ch14_fp

= Satellite Motion = frank and haris did this

**__14.1 Earth Satellites__**
- When a projectile is thrown so that it falls around the earth instead of being pulled down into the earth it is known as a satellite. - The circumstances under which this happens is so that a projectile is thrown at just the right speed in order to match the curvature of the earth and continue to fall around the earth in a circular orbit. - If you are holding an object in the air and you drop it, it will fall straight down. If you throw it sideways it will then follow a curved path. When dropped from rest the object will accelerate at 10 m/s^2 and after on second will fall 5 m vertically. So any projectile, within the first second of motion, will fall a vertical distance below the straight line path that it would take without gravity. - Now that we know how projectiles move it is essential for their motion to match the curvature of the earth in order for them to become an earth satellite. The surface of the earth drops a vertical distance of almost 5 meters for every 8000 meters tangent to the earth’s surface so in order to create an earth satellite it must travel at least 8 km/s. However due to friction an object must be at least 150 kilometers above the earth’s atmosphere so that it does not burn up. __14.2 Circular Orbits__ - The only component of gravity that acts on objects is downward. For moving objects this means that gravity acts upon the object perpendicular to the objects motion. This is also true for a satellite in orbit. This means that gravity does not change the speed of a satellite in circular orbit. - The time it takes for a satellite to orbit around the earth is its period. The period of a satellite is shorter when it is closer to the earth, and at higher altitudes the period is longer.  __14.3 Elliptical__ - Satellites do not always orbit in a circular path; rather they overshoot that circular path and trace an elliptical orbit. An ellipse is a closed path taken by a point that moves in such a way that the sum of its distances from two fixed point (called foci) is constant. - The speed of a satellite, normally constant, varies within an elliptical orbit. Elliptical orbits are a result of an initial speed more than 8 km/s, any slower and it would be a circular orbit. A loss of speed results from this orbit because it moves away from the earth against the force of gravity. The speed lost is regained during the fall back around the earth and this cycle repeats again and again. __14.4 Energy Conservation and Satellite Motion__ - In a circular orbit no force acts on the object in any direction so the speed is constant. This is because the distance between a planet’s center and the satellite is constant so the potential and kinetic energy is the same everywhere. - In an elliptical orbit the speed does change throughout its orbit. This is because there are points in which the satellite is closer to the earth (the perigee) and farther away (the apogee). At the perigee the kinetic energy is the largest and at the apogee the potential energy is greatest, however the sum of both at any point is the same therefore it is constant. Gravity does change the speed in an elliptical orbit. When going away from the apogee the satellite moves with the component of gravity and gains kinetic energy and then after it passes the perigee in moves against the gravity lowering its kinetic energy but due to its high position its potential energy increases. So at the highest point the apogee, potential energy is greatest, and as it falls towards the perigee its potential energy is converted into kinetic energy reaching its peak at the perigee. __14.5 Escape Speed__ - In order to escape from the earth you must attain a speed greater than 11.2m/s (neglecting air resistance). What is essential to note however is that you must first have a vertical thrust and then a horizontal thrust so that it does not come back down. As it gains height its kinetic energy begins to diminish and is then turned into potential energy which is highest at the top of it trajectory. At that point however if no horizontal acceleration is placed on the rocket it will just fall straight back down where it came from. That is why it must be a horizontal component at the top of the rockets trajectory in order for it to tip and then orbit. Escape speeds are different for different planets because of their gravity, so an initial thrust is necessary to reach a speed that is enough to escape that planets gravity. - Pioneer 10 was the first probe to escape into the solar system and was launched in 1972.