
QUIZ #2 is NEXT FRIDAY

28. Dwarf Planet Ceres orbit insertion in early March 2015
about 1% Moon’s mass

29. Thought Question:
If two stars are orbiting each other (and star 1 is more massive than star 2), how does the distance of the center of mass from star 1 (r1) compare to the total separation A?
Answer: C
must be a fraction of the total distance between stars
must be closer to the larger mass
center of mass

30. Example: Earth and Moon
The Earth has about 80 times the mass of the Moon, and the distance to the Moon is about 60 Earth radii. How far is the center of mass from the center of Earth?
center of mass?
TOO HARD AS A TQ WITHOUT MORE EXPLANATION…
Answer: about 60 / 81 of an Earth radius (or about 0.75 Earth radii – it is inside Earth)
Requires a little extra algebra… (total distance is 81 times distance of Earth from center of mass)
Which of planets cause Sun to wobble most?

31. Thought Question:
For the Earth and the Moon, answer one letter for each of these:
More force acts on Earth than Moon
More force acts on Moon than Earth
The same amount of force acts on both
Earth is accelerated more than Moon
Moon is accelerated more than Earth
Both are accelerated the same amount
Earth moves faster than Moon
Moon moves faster than Earth
Both move at the same speed
Answer: CBB
center of mass

32. Center of Mass
If center of mass is to remain between two moving objects, less massive object must move faster in exact opposite direction
From Newton’s 3rd Law:
Conservation of momentum
less massive object accelerates more

33. Acceleration due to Gravity
Galileo’s Experiment:
Two different masses dropped at same time hit ground at same time…
 equal accelerations!
At Earth’s surface, force is
emphasize distance to center of Earth; calculate g
which creates an acceleration:
that doesn’t depend on the mass of the object dropping!

34. Thought Question
In which of the following situations would it be harder to drive along the curve without skidding out?
TOP VIEW:
Slow speed into a sharp turn
Slow speed into a gentle turn
High speed into a sharp turn
High speed into a gentle turn
Answer: C.

35. Acceleration Needed for Circular Path
“distance” traveled by tip of velocity arrow during one circuit
Derivations of centripetal acceleration (under white rectangle)
This is what is NEEDED to stay moving in a circle - it is NOT REQUIRED though!
distance traveled by ball in one circuit (total change in position during orbit)
(total change to velocity arrow during orbit caused by the acceleration)

36. Circular Orbit Speed
If gravity is providing the acceleration to keep something on a circular path:
DERIVATION OF CIRCULAR SPEED - set a_c = g
moon orbit example
mass of object pulling (NOT the one orbiting)
distance between objects (usually radius of orbit)

37. Derivation of Newton’s form of Kepler’s third law for a circle

38. General Form of Kepler’s Third Law
Mtotal: total amount of mass involved (example: star plus planet)
applies to any elliptical orbit
applies to any pair of orbiting masses (Sun + planet; Earth + satellite; Jupiter + moon;…)
AN ASTRONOMER’S MAIN WAY TO DETERMINE MASS!
…just need orbital period and average orbital distance
do a full calculation of something using this; period for something orbiting Earth

39. Forms of Kepler’s Third Law
applies to any pair of orbiting masses (Sun + planet; Earth + satellite; Jupiter + moon; star + star; …)
one object might not dominate mass Mtot (like Pluto + Charon)
make sure units work out!
only applies to objects orbiting Sun
meant to be used with units of yrs and AU

40. Measuring Planet Orbits
Can measure size of planet’s orbit (A) if:
measure P from star’s wobble
determine M for star from its light (and as long as Mplanet << Mstar)
PLANET’S FORCE ON STAR
STAR’S FORCE ON PLANET
Explain “<<“