Transcript universal gravitation pdf

Universal Gravitation
Chapter 8
Isaac Newton and
Gravity
• Newton realized an apple falls because of
force
• Moon follows circular path, force needed
• Newton first to realize gravity causes both.
• Moon is actually “falling” towards earth
• Tangential velocity (sideways) keeps it going
around earth instead of into it
Law of Universal
Gravitation
• Newton extended gravitation theory to all objects,
• Realized gravitational attraction is property of all
mass
• Attractive force is directly proportional to product
of two masses
• Inversely proportional to square of distance
between them
Law of Universal
Gravitation
• F ~ m1 m2/d2
• Proportionality constant G must be used to
make quantities equal
• F = Gm1 m2/d2
• G = force between 2 1-kg masses, 1 m
apart
• Its value is G = 6.67 x 10-11 Nm2/kg2
• Henry Cavendish first to measure G
Law of Universal
Gravitation
• Gravity very weak force
• Force of attraction with earth is weight
• Weight depends on distance from center of
earth
• On top of high mountain, you weigh less
• Using G and radius of earth we can
calculate mass of earth = 6 x 1024 kg
An Inverse-Square
Law
• Force of gravity varies inversely with
square of distance between objects
• For a spherical body, distance is
measured from its center
• If distance is doubled, force is one-fourth
as much; if tripled, force is one-ninth (1/3)2
• If distance is halved, force is 4 times as
much; if distance is 1/3 as much, force is 9
times as great.
An Inverse-Square
Law
• Other inverse-square relationships: light
and sound intensity, magnetic and electric
force.
• Force of gravity weakens rapidly with
distance due to spreading of force into
surrounding space, but never really zero,
even in deep space.
Gravitational Fields
• Gravitational force acts over a distance
without contact
• Caused by interaction with gravitational field
• Field can be thought of as lines of force
radiating from objects
• Strength of field is force per unit mass
exerted on object: g = F/m
Gravitational Fields
• Earth’s grav. field strength is actually
acceleration due to gravity at any location
• Combining g = F/m and F = G mM/R2, we
find g = GMe/ R2, where Me = mass of the
earth and R = distance from center of earth.
• g for any planet can be found using this
formula.
Gravitation and the
Universe
• Planets, moons, stars are spherical due to
gravity
• All planets affect each other, can cause
perturbations (wobbles) in orbits
• Neptune and Pluto were discovered
because of perturbations in Uranus’ orbit.
• Perturbations of distant stars have led to
discoveries of planets, double stars
Gravitation and the
Universe
• “Big Bang” theory says universe hurled
outward from big explosion
• Universe is expanding, only pull of
gravitation can stop it.
• Unknown whether enough matter exists to
stop expansion and begin contraction
leading to “Big Crunch” and another big
bang-expansion-contraction cycle.
Gravitational Field
Inside Earth
• If hole were drilled through earth and you
fell in, what would happen?
• As you fall, mass below you pulls down,
mass above you pulls up.
• No force at center of earth, pull equal in all
directions
• You would accelerate with decreasing
acceleration until you reached the center,
then decelerate as you approach opposite
surface.
Satellites--Circular
Orbits
• In circular orbit, gravity always pulls
perpendicular to velocity
• Speed doesn’t change, only direction.
• Time (period) for close orbit about 90 min.,
greater for higher orbits
• If period of revolution is 24 hours, satellite
remains over same point on earth-communication satellites do this
(geosynchronous orbit)
Satellites--Elliptical
Orbits
• If speed is faster than needed for circular
orbit, elliptical orbit can result
• Ellipse is oval with two focal points (foci)
• Speed varies in elliptical orbit
• Faster speed close to earth, slower when
farther away
• All planets follow elliptical orbits around sun
Tides
• Change in sea level due to difference in
gravitational pull between earth and moon
on opposite sides of earth.
• Causes elongation of earth and moon along
line of force, bulging on near and far side.
• Earth turns underneath high water levels
causing 2 high tides and two low tides per
day.
Tides
• Sun also creates tides but effect is less than
moon because distance difference is not as
large a part of total distance.
• Extra large spring tides caused by sunmoon alignment on same side of earth
• Smaller neap tides occur when sun and
moon are on opposite sides of earth
Eclipses
• When sun-moon-earth alignment is perfect,
eclipses occur
• When earth is between sun and moon,
moon is in shadow and lunar eclipse occurs.
• When moon is between sun and earth, parts
of earth in moon’s shadow see solar eclipse.
Black Holes
• In stars, expansion forces due to nuclear
fusion are balanced by contraction force of
gravity.
• When solar fuel runs out, stars collapse
• Small stars will become dense, cool, black
dwarfs.
Black Holes
• Large stars will continue collapse to
enormous density with gravitational forces
too strong for anything to escape
• Even light, radio communications are
trapped--nothing can escape black hole
(except small amounts of radiation).
• Edge of black hole is called event horizon
Black Holes
• Fabric of space-time is warped by
tremendous gravity inside black hole
• Mass of black hole is same as star that
created it so gravity outside black hole is
same as if original star were still there.