Transcript 5-9 & 5-10 - mrhsluniewskiscience

Chapter 5
Circular Motion; Gravitation
Objectives
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.
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.
© 2014 Pearson Education,
Inc.
Kepler’s Third Law
• Period of a planet, P
• Average distance from the Sun (semimajor axis of ellipse),
R
• P2/R3 = 4p2/(G(m1+m2))
• Approximately, P2earth/R3earth = P2planet/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
describe the fundamental properties of
physical reality.
NEWTON’S THREE LAWS OF MOTION
LAW #1: A body remains at rest or moves
in a straight line at constant speed unless
acted upon by a net outside force.
LAW #2: The acceleration of an object is
proportional to the force acting on it.
LAW #3: Whenever one body exerts a
force on a second body, the second body
exerts an equal and opposite force on the
first body.
Newton also discovered that gravity, the force that
causes objects to fall to the ground on Earth, is the
same force that keeps the Moon in its orbit around
the Earth.
NEWTON’S 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.
Newton’s laws were applied to other objects in our
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, Mars
1.524 AU. Venus takes 224.7 days to circle the
sun. 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.
Summary of Chapter 5
• Newton’s law of universal gravitation:
•Satellites are able to stay in Earth orbit because
of their large tangential speed.