Amusing Problems
The Satellite
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Classes are dismissed for a few days when Dr. J mysteriously leaves town. SAP claims credit, thinking that their annual Phorget Physics campaign has finally taken its toll. In truth, however, Dr. J is on a secret mission for his other employer, the CIA. The situation he is to study is indeed an unusual one. A new satellite has been detected circling the earth, and no one seems to know where it came from. Is it a spy satellite from a third-world country? Could it be a breakthrough in orbital weaponry? Or is it someone's way of advertising in a roundabout way? Dr. J's interest peaks when he reaches the top of a nearby mountain to get a closer look. The satellite has a very low orbit. (It's radius is only 6.4 x 10
^{6}
m.) Although it passes by at a high speed, allowing only a quick glimpse, it returns fairly often. Finally, Dr. J is able to decipher the markings on the side. It is a bumper sticker that reads, "When you advertise with us, the sky is the limit." (I bet their overhead is out of sight!)
Assuming that the mass of the earth is 6 x 10
^{24}
kg, at what velocity is the satellite traveling and how much time elapses between successive passes?
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