Because of their knowledge of physics and interest in the environment, you\'ve g

Question

Because of their knowledge of physics and interest in the environment, you've got a summer job with an organization that wants to put a satellite into orbit to monitor the amount of chloride ions in the upper atmosphere over North America. It has been determined that the satellite must collect samples at an altitude of 100 miles above the surface of the Earth. Unfortunately, at that point air resistance would cause the satellite to remain in orbit for a very short period of time, which would not be useful. You suggest that an elliptical orbit would allow the satellite is close to Earth on North America, where data is desired and also far from Earth, out of almost all of the atmosphere, on the other side of the planet. His colleague estimated that the satellite would be traveling at 10,000 mi / h when farthest from the Earth at an altitude of 1.000 miles. How fast the satellite was traveling when he took air samples if they do not take into account air friction? Use the conservation of energy to determine their response.

Explanation / Answer

Apply conservation of energy to the initial and final states

1/2 mv1^2 - G Mm/r1 = 1/2 mv2^2 - G Mm/r2

1/2v1^2 = 1/2 v2^2 + GM ( 1/r1- 1/r2)

v1 = sqrt v2^2 + 2GM( 1/r1- 1/r2)

= sqrt ( 10000 ( 1609/3600)^2+2 ( 6.67 * 10^-11 ( 5.98 * 10^24 ( 1/100 ( 1609) - 1/1000 ( 1609)

=6.7 * 10^4 m/s

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