Download Newton`s Laws & Gravitation

Gravitation
and the Clockwork Universe
Apollo 11 Lunar Lander
How can satellites orbit
celestial objects without
falling?
The Ancient Greeks Model of the Universe
Geocentric
View
Ancient Astronomers Saw Lights that Wandered About the Sky
Claudius Ptolemy's View of the Universe
Geocentric View
Copernicus worked out the
details of the heliocentric
model of the universe.
Occam’s razor
Too simple to be wrong
Nicolas Copernicus (1473 – 1543)
The Retrograde Motion Was an Optical Illusion
A Comparison of the Average Sun – Planet Distances
Tycho Brahe
Greatest naked eye observer
Trusted the geocentric view
His observations confirmed
the heliocentric theory
Measured the positions of the
stars and planets accurately.
Tycho Brahe looked for stellar parallax
Tycho argued that nearby
stars should shift their
position as the Earth
revolved around the Sun.
Tycho Brahe and Johannes Kepler teamed up.
An Ellipse
Focus
Foci
Major axis
Minor axis
Eccentricity
e = 1 => line
e = 0 => circle
e2 = 1-(b/a)2
Kepler’s Three Laws
The orbit of a planet is an ellipse
with the Sun at one foci
A line joining a planet and the Sun
sweeps out equal areas in equal
times
The harmonic law P2 = a3
(a is the semi-major axis)
The Harmonic Law
The square of the sidereal period of a planet is directly proportional
to the cube of the semi-major axis of the orbit.
Galileo Galilei (1564 – 1642)
Objects fall with constant acceleration
Galileo Discovered Four Moons Orbiting Jupiter
IO
Europa
Ganymede
Callisto
Objects Accelerate as they Fall
Speed increases at a constant
rate.
Falling bodies move with
constant acceleration..
Experimented by rolling balls
down various inclines.
a = dv/dt
Sir Isaac Newton (1642 – 1727)
Newton laid the foundation
for differential and integral
calculus. His work on
optics and gravitation make
him one of the greatest
scientists the world has
known.
Law of Gravity
F = Force
G = Gravitational constant of the universe
6.67 x 10-11 N•m2/kg2
m = mass of objects
r = distance between objects
Action at a Distance
Sun’s Gravitational Force on Earth
G = 6.67 x 10-11 N•m2/kg2
MEarth = 5.98 x 1024 kg
Msun = 1.99 x 1030 kg
rES = 1.50 x 1011
Skating - The laws of Motion
•At rest on a level surface:
–If you just wait, you stay stationary
–If you’re pushed, you start moving
in that direction
Moving on a level surface:
Neglect air resistance
Neglect friction
–If you just wait, you coast steadily
in straight line
–If you’re pushed, you change
direction or speed
Physics Concept
• Inertia
– A body at rest tends to remain at rest
– A body in motion tends to remain in motion
Newton’s First Law
An object that is free of external influences
moves at a constant velocity.
Physical Quantities
•
•
•
•
•
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Position – an object’s location
Velocity – change in position with time
Force – a push or a pull
Acceleration – its change in velocity with time
Mass – measure of its inertia
Speed = distance/time
Mass and Inertia
• Mass is the measure of an object’s inertia.
• Mass is how much matter is contained
within the object.
• The kilogram (kg) is the basic unit of
measure for mass.
• Inertia is the object’s resistance to a change
in it’s motion.
Newton’s Second Law
The force exerted on an object is equal to the
product of that object’s mass times its
acceleration. The acceleration is in the same
direction as the force.
F = ma
force  mass  acceleration
Falling Balls
Check Your Understanding
• Suppose that I throw a ball upward into the air. After
the ball leaves my hand, is there any force pushing the
ball upward?
• Out in deep space, far from any celestial object, would
an astronaut weigh anything? Would the astronaut
have mass?
• If you weight on the moon is one-sixth of what it is on
Earth, what is the moon’s acceleration due to gravity?
w = mg
Weight vs. Mass
• Weight – earth’s gravitational force on object
Relative Motion
The further a satellite is from the Earth the weaker the Earth’s
pull, therefore it should travel slower so gravity can pull it back.