ASTR  1010-­‐004  Spring  2010  -­‐-­‐  Score  Report  for  Quiz  1 "Smallest"  version  of  test First  row:  your  answers,  A  =  1,  B  =  2,  C  =  3,  D  =  4,  E  =  5 Second  row:  BLANK  =  RIGHT,  *  =  WRONG,  @  =  OMITTED,  #  =  MULTIPLE The  number  at  right  is  the  number  of  incorrect  answers.    STUDENT  A                                      3341524233  2413554453                                                          *        **  **  ****  **  *      12

About Quiz 1

The average was very low, only 11.3 out of 20.

Many scores were low enough to suggest randomguessing.

Distribution of Quiz 1 Scores

Score

Num

ber o

f Stu

dent

s

5 10 15 20

05

1015

Makeup for extra credit, up to 2 points

For up to 4 of the questions you missed:

• Look up or figure out the correct answer

• Write a sentence or two explaining what you didwrong

• Turn it in by 7:35 PM Monday, Feb. 8

• Printed, handwritten, or email OK

• If your submission is acceptable, the points will beadded to your score on this test.

Kepler’s Laws of Planetary MotionFirst: what is meant by a physical law

• Description of what happens in nature under specifiedconditions, according to experience

• Written in such a way as to be always correct

• Correctly predicts future events under similar conditions

Kepler’s laws2 describe the planets’ motions as an observerlocated far from the ecliptic plane would see them

More detailed than Copernicus’s description

They are2See chapter 3

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1. The orbit of each planet is an ellipse with the Sun at onefocus

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• The other focus is empty

• For the major planets, the ellipses are very nearlycircular

• This means that the planets’ distances from the Sunchange slightly during the course of their orbital motion

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2. Each planet moves faster when closer to the Sun andslower when farther away [a paraphrase; the original lawspecifies the change in speed more precisely]

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3. Planets with small orbits (closer to Sun) move faster thanplanets with big orbits do [another paraphrase]

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• The original law relates the time to go around once(the period of the orbit) to each planet’s distance fromthe Sun

• Compare Earth and Mars, for example. If they movedat the same speed, Earth would take less time thanMars to go around the Sun because Earth’s orbit issmaller in circumference.

• Kepler’s 3rd Law implies: But the time needed forEarth to go around the sun is disproportionately short,so its speed in its orbit must be greater.

Review: Explore the Solar System in Voyager SkyGazer

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Kepler’s laws can also be worded so they apply to objectsother than the Sun and planets.

• Jupiter and its moons

• Earth, the Moon, artificial satellites

• Planets in orbit around other stars (exoplanets)

• Binary stars

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MotionOur goal: understand orbital motion in general

Newton’s laws explain Kepler’s laws in terms of the behaviorof all moving objects

Basic definitions

Position

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Speed Rate of change of position, without regard todirection (see speedometer)

Velocity Rate of change of position; incorporates direction(see compass)

After a left turn, car’s velocity has changed even if its speedhas not

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Acceleration Rate of change of velocity: speed and/ordirection

Your car speeds up: forward acceleration

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Car slows down: backward acceleration

Note: car continues to move forward.

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Car driving around a circular track at constant speed

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The car’s acceleration is always directed toward the centerof the circle while its velocity is directed along a tangentto the circle.

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Force An identifiable, physical mechanism that can act on anobject and tend to cause acceleration

• Example: friction, a contact force that opposes motion,causing moving objects to slow down

Mass Two alternative definitions

• An object’s resistance to acceleration or its inertia(o�cial definition)

• Quantity of matter contained in an object; in detail,the total mass of all the protons, neutrons, andelectrons in the object(more user-friendly definition)

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Example: a car.

• Its mass is not the same as its volume.

• If the car were squashed flat with no material lost, itsmass would be unchanged.

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Newton’s Laws of Motion

1. In the absence of an applied net force, an object moves atconstant velocity.

Two equal and opposite forces acting on an objectsimultaneously will have no net e↵ect, therefore will causeno acceleration.

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2. A force applied to an object causes the object to undergoan acceleration that is

(a) in the same direction as the force

(b) proportional to the force

(c) inversely proportional to the object’s mass

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This means that

• If you push on an object, the object will move in thedirection in which you push, provided no other forceacts on it.

• The stronger the push, the greater the object’sacceleration.

• In order to bring about a given acceleration, it takes astronger push on a large mass than on a small mass.

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3. If agent A exerts a force on agent B, then B also exertsan equal and opposite force on A (law of action andreaction).

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Newton’s law of gravityGravity (or gravitation) is an example of a force.

Every object exerts a gravitational force on every other objectas follows:

Direction Along a line between their centers; attractive

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Amount For most purposes, it is enough to know that: theforce is smaller, the greater the distance.

(Forces are smaller than before)

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Amount Proportional to masses of both

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Falling objects near Earth’s surfaceA dropped object falls toward the center of the Earth,gradually picking up speed.

Rate of increase of speedis acceleration of gravity.It does depend on themass of the planet.Example: acceleration ofobject dropped on Moonis 1/6 that on Earth.

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Doesn’t depend on the mass of the falling object

On airless Moon, leaf andlead brick reach ground atsame time.

But the force of gravity onthe falling object does dependon its mass.

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An apple tossed straightupward slows down, comes torest for an instant

From then on, motion is sameas if dropped from rest

Acceleration is directed towardthe center of the Earththroughout.

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