Lets say that there is a small spacecraft (mass doesn't matter due to Earth's huge mass) orbiting Earth with a current distance from the center at 6,700,000 m. This whole problem is on a 2D plane with the spacecraft's current position at (0,6700000). It's current velocity is at 8,000 m/s along the x-axis. I would like to know how to determine the spacecraft's x and y coordinates at any point in time. I've made this problem only to satisfy my mathematical curiosity.
Acceleration to Earth: F=GM/r^2
G= Gravitational Constant = 6.67384e-11 (m^3/kg*s^2)
Earth's Mass: 5.97e24
The Attempt at a Solution
I have tried multiple ways to get the solution and most of them ended up nowhere. So, please, can you explain how to get the answer? Thanks for your replies.