Elliptical motion, related rates

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

A satellite is in an orbit around earth. The distance from the center of the earth is described by

r= 4995/(1+.12cos@) R earth= 3960 mi

find the rate at which the altitude is changing at the instant where @=120 degrees. d@/dt= 2.7 degrees/min

**2. Notes**

altitude equals r - (R earth)

"@" describes the angle the satellite forms with the Perigee of earth (the closest point)

**3. The attempt at a solution**

a = r - (R earth) = 4995/(1+cos@) - 3960

da/dt= [-4995(-sin@)d@/dt]/(1+cos@)^2

by plugging in the values I get: ~ 46,700 mi/min

**The answer from back of book is 27.7 mi/min **

I do find it a mystery that the R earth is not used, that may be a key to solving it. Help!