CH10 – Projectile and Satellite Motion Satellite Motion Circular and Elliptical Orbits Kepler’s Laws

Satellites Satellites are fast moving projectiles at great distances (for earth above atmosphere, not above gravity). Satellites fall around other objects—moon around earth, space station around earth, earth around sun, etc. The speed must be enough to keep the projectile from falling into the earth, sun, planet, etc.

Satellites The earth’s curvature requires a projectile to be moving about 8,000 m/s. This speed would cause most objects to burn up in earth’s atmosphere, thus satellites typically orbit above the atmosphere 150,000 m. There still is gravity above the atmosphere!

Satellites Objects in space must have the correct speed, or they get pulled into the sun (largest gravity) This happened a long time ago for most objects.

Satellite Example Is the following explanation valid? Satellites remain in orbit instead of falling to the Earth because they are beyond the main pull of Earth’s gravity. NO! Satellites remain in orbit because they are being pulled by gravity!

Circular Orbit Objects with a circular orbit have a constant speed which is high enough to fall around the earth. Mostly only man-made satellites have very circular orbit. Geosynchronous satellites  Communication satellites are geosynchronous  Located at about 5.5 x radii above the surface of earth  At this location, satellites take 24 hours to complete their orbit  They stay above the same point on the earth.

Circular Orbit “Period” is the time it takes to complete one orbit. The higher the orbit  less speed needed  longer path  therefore, longer period. Rocket launches— mostly vertical, then tipped horizontal and given “push” for speed to fall around the earth.

Elliptical Orbit When projectiles have velocity > 8,000 m/s, but not fast enough to “get away”, they will orbit in an oval shape called an ellipse. Parabolic paths are a portion of an ellipse.

Elliptical Orbit Ellipse is a curve that results when the sum of the distances from 2 fixed points is always the same (constant). The 2 points are each called a focus (foci). Foci

Elliptical Orbit Satellites with elliptical orbits will change their speed (unlike circular). As they approach, gravity pulls them and speed increases. As they whip by and pass, gravity will pull back to slow them down. Closer to planet means faster and farther away means slower.

Kepler’s Laws Johannes Kepler ( ) was a German astronomer. He spent many years studying our solar system Explain planetary motion with 3 laws (but did not understand gravity)

Kepler’s Laws First Law:  Planets move in elliptical orbits around sun, and sun is at 1 focus Second Law:  [Planets speed up and slow down during orbit (like throw up & down)] Using imaginary spokes from the sun to any planet, the planet will sweep out the same area in its orbit during a specific amount of time. Third Law:  A planet’s time for 1 revolution (period) is proportional to the distance away from the sun, specifically, T 2 ~ d 3

Orbital Review 1.Why does the force of gravity change the speed of a satellite in an elliptical orbit? 2.What is so special about communication satellites? 3.The period of a satellite (the time it takes for a complete revolution), depends on what?