Gravitation

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Chapter 7 Gravitation
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7.1 Planetary Motion
Planets move through the sky with More
complicated paths than Stars do.
We begin with Keplers Laws in Order to find out
how.
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Keplers Laws of planetary motion Are stated as

• The paths of 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.
Thus planets move faster when They are closer
to the sun, and Vise-versa.
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3) The square of the ratio of the Periods of any
two planets Revolving about the sun is Equal to
the cube of the ratio Of their average distances
From the sun.
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3
TA TB
rA rB

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2
3
TA TB
rA rB

T the planets periods Of revolution
r the average distance From the sun (or another
focus)
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The first 2 laws apply to each Individual
planet, moon, or Satellite.
The 3rd law relates to the motion Of several
satellites about a Single body.
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Problem...
Io has a period of 1.8 days and is 4.2 units away
from Jupiter. Callisto has a period of 16.7
days. What is the distance away From Jupiter?
rc 19 units
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Problem...
The moon has a period of 27.3 Days and a mean
distance from Earth of 3.9 X 105 km. Find
the Period of a satellite that is in Orbit 6.7 X
103 km.
88.6 mins
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Newton also played around With a few formulas
for gravitation.
Newton said that there was an Attractive force
between All objects, this is called
the Gravitational force.
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Newton was so confidant that He came up with a
law to find The quantity of gravity.
The Law of Universal Gravitation
mAmB d2
F G
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mAmB d2
F G
m mass
d distance between The center of the objects
G 6.67 X 10-11 Nm2 / kg2
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Without showing all the math, The force equals
something else.
mp4p2r T2
msmp d2
F
G
And rearranged again
4p2 Gms
T2
r3
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Problem...
Jeff (75 kg) and Racheal (60 kg) sit about 4
Meters away from each other. Racheal looks up
and feels an Attraction. Find the
gravitational Force between them.
F 1.87 X 10-8 N
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7.2 Using the Law of Universal Gravitation
An object that is falling at the Same rate at
which the earth is Curved is said to be in orbit.
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Use Newtons thought experiment On page 179 to
see how.
For an object to be in orbit, air resistance
Must be taken away, which Means that it must be
at least 150 km above the earth.
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We can continuously derive New formulas to find
out things.
GmE r
v
r3 GmE
T 2p
These formulas only Work for the earth.
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Problem...
A satellite orbits Earth 225 km Above its
surface. What is its Speed in orbit and its
period?
v 7760 m/s T 1.5 hr
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As you move farther from Earths Center, the
acceleration due To gravity changes.
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rE d
a g
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There are 2 kinds of mass
Inertial mass And Gravitational mass
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Inertial mass is a measure of an Objects
resistance to an type Of force.
Fnet a
minertial
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The gravitational mass is the size Of the
gravitational force Between the objects.
r2Fgrav Gm
mgrav
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Einstein proposed that gravity Is not a force,
but an effect Of space itself.
According to Einstein, mass Changes space itself,
Making it curved.
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Bodies are thus accelerated Because they follow
this Curved space toward the center.
This is Einsteins Special Theory of Relativity.
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THE END