Transcript My Gravity PP

ISCI 2002
Chapter 5
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(1). Gravity is a force of attraction that exists
between any two masses, any two bodies,
any two particles
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(2). Attraction that exists between all objects
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Throughout the universe
(3). Gravitational force is proportional to the
masses of the two objects that are
attracting each other.
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so that an object with twice the mass will attract
with twice the force.
Any point source which spreads its influence equally in all directions
without a limit to its range will obey the inverse square law. This comes
from strictly geometrical considerations. The intensity of the influence at
any given radius r is the source strength divided by the area of the sphere.
Being strictly geometric in its origin, the inverse square law applies to
diverse phenomena. Point sources of gravitational force, electric field,
light, sound or radiation obey the inverse square law. It is a subject of
continuing debate with a source such as a skunk on top of a flag pole; will
it's smell drop off according to the inverse square law?
The greater the distance from the Earth’s center, the less gravitational
force. See figure 5.7. The girl at the top of the ladder weighs ¼ less
than she weighs on the Earth.
As you move twice the distance from the Earth’s center your weight
(gravitational effect) decreases by ¼.
The Force of Gravity is dependent on:
(1). Distance between objects
(2). Mass of those objects
G = gravitational constant (similar to pie) The constant of
proportionality G is known as the universal gravitational constant. It
is termed a "universal constant" because it is thought to be the same
at all places and all times, and thus universally characterizes the
intrinsic strength of the gravitational force.
 (1).

Weight is determined by
Mass x acceleration due to gravity
 (2).
If you not accelerating, you will not
experience weight.
 (3).
Your weight is a force that is applied
against a floor, scale, etc.
 (4).
Elevator in free fall – supporting force is
decreased (bottom of the elevator)


Although the Earth's gravity has a lesser effect on an astronaut orbiting
the Earth in a spaceship than on a person on the surface of the Earth,
this is not the reason why an astronaut experiences weightlessness. The
space shuttle, International Space Station and most other manned
vehicles don't get that far from the Earth. The Earth's gravitational
attraction at those altitudes is only about 11% less than it is at the Earth's
surface. If you had a ladder that could reach as high as the shuttle's
orbit, your weight would be 11% less at the top. Put another way, a
person who weighs 100 pounds on the Earth's surface would weigh about
89 pounds at the top of the ladder.
The reason why the person wouldn't feel weightless is because they are
being pushed by the ladder - it is keeping them from falling. If they were
to jump off the ladder, then they would feel weightless, at least up until
the time they splatted on the ground. This is why astronauts feel
weightless. The astronaut, the spaceship and everything inside it are
falling towards the Earth. The reason why the astronaut doesn't go
splat is because the Earth is curved and the astronaut, the spaceship
and everything inside it are moving 'sideways' fast enough that, as
they fall towards the Earth, the surface of the Earth curves away from
them. They are always falling towards the Earth, but they never get
there.

The reason why you don't see gravitational effects between objects in a
spacecraft is because gravity is a very, very weak force. Of the four basic forces
that scientists are sure about, gravity is, by far, the weakest one. Have you
ever tripped and fallen down? Well, it took the whole planet to do that to you.
Have you ever seen a sock stick to a shirt after it has come out of a dryer? That
static cling, created by a slight imbalance of charge between the sock and the
shirt, is stronger than the gravitational attraction of the Earth. The
gravitational attraction between two small objects in a spacecraft would be
overwhelmed by other forces, such as the force of the air being circulated
throughout the spacecraft. Although the force of attraction is there, it is so
weak that special care would have to be taken to notice it.
 (1).
Calculating the distance of an object
falling vertically. (d = 1/2gt2)
 (2).
For a projectile there are two forces:


X direction (horizontal)
Y direction (vertical) force of gravity.

The force of gravity acts downward and is unable to alter the horizontal motion. There must
be a horizontal force to cause a horizontal acceleration. (And we know that there is only a
vertical force acting upon projectiles.) The vertical force acts perpendicular to the
horizontal motion and will not affect it since perpendicular components of motion are
independent of each other. Thus, the projectile travels with a constant horizontal velocity
and a downward vertical acceleration
.

Now suppose that our cannon is aimed upward and shot at an angle to the horizontal from
the same cliff. In the absence of gravity (i.e., supposing that the gravity switch could be
turned off) the projectile would again travel along a straight-line, inertial path. An object in
motion would continue in motion at a constant speed in the same direction if there is no
unbalanced force. This is the case for an object moving through space in the absence of
gravity. However, if the gravity switch could be turned on such that the cannonball is truly a
projectile, then the object would once more free-fall below this straight-line, inertial path.
In fact, the projectile would travel with a parabolic trajectory. The downward force of
gravity would act upon the cannonball to cause the same vertical motion as before - a
downward acceleration. The cannonball falls the same amount of distance in every second
as it did when it was merely dropped from rest (refer to diagram below). Once more, the
presence of gravity does not affect the horizontal motion of the projectile. The projectile
still moves the same horizontal distance in each second of travel as it did when the gravity
switch was turned off. The force of gravity is a vertical force and does not affect horizontal
motion; perpendicular components of motion are independent of each other.
 (1).
Range refers to the distance travelled by
a projectile (horizontally)
 (2).
The same range can be obtained from
two different projection angles


Add up to 90 degrees
Object thrown into the air at 60 degrees will
have the same range as an object thrown in the
air at 30 degrees (same speed)
In the absence of air drag or resistance, speed lost while going up equals
speed gained while going down.
Air drag is a reality. It will affect the range of projectiles. They fall
short of a predicted parabolic path with no air resistance or drag.
 (1).
If you know the initial velocity, you can
use the formula to determine the range
or (d)

V = d/t

Rearranged would be:

d = (v)(t)

Satellites stay in orbit due to the balance of two factors: velocity, or the speed at
which it would travel in a straight line

the gravitational pull between the Earth and the satellite.

Satellites never fall into the Earth this because Earth is round and curves. The
Earth curves approximately 5 meters downward for every 8000 meters along its
horizon. In order for a satellite to successfully orbit the Earth, it must travel a
horizontal distance of 8000 meters before falling a vertical distance of 5 meters.
Since a horizontally-launched projectile falls a vertical distance of 5 meters in its
first second of motion, a orbiting projectile must be launched with a horizontal
speed of 8000 m/s. When launched at this speed, the projectile will fall towards
the Earth with a trajectory which matches the curvature of the Earth. As such, the
projectile will fall around the Earth, always accelerating towards it under the
influence of gravity, yet never colliding into it since the Earth is constantly curving
at the same rate. Such a projectile is an orbiting satellite.

Man-made satellites circle the Earth in many ways including polar and geostationary
orbits.
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

Polar orbit: The satellite in a polar orbit travels over the North and South
Poles. A polar orbit may be from several hundred miles to several thousand
miles above Earth. This type of satellite circles the Earth approximately 14
times each day. Because the Earth is turning more slowly than the satellite,
the satellite gets a slightly different view on every revolution. Over the course
of a few days, a satellite in a polar orbit will cover almost all the planet.
Geostationary orbit: The satellite in a high-altitude, geostationary orbit circles
the earth once every 24 hours, the same amount of time it takes for the Earth
to spin on its axis. The satellite turns eastward (like our Earth) along the
Equator. It stays above the same point on Earth all the time. To maintain the
same rotational period as the Earth, a satellite in geostationary orbit must be
22,237 miles above the Earth. At this distance, the satellite can view a huge
portion of the Earth's surface. Because the high-altitude satellite appears to
remain fixed in one position (it's really orbiting at the same rate as the Earth
turns), it requires no tracking to receive its downlink signal. That is why when
we turn our home satellite dish on to receive the TV signal from a particular
geostationary satellite, we don't have to keep jumping up to adjust its
position.
One of the advantages of geostationary satellites is that imagery is obtained
and displayed every 30 minutes, compared to imagery transmitted by polar
orbiting platforms taken every 6-12 hours.