Related Rates Satellite Problem

[Lynn1111]

Please Help! Related Rates Satellite Problem

Homework Statement

A satellite is in an elliptical orbit around the earth. When the satellite is located at any point P on this elliptical orbit, the distance r (in miles) from the center of the Earth at point E to Point P is given by the equation:

r=4995/(1+.12costheta)

where theta is the angle formed by segment EP and a line drawn from Point E through the point locating the satellite at perigee (point on the orbit closest to the earth). At the instant when theta=120 degrees, the angle is increasing at a rate of 2.7 deg/min. Determine the altitude of the satellite and the rate at which the altitude is changing at this instant. Round off your answers to the nearest hundredth. Express the rate in units of mi/min. (Note: Use 3960 mi as the radius of the Earth)

Homework Equations

r=4995/(1+.12costheta)

The Attempt at a Solution

r=4995/(1+.12cos120)
=5313.829787 mi
Altitude = 5313.83 - 3960
= 1353.83 mi

Then I'm not really sure about the rate...I know I need to take a derivative of something but...

Anyway...please help. It's kind of urgent :(

 

[HallsofIvy]

The rate is the derivative!

What is dr/dtheta? Then the chain rule says that dr/dt= (dr/dtheta)(dtheta/dt). You are given dr/dt and just calculated dr/dtheta so solve for dtheta/dt.