According to some wives' tales Fob = 0.00162*e^((x- 4066.96)/17.37) must act through the C.G. in which case Fob is a constant Fob = 0.00162*e, where e=2.718.
That means v = ((Orbs+6371)*0.00162*e)^(0.5).
When the moon is at its perigee Om = 363104+6371 = 369475 km
v = ((369475)*0.00162*e)^(0.5) = 40.3 kms-1.
When the moon is at its apogee Om = 406696+6371 = 413067 km
v = ((413067)*0.00162*e)^(0.5) = 42.6 kms-1.
The average orbital speed is v = 41.4 kms-1. Which is still one order higher than 1.03 kms-1
And where did all the GPE go? GPE increases plateau off then decreases. What is it converted to? If it is converted to rotational KE, rotation about Earth at radius r = Orbs + re then,
GPE = Rotational KE = \(\cfrac{1}{2}.{v}^{2}_{o}\) = 63 numerically obtained from graph
vm = 11.22 kms-1.
Which is closer to 1.03 kms-1 but not much better. (Note: per unit mass all)
