1. 7.4 Satellite Motion Circular Motion Principles for Satellites
Mathematics of Satellite Motion
Weightlessness in Orbit

2. 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.

3. 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.

5. 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
The speed of satellite is determined by its location R and mass of the central body Mcentral.

6. 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

7. 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.

8. Test your preconceived notions about weightlessness:
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.
c. space is a vacuum and there is no air resistance in a vacuum.
d. the astronauts are far from Earth's surface at a location where gravitation has a minimal affect.

9. 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).

10. 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.

11. Fnorm equals Fgrav Fnorm = 784 N Fnorm > Fgrav by 400 N
Fnet = m*a
Fnet = 0 N
Fnet = 400 N, up
Fnet = 400 N, down
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

12. Weightlessness in Orbit
Earth-orbiting astronauts are weightless for the same reasons that riders of a free-falling amusement park ride or a free-falling 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.

13. 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 a constant velocity of at 2.0 m/s?
c. As Otis approaches the top of the building, the elevator slows down at a rate of 0.40 m/s2. 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?
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 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
Fnorm = 784 N
Fnorm = 752 N
Fnorm = 752 N
Fnorm = 816 N