Transcript 7.4 Satellite Motion

7.4 Satellite Motion
– Circular Motion Principles for Satellites
– Mathematics of Satellite Motion
– Weightlessness in Orbit
Circular Motion Principles for Satellites
• A satellite is any object that is orbiting the earth, sun or other
massive body. Satellites can be categorized as natural
satellites or man-made satellites.
• The moon, the planets and comets are examples of natural
satellites.
• satellites launched from earth for purposes of
communication, scientific research, weather forecasting,
intelligence, etc. are man-made satellites.
• Every satellite's motion is governed by the same physics
principles and described by the same mathematical
equations.
Velocity, Acceleration and Force Vectors
• The motion of an orbiting satellite can be described by the
same motion characteristics as any object in circular motion.
– The velocity of the satellite would be directed tangent to
the circle at every point along its path.
– The acceleration of the satellite would be directed towards
the center of the circle - towards the central body that it is
orbiting.
– And this acceleration is caused by a net force that is
directed inwards in the same direction as the acceleration.
This centripetal force is supplied by gravity - the force that
universally acts at a distance between any two objects that
have mass.
Mathematics of Satellite Motion
• If the satellite moves in circular motion, then the net
centripetal force is provided by the gravity:
Fgrav = ( Msat • v2 ) / R
Fgrav = ( G • Msat • Mcentral) / R2
GM s M central M s v 2

2
R
R
GM central
v
R
The speed of satellite is determined by its location R and mass of the central body Mcentral.
Check your understanding
• A satellite is orbiting the earth. Which of the
following variables will affect the speed of the
satellite?
a. mass of the satellite
b. height above the earth's surface
c. mass of the earth
Weightlessness in Orbit
• Astronauts who are orbiting the Earth often
experience sensations of weightlessness. These
sensations experienced by orbiting astronauts are
the same sensations experienced by anyone who has
been temporarily suspended above the seat on an
amusement park ride.
• Not only are the sensations the same (for astronauts
and roller coaster riders), but the causes of those
sensations of weightlessness are also the same.
Unfortunately however, many people have difficulty
understanding the causes of weightlessness.
Test your preconceived notions about
weightlessness:
•
a.
b.
c.
d.
Astronauts on the orbiting space station are
weightless because...
there is no gravity in space and they do not weigh
anything.
space is a vacuum and there is no gravity in a
vacuum.
space is a vacuum and there is no air resistance in a
vacuum.
the astronauts are far from Earth's surface at a
location where gravitation has a minimal affect.
Contact versus Non-Contact Forces
• As you sit in a chair, you experience two forces – Fg and FN
• The normal force and results from the contact between the
chair and you. You can feel this force because of the contact you
have with the chair.
• The force of gravity acting upon your body is a field force, which
is the result of your center of mass and the Earth's center of
mass exerting a mutual pull on each other; this force would even
exist if you were not in contact with the Earth.
• The force of gravity can never be felt. Forces that result from
contact can be felt. And in the case of sitting in your chair, you
can feel the chair force; and it is this force that provides you
with a sensation of weight. Without the contact force (the
normal force), there is no means of feeling the non-contact force
(the force of gravity).
Scale Readings and Weight
Now consider Otis L. Evaderz who is conducting one
of his famous elevator experiments. He stands on a
bathroom scale and rides an elevator up and down.
As he is accelerating upward and downward, the
scale reading is different than when he is at rest
and traveling at constant speed.
Fnet = m*a
Fnet = 0 N
Fnet = m*a
Fnet = 400 N, up
Fnet = m*a
Fnet = 400 N, down
Fnet = m*a
Fnet = 784 N, down
Fnorm equals
Fgrav
Fnorm = 784 N
Fnorm > Fgrav by
400 N
Fnorm = 1184 N
Fnorm < Fgrav by
400 N
Fnorm = 384 N
Fnorm < Fgrav by
784 N
Fnorm = 0 N
Weightlessness in Orbit
• Earth-orbiting astronauts are weightless for the same reasons
that riders of a free-falling amusement park ride or a freefalling elevator are weightless. They are weightless because
there is no external contact force pushing or pulling upon
their body.
• In each case, gravity is the only force acting upon their body.
Being an action-at-a-distance force, it cannot be felt and
therefore would not provide any sensation of their weight.
But for certain, the orbiting astronauts weigh something; that
is, there is a force of gravity acting upon their body.
• In fact, if it were not for the force of gravity, the astronauts
would not be orbiting in circular motion. It is the force of
gravity that supplies the centripetal force requirement to
allow the inward acceleration that is characteristic of circular
motion.
• The astronauts and their surroundings are falling towards the
Earth under the sole influence of gravity.
1. Otis stands on a bathroom scale and reads the scale while ascending and
descending the John Hancock building. Otis' mass is 80 kg.. Use a free-body
diagram and Newton's second law of motion to solve the following problems.
a. What is the scale reading when Otis accelerates upward at 0.40 m/s2?
b. What is the scale reading when Otis is traveling upward
at= a816
constant
velocity
F
N
norm
of at 2.0 m/s?
c. As Otis approaches the top of the building, the elevator
slows
down
at a rate
F
=
784
N
2
norm
of 0.40 m/s . Be cautious of the direction of the acceleration.
What does the
scale read?
d. Otis stops at the top floor and then accelerates downward at a rate of 0.40
m/s2. What does the scale read?
Fnorm = 752 N
e. As Otis approaches the ground floor, the elevator slows down (an upward
acceleration) at a rate of 0.40 m/s2. Be cautious of the direction of the
Fnorm = 752 N
acceleration. What does the scale read?
• Use the results of your calculations above to explain why Otis fells less
weighty when accelerating downward on the elevator and why he feels heavy
when accelerating upward on the elevator.
Fnorm = 816 N