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# The Night Sky

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```									     Newton’s laws of motion

A body remains at rest or moves in a straight
line at a constant speed unless acted on by a
net external force.

Force = mass  acceleration

For any force there is always an equal and
opposite reaction force.
Newton’s Universal Law of
Gravity

• Every mass attracts every other mass
through a force called gravity
• The force is directly proportional to the
product of their masses
• The force is inversely proportional to the
square of the distance between them
Newton’s law of gravity

M1M 2
F G    2
d
Discussion

You dig a very deep mine shaft. As you get
closer to the center of the Earth, does your
weight increase, decrease or remain the same?
Why?

(Hint: consider what the force of gravity will be
at the very center of the Earth.)
Where does it come from?

For a planet to orbit the Sun, it must constantly
accelerate toward the Sun, otherwise it would
fly off in a straight line at a constant velocity.
Discussion

If I drop two balls at exactly the same time and
from exactly the same height, with each ball
exactly same shape and size but very different
masses, which ball hits the ground first?
Discussion

If I drop two balls at exactly the same time and
from exactly the same height, with each ball
exactly same shape and size but very different
masses, which ball has the greater force acting
on it?
Why proportional to the mass?

All objects, regardless of their mass, fall with
the same acceleration. Because F = ma,

Fgrav     To keep the acceleration
a             constant, the force must vary
m
proportional to the mass.
Discussion

If I swing a ball in a circle over my head
with a short string and a long string with
each ball moving at the same speed,
which ball has the greater force acting on
it? Explain why.
Why the square of the distance?

An inverse square central force law is
required to get stable orbits that are conic
sections, i.e. orbits that are elliptical.
Discussion
A ball held on a string is coasting around in a
large horizontal circle. The string is then
pulled so the ball coasts in a smaller circle.
When coasting the smaller circle its speed is

a) Greater
b) Less
c) Unchanged
Newton’s form of Kepler’s 3rd law

     4      2
 3
P 
2
 a
 G (m1  m2 ) 
Discussion

Notice that we can only determine the
sum of the masses using Newton’s from
of Kepler’s 3rd law. In the case of the
solar system this sum is dominated by
the Sun. Why can’t we figure out the
mass of an object by observing its orbit?
Can’t we get the force necessary to keep
it in orbit and figure out the mass?
All objects fall in a gravitation field with the
same acceleration regardless of mass.

Because being in orbit is just falling, all
objects will orbit the same regardless of
their mass as long as the mass of the
orbiting object is much less than that of the
object it is orbiting.
Discussion

The Moon’s mass (consider it all at the center of
the Moon) attracts every atom on the Earth. If
every atom has exactly the same mass, is the
gravitational attraction of the Moon the same
on each atom on the Earth? Explain.
Tidal Forces

Different distances from a mass will experience
different forces and therefore different
accelerations.
Discussion

Consider yourself sitting on the center ball,
number 2 in the previous diagram. How will
you perceive the motion of the other two
balls relative to you?
Tidal Forces

Tidal forces act to stretch things out along
the direction of a gravitating source and
squeeze them in the middle.
Discussion

Does it matter that all the atoms on the earth
have the same mass? Or that all three billiard
balls have the same mass? Why or why not?

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