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I realize that this is a relatively easy problem to solve when gravity is always aiming in the same direction, but in the particular case I am trying to solve, gravity is varying as it flies through the air. Basically think of a projectile being hit around a mini planet (see the image below), where the force of gravity on the projectile is,

g = G

_{const}* m

_{mass planet}/ r

_{dist}

^{2}

The trajectory trail in the image below is generated from simulating the projectile's flight and adding or removing initial speed to bring it closer to the target position based on the "final" position. This would obviously be done more efficiently by using an equation that would allow me to solve for the initial speed given the initial direction and final position.

Any help solving this is very much appreciated.