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Universal
Gravitation
A space station revolves around the earth as a
satellite, 100 km above Earth’s surface. What is
the net force on an astronaut at rest inside the
space station?
A.
B.
C.
D.
Equal to her weight on Earth.
Zero (she is weightless).
Less than her weight on Earth.
Somewhat larger than her weight on Earth.
What is Gravity?
Fundamental Forces:
Strong Force – The force that is involved in
holding the nucleus of an atom together
Electromagnetic Force – The force that exists
between charged particles
Weak Force – The force involved in nuclear
decay
Gravity – The force that exists between any two objects that
have mass.
- Always attractive
Newton’s Law of Universal Gravitation
If the force of gravity is being exerted on
objects on Earth, what is the origin of that
force?
Newton’s realization was
that the force must come
from the Earth.
He further realized that
this force must be what
keeps the Moon in its
orbit.
Newton’s Law of Universal Gravitation
The gravitational force on you is one-half of a
Newton’s Third Law pair (the action force):
The Earth exerts a downward force on you, and you
exert an upward force on the Earth.
When there is such a
difference in masses, the
reaction force is
undetectable,
but for bodies more
equal in mass it can be
significant.
Newton’s Law of Universal Gravitation
Therefore, the gravitational force must be
proportional to both masses.
By observing planetary orbits, Newton also
concluded that the gravitational force must
decrease as the inverse of the square of the
distance between the masses. (This is called the
inverse square law)
In its final form, the law of universal gravitation
reads:
Where:
Inverse Square Law for universal gravitation:
As the distance decreases, the strength of Fg increases by
the square of the number the distance went up by.
If d is halved (1/2) the force will be 4 times what it was.
Review of Scientific Notation.
Newton’s Law of Universal Gravitation
The magnitude of the
gravitational constant G
can be measured in the
laboratory.
This is the Cavendish
experiment.
Gravitational Attraction of Spherical Bodies
Even though the gravitational force is very small,
the mirror allows measurement of tiny deflections.
Measuring G also allowed the mass of the Earth to
be calculated, as the local acceleration of gravity
and the radius of the Earth were known.
Gravitational Attraction of Spherical Bodies
Gravitational force between a point mass and a
sphere: the force is the same as if all the mass
of the sphere were concentrated at its center.
(ignore)
Newton’s Law of Universal Gravitation
Using calculus, you can show:
Particle outside a thin spherical shell:
gravitational force is the same as if all mass
were at center of shell
Particle inside a thin spherical shell:
gravitational force is zero
Can model a sphere as a series of thin
shells; outside any spherically symmetric
mass, gravitational force acts as though all
mass is at center of sphere
Gravitational Attraction of Spherical Bodies
The acceleration of gravity decreases slowly with
altitude:
Gravitational Attraction of Spherical Bodies
Once the altitude becomes comparable to the
radius of the Earth, the decrease in the
acceleration of gravity is much larger:
Tides
Usually we can treat planets, moons, and stars
as though they were point objects, but in fact
they are not.
When two large objects exert gravitational
forces on each other, the force on the near side
is larger than the force on the far side, because
the near side is closer to the other object.
This difference in gravitational force across an
object due to its size is called a tidal force.
Tides
This figure illustrates a general tidal force on
the left, and the result of lunar tidal forces on
the Earth on the right.
Second high tide (smaller
Gravity of moon
Moon’s pull is greatest here
because it is closer. Highest
tide
then the other) because
this side is pulled the least
Tides
Tidal forces can result in orbital locking,
where the moon always has the same face
towards the planet – as does Earth’s Moon.
If a moon gets too close to a large planet, the
tidal forces can be strong enough to tear the
moon apart. This occurs inside the Roche
limit; closer to the planet we have rings, not
moons.
Tidal locking
This is what allows only one side
of the moon to face the Earth
It can even keep
moons from
forming!
Newton’s Law of Universal Gravitation
Example 6-1: Can you attract another
person gravitationally?
A 50-kg person and a 70-kg person are
sitting on a bench close to each other.
Estimate the magnitude of the
gravitational force each exerts on the
other.
So…
If gravity is always present and goes on for ever and ever, why
hasn’t the Moon crashed into the Earth?
It is true that the moon is technically falling towards Earth
because of gravity. BUT, it is also speeding along with a
velocity. It is this velocity that keeps it from falling into Earth!
Newton’s Thought Experiment
To make something orbit the
Earth, all you need to do is
shoot it with a horizontal
velocity that will make it fall
along with the curve of the
Earth.
As a satellite or the Moon falls
towards Earth, the earth also
falls (or curves) away from the
satellite at the same rate!
Gravity and Orbits
• Centripetal acceleration
– The acceleration towards the center if
something going in a circle
– ac= v2/r
• Centripetal Force
– The force that causes this acceleration (also
towards the center
– Fc= mac
Lets try one!
If the distance between the Earth and the Moon is
384,405,000m and the moon travels around Earth with an
orbital velocity of 1023 m/s, what is the centripetal
acceleration on the moon?
All of the planets as a system.
The deviation of a planet
from its normal orbit is
called a perturbation. It is
caused by other planets.
Some more facts about angles
and planetary motion
Angular Velocity
Just like how velocity is the rate at which an object covers a
distance, Angular Velocity is the rate at which an angle (or
an amount of degrees) is covered.
Moment of Inertia and Angular
Momentum
Inertia is_____________________?
Moment of Inertia
The further mass is from its spinning axis, the harder it is to
make it spin.
- Just like with regular
inertia, things that are
spinning also don’t like to
change.
Gyroscopic Motion
A device used to both measure and
maintain its orientation while it is
spinning.
Works based on the principles of
conservation of angular momentum.
Bicycles
Airplanes
Hubble space telescope
Yo Yos
Frisbees
Conservation of Angular
Momentum and the seasons
of Earth