# Motion of an object in a varying gravitational field

Let $E(x,y,z)$ denote the gravitational field,

then in an uniform gravitational field( $E(x,y,z) = k$), the equation

$\mathbf{s(t)} = \mathbf{u}t + \frac{1}{2}kt^2$ holds (where $\mathbf{s}$ is the displacement as a function of time and $\mathbf{u}$ is the initial velocity).

So, my question is:

Is it possible to obtain an expression which relates $s(t)$ with $E(x,y,z)$ in a non-uniform gravitational field.

The answer, I believe is no. According to me this is an iterative process.

• Of course it is not. The equation of motion you mentioned is valid only if the acceleration is constant which in this case is not because the gravitational field is not constant Sep 25 '16 at 14:19

The answer depends on the form of $E$: for some forms you can solve the differential equations exactly, for some, obviously, you can't.