Find the altitude of the satellite

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SUMMARY

The discussion focuses on calculating the altitude of a satellite when the angle theta is 120 degrees, with theta increasing at a rate of 2.7 degrees per minute. The altitude was determined to be 1354 miles using the equation r = 4995/(1+0.12cos(theta)), where the Earth's radius is 3960 miles. The user struggled to find the rate of change of the altitude, mistakenly deriving a result of zero. Clarification was needed regarding the relationship between satellite altitude and angular velocity.

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Homework Statement



At the instant when theta is 120 degrees, the angle theta is increasing at the rate of 2.7 degrees per min. Find the altitude of the satellite and the rate at which the altitude is changing at this instant. Express the rate in units of mi/min.

Homework Equations



r = 4995/(1+0.12cos(theta))
earth's radius = 3960 mi

The Attempt at a Solution



I think I found the altitude alright. I plugged in 120 degrees to the equation and subtracted the radius and got 1354 mi. But I've been working on the other part for the past half hour and I haven't gotten anywhere helpful. I tried to take the derivative of the equation but I get 0. And I'm just so stumped. Can anyone help me out?
 
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I'm sorry but I don't quite understand this problem. Don't satellites orbit the Earth so the altitude above the surface is constant. Obviously if the satellite is higher but goes faster then the rate at which the angle changes will be equivalent to slower and lower altitude satellite. Obviously I'm not understanding it because I don't even know how the info of the radius of the Earth fits into this.
 

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