Chapter 5

Circular Motion; Gravitation

1. Explain Kepler's laws of planetary motion.2. Use Kepler's third law to solve word problems involving planetary motion.3. Use Newton's second law of motion, the universal law of gravitation, and the concept of centripetal acceleration to derive Kepler's third law.4. Solve word problems related to Kepler's third law.5. Identify the four forces that exist in nature.

Objectives

5-9 Kepler’s Laws and Newton's Synthesis

Kepler’s laws describe planetary motion.

1. The orbit of each planet is an ellipse, with the Sun at one focus.

Kepler’s first law

• planet’s orbit the Sun in ellipses, with the Sun at one focus.

• the eccentricity of the ellipse, e, tells you how elongated it is.

• e=0 is a circle, e<1 for all ellipses

e=0.02 e=0.4 e=0.7

5-9 Kepler’s Laws and Newton's Synthesis

2. An imaginary line drawn from each planet to the Sun sweeps out equal areas in equal times.

Kepler’s second law

• The line joining the Sun and a planet sweeps out equal areas in equal time intervals.

• As a result, planets move fastest when they are near the Sun (perihelion) and slowest when they are far from the Sun (aphelion).

If it sweeps out equal areas in equal times, does it travel faster or slower when it is far from the Sun?

If is sweeps out equal areas in equal times, does it travel faster or slower when far from the Sun?

If is sweeps out equal areas in equal times, does it travel faster or slower when far from the Sun?

Same Areas

5-9 Planets, Kepler’s Laws, the Moon,and Newton’s Synthesis

The ratio of the square of a planet’s orbital period is proportional to the cube of its mean distance from the Sun.

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Kepler’s Third Law

• Period of a planet, P• Average distance from the Sun (semimajor axis of ellipse), R• P2/R3 = 42/(G(m1+m2))• Approximately, P2

earth/R3earth = P2

planet/R3planet

• Sometimes we use Earth-years and Earth-distance to the Sun (1 A.U.) as units.

• The constant of proportionality depends on the mass of the Sun--and that’s how we know the mass of the Sun.

• We can apply this to moons (or any satellite) orbiting a planet, and then the constant of proportionality depends on the mass of the planet.

Isaac Newton formulated three laws to Isaac Newton formulated three laws to describe the fundamental properties of describe the fundamental properties of physical reality.physical reality.

NEWTONNEWTON’’S THREE LAWS OF MOTIONS THREE LAWS OF MOTION

LAW #1: A body remains at rest or moves LAW #1: A body remains at rest or moves in a straight line at constant speed unless in a straight line at constant speed unless acted upon by a net outside force.acted upon by a net outside force.

LAW #2: The acceleration of an object is LAW #2: The acceleration of an object is proportional to the force acting on it.proportional to the force acting on it.

LAW #3: Whenever one body exerts a LAW #3: Whenever one body exerts a force on a second body, the second body force on a second body, the second body exerts an equal and opposite force on the exerts an equal and opposite force on the first body.first body.

Newton also discovered that gravity, the force that Newton also discovered that gravity, the force that causes objects to fall to the ground on Earth, is the causes objects to fall to the ground on Earth, is the same force that keeps the Moon in its orbit around same force that keeps the Moon in its orbit around the Earth. the Earth.

NEWTONNEWTON’’S LAW OF UNIVERSAL GRAVITATIONS LAW OF UNIVERSAL GRAVITATION

Two objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

With his laws, Newton was able to derive Kepler’s three laws, as well as predict other possible orbits.

NewtonNewton’’s laws were applied to other objects in our s laws were applied to other objects in our solar system.solar system.

Using Newton’s methods, Edmund Halley worked out the details of a comet’s orbit and predicted its return.

Deviations from Newton’s Laws in the orbit of the planet Uranus led to the discovery of the eighth planet, Neptune.

Third Law Practice Problem

Venus is about 0.723 AU from the sun, Mars1.524 AU. Venus takes 224.7 days to circle thesun. Figure out how long a Martian year is.

5-10 Types of Forces in Nature

Modern physics now recognizes four fundamental forces:

1. Gravity

2. Electromagnetism

3. Weak nuclear force (responsible for some types of radioactive decay)

4. Strong nuclear force (binds protons and neutrons together in the nucleus)

5-10 Types of Forces in Nature

So, what about friction, the normal force, tension, and so on?

Except for gravity, the forces we experience every day are due to electromagnetic forces acting at the atomic level.

Homework for Chapter 5

Problems: # 58, 63, 64

Kahoot

Summary of Chapter 5

• An object moving in a circle at constant speed is in uniform circular motion.

• It has a centripetal acceleration

• There is a centripetal force given by

•The centripetal force may be provided by friction, gravity, tension, the normal force, or others.

• Newton’s law of universal gravitation:

•Satellites are able to stay in Earth orbit because of their large tangential speed.

Summary of Chapter 5