Is it possible to solve for the initial speed of projectile hitting a target given that we know the direction (vector) that it is released at and the point on a the surface that it is hitting? If so how would you go about finding an equation to solve for this? 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 = Gconst * mmass planet / rdist2 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.