For Wednesday, Feb. 18

Reading: Section 4.1 (including Math Tools 4.1)

Assignments: Homework #2 (due today)

Homework #3 (due Wed. Feb 23)

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?

The “Asteroid Tugboat”

Thought Question:Which of the following is an example ofconstant velocity?

A. a car speeding up on a straight road

B. a car slowing down on a straight road

C.a car maintaining a steady speed on a straight road

D.a car speeding up on a curved road

E. a car slowing down on a curved road

F. a car maintaining a steady speed on a curved road

Newton’s Laws of Motion

• First Law: An object will maintain a constant velocity if there is no net force acting on it.

• speed: how fast an object’s position changes measured by speedometers, radar guns

• velocity: speed and direction of travel measured by weather vanes

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)

Newton’s Laws of Motion

• Second Law: For an unbalanced force,

a: acceleration (units: )

m: mass (units: kg)

F: force (units: Newton = )

• force: strength and direction of a push or pull any effort that can cause acceleration

MASS REDUCES ACCELERATION

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

Explosion…Bad!

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?

VIEW FROM ABOVE:

A

BC

DE

Orbits are Curved PathsNewton’s First Law says: If object travels on a curved

path, there MUST BE an unbalanced force.

VELOCITY

FORCE

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)

(friction between tires

and road)

TOP VIEW:

VELOCITY

FORCE(gravity)

PATHPATH

Thought Question:The picture below shows the velocity of a planet at different

times in its orbit (larger arrow means larger speed).

Draw the direction of the force on the planet at the different positions shown.

2

3

1For position #3, which combination of these describes the direction the force is acting:A.To the right of the velocity arrowB.To the left of the velocity arrowC.Forward (with the velocity arrow)D.Back (against the velocity arrow)

Enter all that apply.

Ellipse Orbit:SUN’S FORCE TURNS AND SPEEDS PLANET

PLANET’S VELOCITY

PLANET’S VELOCITY

SUN’S FORCE TURNS AND SLOWS PLANET

SUN’S FORCE JUST TURNS PLANET

(ALWAYS TANGENT TO ORBIT)

THE FORCE POINTS TOWARD THE SUN!

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: ROCKET’S FORCE ON GASGAS FORCE ON ROCKET

USA

ICE

SKATER FORCES ON EACH OTHER

Measuring New PlanetsNewton’s Third Law: star moves slightly

as planet orbits

PLANET’S FORCE ON STAR

STAR’S FORCE ON PLANET

“wobble” of star depends on star and planet masses, and size of planet orbit

Thought Questions:A compact car and a large truck collide head-on and

stick together. 1) Which one feels the largest force during the

collision?2) Which one receives the largest acceleration?(Enter both letters of your answers, then hit “Enter”.)

A. The car.

B. The truck.

C. Both experience the same amount.

D. You can’t tell without knowing how fast they were moving before the collision.

Newton’s Third LawForces have equal strength, but accelerations may differ:

MORE MASS, LESS ACCELERATION

BOAT’S FORCE ON MANMAN’S FORCE ON BOAT

FORCEFORCE

For Friday, Feb. 20

Reading: Section 4.2 (including Math Tools 4.2), Appendix 7

Assignments: Homework #3 (due Mon. Feb. 23)

Asteroid Ida (and Dactyl)

54 km

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?

The “Gravity Tractor”

Thought QuestionA 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

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

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.)

USA

A B C

Weight on Planets

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

strength of force is same as if WHOLE mass is distance d = Rplanet away

(radius of planet)

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?

A. The same as on Earth

B. 1/2 (50%) the weight on Earth

C. 2/5ths (40%) the weight on Earth

D. 1/4th (25%) the weight on Earth

E. 1/5th (20%) the weight on Earth

F. 1/10th (10%) the weight on Earth

Your weight will be:

or 40% what it is on Earth

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

Mass in Astronomy.

Center of Mass

center of mass

Center of Mass

“balance point” is closer to more massive object:

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

Dwarf Planet Ceres

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?

center of mass

Example: Earth and MoonThe 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?

Thought Question:For the Earth and the Moon, answer one letter for each of

these:A. More force acts on Earth than MoonB. More force acts on Moon than EarthC. The same amount of force acts on both

center of mass

A. Earth is accelerated more than MoonB. Moon is accelerated more than EarthC. Both are accelerated the same amount

A. Earth moves faster than MoonB. Moon moves faster than EarthC. Both move at the same speed

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:

less massive object accelerates more

Acceleration due to Gravity

At Earth’s surface, force is

Galileo’s Experiment:

which creates an acceleration:

Two different masses dropped at same time hit ground at same time…

equal accelerations!

that doesn’t depend on the mass of the object dropping!

In which of the following situations would it be harder to drive along the curve without skidding out?

A. Slow speed into a sharp turnB. Slow speed into a gentle turnC. High speed into a sharp turnD. High speed into a gentle turn

Thought Question

TOP VIEW:

Acceleration Needed for Circular Path

distance traveled by ball in one circuit (total change in position during orbit)

“distance” traveled by tip of velocity arrow during one circuit

(total change to velocity arrow during orbit caused by the acceleration)

Circular Orbit SpeedIf gravity is providing the acceleration to keep something on a circular path:

mass of object pulling (NOT the one orbiting)

distance between objects (usually radius of orbit)

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

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

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