It appears that gravity drops linearly from its maximum value of 9.81 m/s (henceforce referred to as ) at 500 m altitude to zero at 900 m. Let , or the altitude relative to the edge of gravity. In this range, we have
This is similar to the equation of a harmonic oscillator, except the sign is the opposite.
The solution to this equation is of the form
To find , we use our initial conditions :
In analogy to the solution to the harmonic oscillator being a sum of sine and cosine, we can also express this as a sum of hyperbolic sine and cosine: