You can input initial position and velocity and run a simulation. The satellite will move around the Earth according to the initial condition. You can check that the satellite may escape the Earth at some initial condition. You can change the simulation speed and screen scale. By changing the initial position and velocity, the satellite orbit becomes a circle or an ellipse, or a hyperbola (escape the Earth).
This simulation uses the exact values, so the orbit is very accurate. You can vary the initial values and see the effect of each parameter.
Enjoy the physics!