the milky way · understanding orbital motion the universal law of gravity allows us to understand...

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“… the shuttle blasts off … Then comes the tremendous pressure of three G’s and the sudden release into weightlessness as the ship leaves the gravitational field behind…” -from The Arizona Republic

Monday, October 3, 2011

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Quiz #3: WednesdayChp. 2-4

Next homework (due Wednesday)Chp. 5Problems: 1, 2Learning to look: 1, 2


Newton, Einstein, and Gravity

Chapter 5


I. Galileo and Newton A. Galileo and Motion B. Newton and the Laws of Motion C. Mutual GravitationII. Orbital Motion and Tides A. Orbits B. Orbital Velocity C. Calculating Escape Velocity D. Kepler's Laws Re-examined E. Newton's Version of Kepler's Third Law F. Tides and Tidal Forces G. Astronomy After NewtonIII. Einstein and Relativity A. Special Relativity B. The General Theory of Relativity C. Confirmation of the Curvature of Space-Time

Outline


A New Era of Science

Mathematics as a tool for understanding physics


Isaac Newton (1643 - 1727)• Building on the results of Galileo and Kepler

Major achievements:1. Invented Calculus as a necessary tool to solve

mathematical problems related to motion

• Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler

2. Discovered the three laws of motion

3. Discovered the universal law of mutual gravitation


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An object continues in a state of rest or in a state of uniform motion at a constant speed along a straight line unless compelled to change that state by a net force.

Why? Because objects have “inertia”

Newton’s 1st Law of Motion


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Uniform Motion: same speed, same direction

Uniform Motion


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The “tendency” that Newton observed for objects at rest to stay at rest and objects in motion to stay in uniform motion in a straight line.

How do we measure inertia?

MASS

Inertia


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Force


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Net force = sum of all forces:

Here, we say that the NET force is zero!

Force


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Net force = sum of all forces:

Here, we say that the NET force is zero!

The box stays at rest. There is no change in its state of motion – no net force is acting on it.

Force


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The ball moves over my head at a constant speed as shown. Is the ball changing its state of motion? Is there a net force acting on the ball?

a. Yes. Yes. b. No. No.c. Yes. No.d. No. Yese. Yes/Yes if I am moving

my hand back and forth.


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Natural state of motion is at a constant speed, in a straight line.

Ball wants to travel in a straight line, but the string continuously pulls it back toward the center of the circle.

Force and Inertia


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A change in velocity (state of motion)

Refers to an increase in velocity OR a decrease in velocity OR a change in the direction of velocity.

A net force acting on an object will cause that object to accelerate.

Acceleration


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Acceleration: can be a change in speed, either increasing or decreasing.

Acceleration


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Acceleration: can be a change in direction

Acceleration


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The amount of acceleration (a) produced by a force(F) depends on the mass (m) of the object beingaccelerated.

Newton’s 2nd Law of Motion


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The amount of acceleration (a) produced by a force(F) depends on the mass (m) of the object beingaccelerated.

Mathematically:

F = m×a

Alternatively:

a = F/m



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Which of the objects are NOT accelerating?

a) a car traveling at a constant speed around a bend. b) a ball that has been thrown up into the air just before it begins falling back down. c) a car traveling at 65 mph down a straight highway. d) a car getting off the freeway on a straight off-ramp. e) an electron circling around an atomic nucleus.


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Law of Gravitation


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G=6.67×10-11

Law of Gravitation


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Question:A linebacker and a kitten are put into space far from any other object. How do the gravitational forces each feels compare? How do their accelerations compare?a. Linebacker feels larger force, but accelerates less.b. Kitten feels larger force and accelerates more.c. Both feel same force, but kitten accelerates more.


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Example


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The linebacker and the kitten on Earth:

How do the forces that they feel (due to the Earth’s gravity) compare? How do their accelerations compare if they both jump off a table?a. Forces equal, kitten

accelerates more.b. Larger force on

linebacker, accelerations equal.

c. Forces equal, accelerations equal.

Example


Acceleration of Gravity

http://video.google.com/videoplay?docid=6926891572259784994




Acceleration of GravityAcceleration of

gravity is independent of the mass (weight) of the falling object!






gravity is independent of the mass (weight) of the falling object!Iron ball






gravity is independent of the mass (weight) of the falling object!Iron ball Wood ball





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Weight:

Weight is NOT the same as “mass”.

Weight is equivalent to the gravitational force the Earth exerts on your body.

Weight


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Are you weightless on the Moon? a) yes b) no c) depends


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Are you weightless on the Moon? a) yes b) no c) depends

Is there “gravity” on the Moon?


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Weight on Earth, Mars, and Saturn:

Mmars = 0.1 Mearth Rmars = 0.5 Rearth

Weight on other planets


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Weight on Earth, Mars, and Saturn:

Mmars = 0.1 Mearth Rmars = 0.5 Rearth

Msaturn = 95 Mearth Rsaturn = 9.4 Rearth

Weight on other planets


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Are the astronauts orbiting the Earth weightless? a) yes b) no c) depends


Understanding Orbital MotionThe universal law of gravity allows us to understand orbital motion of planets and moons:

• Earth and moon attract each other through gravitation.Example:

Earth

Moon

v v’

F

• Since Earth is much more massive than the moon, the moon’s effect on Earth is small.• Earth’s gravitational force constantly accelerates the moon towards Earth.• This acceleration is constantly changing the moon’s direction of motion, holding it on its almost circular orbit.


Orbital Motion (2)In order to stay on a closed orbit, an object has to be within a certain range of velocities:

Too slow => Object falls back down to Earth

Too fast => Object escapes Earth’s gravity


Geosynchronous Orbits


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What’s wrong with this….

“… the shuttle blasts off … Then comes the tremendous pressure of three G’s and the sudden release into weightlessness as the ship leaves the gravitational field behind…” -from The Arizona Republic


Kepler’s Third Law Explained by Newton



Balancing the force (called “centripetal force”) necessary to keep an object in circular motion

with the gravitational force →

expression equivalent to Kepler’s third law



Balancing the force (called “centripetal force”) necessary to keep an object in circular motion

with the gravitational force →

expression equivalent to Kepler’s third law

Py2 = aAU

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The following questions are offered for additional practice. They are not meant to represent the exact content or type of questions that will be on the quiz. They are also not meant to represent the totality of the information that will be on the quiz.

The lecture notes and their embedded class participation questions should give you a good idea of the content covered in class.


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1. The period of Jupiter's orbit around the sun is approximately 12 years. What is the approximate distance from the sun to Jupiter?a. 144 AUb. 1728 AUc. 42 AUd. 5.2 AUe. 2.3


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2. In pre-Copernican astronomy, it was almost universally believed thata. the planets traveled in elliptical orbits about the Earth.b. the center of the universe was the Sun with the Milky Way representing other distant planets.c. the Sun was at the center of the universe.d. the Earth was at the center of the universe.e. None of the above was believed.


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3. An apparent westward motion of a planet in the sky compared to the background stars (as viewed from the Earth) when observed on successive nights is referred to asa. epicycleb. retrograde motionc. prograde motiond. heliocentric motione. deferent


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4. The purpose of using epicycles and deferents to explain the motion of the planets in the night sky was to account fora. prograde motion.b. Mercury and Venus' limited angular distance from the Sun.c. retrograde motion.d. non-uniform speed of the planets in their orbits.e. precession of the equinoxes.


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5. The greatest inaccuracy in Copernicus' model of the solar system was that the planetsa. travel in circular orbits with uniform motion.b. traveled on epicycles whose centers followed orbits around the Sun.c. traveled in elliptical orbits.d. were allowed to travel backwards in their orbits.e. the planets orbited the Sun.


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6. The orbit of the planet Jupiter is ellipse with the Sun at one focus. What is located at the other focus?a. The asteroid beltb. Earthc. Saturnd. Jupitere. Nothing


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7. Which of the following statements best describes Kelper's 3rd law of planetary motion?a. The smaller the diameter of a planet, the faster its rotational period.b. The orbital period of a planet is directly proportional to the diameter of the planet.c. The smaller the orbit, the longer its orbital period.d. The larger the orbit, the longer its orbital period.


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8. Why did Galileo's observations of moons orbiting Jupiter disagree with the geocentric model of the universe of his time?a. The moons moved in non-circular orbits about Jupiter.b. The moons did not appear to orbit the Sun.c. The moons did not appear to orbit the Earth.d. The moons appeared to be too small, and therefore too far away, to be considered part of the solar system.


1.d2.d3.b4.c5.a6.e7.d8.c

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