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I'm working on it, but first let me say that the speed needed to escape the gravitational field doesn't apply here.
Escape velocity is for unpowered projectiles. Every rocket becomes an unpowered projectile when it runs out of fuel, but more on that later.
Ug=-G*M1*M1/r
Ug= potential energy of gravity (eg. your energy needs to be this big to escape)
G = Gravitational constant. _NOT 9.8M/S^2!_ that's gravitational acceleration at the surface. 6.7x10^-11 (in SI units).
M1 mass of first object (in kg)
M2 mass of second object
r distance between both object's center of mass (the center of the earth, not surface)
at the surface this comes to 11 km/s. nothing we have ever launched has moved that fast before leaving the atmosphere. Bullets don't move nearly that quickly. If that's all we had to go on then we couldn't have launched voyager or anything else.
if however you have a rocket that remains powered until r gets really really big, then it can be traveling at a velocity large enough for it's location. All rockets space probes (voyager etc) remain a powered rocket until it's moving fast enough and is far enough out that it will never return.
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