Gravity

1
Gravity Orbits Forces Energy
2
Gravity is always attractive, never
repulsive Gravity is the weakest of the four
fundamental forces. Gravity operates over long,
long, long, long, long distances
3
Every object in the Universe attracts every
other object in the Universe with a force that is
directed along the line of centers for the two
objects and that is proportional to the product
of the masses of the two objects and inversely
proportional to the square of the distance
between the two objects.
D
M2
M1
4
Force can be expressed as
M mass of Earth, m your mass, R radius of
the Earth
G6.67 x 10-11 (mks units) -- Newton did not
know its value.
5
Acceleration due to gravity depends only on mass
of the world and its radius.
Your weight a measure of the force between you
and the Earth
F mg (in Newton language)
Weight on Other Worlds
(click)
6
The mass of one object doubled?The mass of both
objects doubled?The distance doubled?The
distance is half as much?
Page 11-14 of CoursePak
How would the force change if
7
Orbital Motion
8
Newton wanted to link the motion of objects
falling to the Earth with the motion of the
Moon. Thought experiment cannonball shot
from a mountain
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10
Newton took this idea and figured out that the
Moon was falling around the Earth in precisely
the way the mathematics predicted!
11
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12
Keplers Laws of Planetary Motion
(pre-gravity descriptive mathematically but not
physically)
13
Orbits of planets are ellipses, with the Sun at
one focal point.
14
Kepler's First Law

• Focus
• Semi-Major Axis
• Major Axis
• Center

X
X
15
Eccentricity ??
X
X
A geometric description of the orbits. 0 lt e lt
1
X
X
X
X
X
16
Working with Keplers first law
17
Keplers Second Law Conservation of ANGULAR
momentum
Or a F/m ( Newtons 1st)
18
Keplers Third Law (Distance)3
(Period)2 Distance must be in AUs, and Period
in Years if using in its simplest form.
Orbit Simulator
19
Newtons Laws of Motion

• Every object in a state of uniform motion tends
  to remain in that state of motion unless an
  external force is applied to it.
• The relationship between an object's mass m, its
  acceleration a, and the applied force F is F
  ma. a F/m
• For every action there is an equal and opposite
  reaction.

20
1st Conservation of Momentum (Law
of Inertia) Momentum mass velocity
Asteroid -- Ida and its moon Dactyl
21
Force change in momentum mass change
in velocity mass acceleration
2nd F ma, a F/m
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3rd Forces come in pairs. For every action
there is an equal and opposite reaction
23
Energy
Will cover in more detail a bit later in the
quarter.
For the rest of the class period, work in small
groups (2 or 3) on tutorial Relationship between
orbital distance and orbital period pages
15-17 of the CoursePak