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lecture12

# lecture12 - 5.5 Satellites in circular orbits There are...

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5.5 Satellites in circular orbits here are many different satellites and other objects currently orbiting the There are many different satellites and other objects currently orbiting the earth. How did they get there??? et’s start shooting projectiles horizontally ach time with increasing speed: Let’s start shooting projectiles horizontally – each time with increasing speed: But, if I shoot the projectiles fast enough, so that they cover a large distance, the ground beneath does not stay flat, since the earth is curved.

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Let’s say the elephant’s trunk 1 m above the ground. is 1 m above the ground. The last projectile he fired is moving very fast, so it covers a lot of ground as it falls due to gravity. By the time it falls a distance of 1 m, the earth’s surface has curved away by 1 m, so the projectile is still 1 m above the surface. The projectile always stays 1 m above the surface. Thus, the projectile is in a 1-m igh orbit! high orbit! When a satellite is launched, a rocket takes it above the atmosphere, and then we give it enough horizontal speed such that it falls toward the earth at the same rate as which the earth curves away beneath it. Thus, satellite motion is circular motion , and we should be able to identify a centripetal force:
The only force we have is the gravitational force. F G F G is also a radial force, and the only one, thus: C G F F = r v v m m m s s e 2 r r G 2 Now I can solve for r , the radius of the satellite’s circular orbit. 2 v m G r e = Notice, the radius of the orbit does not depend on the mass of the satellite, but only on its speed. Thus, for each orbital speed, v , there is one and only one (unique) radius of orbit. Note:

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lecture12 - 5.5 Satellites in circular orbits There are...

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