# Thread: Related Rates Elliptical Orbit/Satellite Problem

1. ## Related Rates Elliptical Orbit/Satellite Problem

1. The problem statement, all variables and given/known data
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)

2. Relevant equations

r=4995/(1+.12costheta)

3. 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

2. $\displaystyle \frac{dr}{dt}=\frac{dr}{dx}\cdot\frac{dx}{dt}$
$\displaystyle \frac{4995 \cdot sin(x)}{(1+0.12cos(x))^2}\cdot 2.7$
Just showing you the principle be careful of the units.

### calculus related rates eliptica

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