Well, that's one thing in your formula's favor. You didn't write the formula with the quantity (4000/(4000+h))^2, you only wrote it with the denominator squared. So my answer below is wrong.

That might fix it. The formula would be Newton's gravitation formula equated with the weight force:

$\displaystyle F = \frac{GmM}{(R + h)^2} = mg$

where G is the Universal gravitation constant, m is the mass of the object, M is the mass of the planet, R is the radius of the planet, h is the height above the planet's surface, and g is the acceleration due to gravity at the height h.

Now, weight is defined as w = mg, so

$\displaystyle w = \frac{GmM}{(R + h)^2}$

Now, a couple of things are happening here. The object's mass is being weighed in lbs so on the RHS we have a mass m (a constant) in lbs, but we are looking for the weight (which depends on h) in lbs. This seriously messes with my head. The other thing is I have no idea what G is in the English system and I'm not about to try and figure it out.

With the change in the formula this may now be correct. I'm just not about to spend the time to prove it now.

-Dan