Say you have an object that starts at a distance r, from a massive point-mass m that attracts it. This object has an initial velocity v tangential to said distance.
For initial velocity = zero, the trajectory is simple: it's a straight line. For any velocity larger than what is required to stay in orbit, the trajectory will be a circle, parabola, or hyperbola depending on eccentricity
What would be the trajectory of an object who's speed is too low to stay in orbit? How would you mathematically and precisely define said trajectory?