Transcript Universal Gravitation

Universal
Gravitation
Physics
Mr. Padilla
Falling
Apple hits Newton on the head.
According to the law of inertia, it would
not fall unless acted upon by an outside
force.
 If the moon did not fall, it would move
off in a straight line and leave orbit.
 The moon is, therefore just a projectile
circling Earth under the attraction of
gravity
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Newton & Gravity
Newton did not discover gravity.
 Newton showed that the gravity of a
regular sphere is the same as if the
mass were concentrated at its center.
 Developed the law of universal
gravitation.
 This theory confirmed the Copernican
theory of the solar system.
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Law of Universal Gravitation
Everything pulls on
everything else.
 This pull involves
only an objects
mass and their
distance apart.

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Law of universal
gravitation – every
object acts on every
other object with a
force that for any
two objects is
proportional to the
mass of each object.
Law of Universal Gravitation
The force decreases
as the square of the
dist. between
objects increases.
 The greater the
distance the less the
force.
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Universal
Gravitational
Constant – G
 Force of gravity
between two objects

 Fg
= G m1m2
r2
Gravitational Constant
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The gravitational constant was first
calculated by Henry Cavendish, 150
years after Newton’s discovery, and
then again later by Phillip von Jolly
G  6.67 10
11
2
Nm
2
kg
Example Problem
The Earth has a mass of 5.98x1024 kg
and rotates around the Sun at a
distance of 1.50x1011 m. If the sun has
a mass of 1.99x1030 kg, what is the
force of gravity the Sun exerts on the
Earth?
 Force of gravity = 3.53x1022 N
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Sample Problem 7I

Find the distance between a 0.300 kg
billiard ball and a 0.400 kg billiard ball if
the magnitude of the gravitational force
is 8.92 x 10-11 N.
Gravity and you
Estimate your mass.
 If the radius of the Earth is 6.67x106 m,
can you calculate the force of gravity
exerted on you by the Earth? (Do it)
 Is there another way to do it?

Gravity
Gravity is considered to be a very weak
force.
 We sense gravity only when large
masses like the Earth are involved.
 Is your mass the same at sea level as it
is on a high mountain?
 Is your weight the same?
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Inverse Square Law
This law applies to
the weakening of
gravity with distance
 The quantity varies
as the inverse
square of its
distance from its
source.
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Inverse Square
The greater the
distance from the
Earth the less it will
weigh.
 No matter how great
the distance Earth’s
gravity does not
drop to zero.
 The gravitational
influence of every
object is exerted
through all space.
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Universal Gravitation
Particles exerting gravity on each other
created round planets.
 Planets exert gravity on each other.
When these planets are close enough,
they can disturb each others orbits.
 This deviation is called a perturbation.
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Gravity in the Universe

The perturbations of
Uranus led to other
planets being
discovered.


Neptune in 1846
Pluto in 1930
The universe may
have been created
10-15 bill. years ago
(big bang)
 Since then its been
constantly
expanding
 Gravity may stop, or
even reverse this
expansion

Gravitational Interactions

Gravitational field – force field that
surrounds massive objects = gravity
Outside the planet
 Inside the planet
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Weight and weightlessness
 Ocean Tides
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Orbits
Circular – A satellite in a circular orbit,
always moves perpendicular to the
force of gravity, so it always moves at a
constant speed
 The time it takes for a satellite to
complete one orbit is called the period.
 Not all satellites follow a circular orbit.
Some will travel along an oval path
called an ellipse.

Ellipse
A closed path taken by a point
(satellite) that moves in such a way that
the sum of it distances from two fixed
points is constant.
 These points are called foci

Ellipse
Satellite speed varies in an ellipse.
 Satellites speed up as they approach
and slow as they go away.
 The satellite will continue to orbit unless
it reaches escape speed
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Planetary motion is caused by,
yes you guessed it, gravity.
Tycho Brahe (15461601) was one if the
first to make exact
measurements of
the position of the
planets and stars.
 He still believed that
the Earth was the
center of the solar
system

Johannes Kepler,
one of his
assistants, used
Brahe’s data and
with the sun as the
center of the solar
system, and was
able to explain the
behavior of every
satellite and planet.
Kepler’s Laws
of Planetary Motion
1. The paths of the planets are ellipses,
with the sun at one focus.
 2. An imaginary line from the sun to a
planet sweeps out equal areas in equal
time intervals. (Planet travels faster
when closer to the sun)
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Kepler’s Laws

3. The square of the
ratio of the periods
of any two planets
revolving around the
sun is equal to the
cube of the ratio of
their average
distances from the
sun.
2
 TA   rA 
    
 TB   rB 
3
Escape Speed: Take off…
Speed necessary for
an object to escape
gravity and not
come crashing back
down.
 Escape velocity
varies from planet to
planet because each
planet has a
different amount of
gravity.
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Here are some
escape velocities
Earth – 11.2 km/s
Moon – 2.4 km/s
Mars – 5.0 km/s
Jupiter – 60.2 km/s
Sun’s gravity from
Earth – 42.2 km/s
Sun – 620 km/s
Stars
Produce energy through fusion of
Hydrogen
 The more fusion, the bigger and hotter
the star
 Less fusion, smaller and cooler
 When a star runs out of fuel, gravity
will dominate and the start will collapse
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Sun
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After Hydrogen is
gone
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Helium will fuse
into carbon
Causes sun to
expand into a red
giant
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It will expand
beyond Earth’s
orbit
Won’t take place
for about 5 billion
years

When Helium is
used up…
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Red Giant will
collapse into a
black dwarf

It will no longer
give off heat and
light.
Black Holes
Happens for stars at least twice as big
as ours
 When gravitational collapse takes over
it doesn’t stop.
 Density becomes infinite
 Gravity is so great that nothing can get
out.
 Gravitational field does not change.
 Black Holes can not be seen
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