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Gravity
Review Question
What are Kepler’s laws of planetary motion?
Review Question
What time of year does the Earth move the
fastest in its orbit around the Sun?
Review Question
What does it mean for something such as the
Moon to be in synchronous rotation?
Discussion
Although the Moon is in synchronous
rotation, we can actually see 59% of its
surface from the Earth. Explain why this is
the case using Kepler’s laws.
Review Question
What are Newton’s 3 laws of motion?
Discussion
Is there a force acting on the Moon? How can
you tell?
What was Newton thinking?
Consider tossing a baseball. It travels a
certain distance before it hits the ground.
Now image throwing it as hard as you
can. It travels farther before it hits the
ground.
Now imagine throwing it even harder.
The Moon is falling
The nearly circular orbit of the Moon is
constantly accelerating toward the Earth.
The Moon is constantly falling toward the
Earth.
Discussion
If I swing a ball in a circle over my head
with a short string and a long string with
the same speed, which ball has the greater
force acting on it? Explain why.
Force on the planets depends on
distance
The higher the speed an object moves in a
circle the greater acceleration and the force
needed to hold it in that circle.
The force on the planets closest to the Sun
has to be greater than that on the planets
farther away.
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
M 1M 2
F G
2
d
Discussion
Consider the gravitational force between two
objects with mass M1 and M2 separated by a
distance d. How would the gravitational force
change if the distance between them increases
to 3  d. How will it change in the distance in
decreased to 0.1  d?
Why the square of the distance?
An inverse square central force law is required to
get orbits that are conic sections, i.e. orbits that
are elliptical.
Why is the force of gravity
proportional to the mass?
All objects, regardless of their mass, fall with
the same acceleration. Because F = ma,
F
a
m
To keep the acceleration
constant, the force must vary
proportional to the mass.
Discussion
Newton’s third law tells us that the force of
the Sun on the Earth is the same as the force
of the Earth on the Sun. Why then does the
Earth orbit the Sun instead of the other way
around?
Gravitational forces between
spherical masses
d
The distance to use is the distance between the
two spheres centers.
Discussion
Suppose a new planet is discovered out in
the Kuiper belt. This planet has twice the
mass of the Earth but is also twice the
radius. Is the surface gravity of this new
planet greater than, less than or the same as
the surface gravity of the Earth?
Discussion
You dig a very deep mine shaft. As you get
closer to the center of the Earth, does your
weight increase or decrease? Why?
(Hint: consider what the force of gravity will be
at the very center of the Earth.)
Escape Velocity
If an object is thrown up with a high
enough velocity it will leave Earth forever.
For Earth this velocity is about 11 km/sec.
Discussion
If the Earth were the same mass but
twice the radius, would the escape velocity
be greater or less than 11 km/sec? Why?
The escape velocity from the Moon is less
than that from the Earth because of the
Moon's
a) lower density.
b) smaller mass.
c) smaller radius.
d) distance from the Earth.
Newton’s law of gravity
explained the ocean tides
Because the force of gravity falls off rapidly with
distance, the pull of the Moon and Sun are
stronger on the side of Earth that is closer to, or
faces, the Moon or Sun.
And it is weakest farthest from the Moon or
Sun.
Spring Tides and Neap Tides
The Sun also contributes to the Earth’s tides.
When the Sun and Moon line up to produce
higher tides, this is called spring tides.
Neap tides occur when the Moon and Sun
Partially cancel each other.
What phases of the Moon do spring and
neap tides occur?
Note: Tidal forces
Tidal forces are not a new kind of force that
stretch and squeeze things.
Are the name given to the difference in
accelerations across an finite sized object
due to differences in distance from a
gravitating source
Discussion
Due to tidal friction, what happens to the
rotation rate of the Earth over time?
The Earth-Moon system
The Moon exerts a force on the tidal
bulges on Earth, trying to twist the tidal
bugles back to face the Moon. This torque
slows the rotation of the Earth.
Conservation of angular
momentum
Any object that is spinning or orbiting has
angular momentum which is equal to the
mass × velocity × radius.
In the absence of an external torque, or
twisting force, the angular momentum
will remain constant.
Discussion
The Moon is slowing the Earth’s rotation
and the Earth is losing angular momentum.
Where does that angular momentum go?
Orbit of the Moon
Due to conservation of angular momentum, the
slowing of Earth’s rotation requires the Moon to
move faster in its orbit. Because the force of
Earth’s gravity does not change, this means the
Moon is getting farther away, by about 2 inches
per year.
Discussion
What do you think will be the ultimate fate
of the Earth Moon system?
Fate of the Earth Moon System
Over billions of years the length of the month
and the length of the day will be the same,
about 47 days. The Moon will stationary in the
sky and will be too small for total solar eclipses.