I have totally forgotten DiffEq.

Oh the shame, the shame (haha).

Gravity accelerates a distant object,

beginning at rest 80 km away from Earth.

Differential equations to get from

0.5·m·v^2 = ∫G·M·m/r^2·dr

to Velocity(time in seconds) = ???

G = 6.67E-11 m^3/(kg·s^2)

M = 5.97E24 kg

r_initial = 80,000 m

I know how to get

V(any dist x) = {2∙M∙G∙[1/(r_i - x) - 1/r_i ]}^0.5

I know how to do the problem numerically,

in a spreadsheet or with mathcad, for time

acceleration and so on, bit by bit.

But I don't know how to manipulate the

equations to get an exact solution to velocity

for a given time (up to dist x ~> r_initial...

up to before the thing impacts).

Would appreciate [short-bus] baby steps.

Any takers?

Thanks!