Physics

The key is recognizing that escape velocity and orbital velocity are both rooted in energy and gravitational force, but they answer different questions. Escape velocity is the minimum speed needed to break free from gravity entirely (reaching infinite distance with zero speed), while orbital velocity is the speed required to fall around Earth in a circular path. Both depend on $\sqrt{GM/r}$, but escape velocity needs twice the kinetic energy, so their ratio is a clean, memorable constant you can derive from energy conservation.

The key is recognizing that escape velocity and orbital velocity are both rooted in energy and gravitational force, but they answer different questions. Escape velocity is the minimum speed needed to break free from gravity entirely (reaching infinite distance with zero speed), while orbital velocity is the speed required to fall around Earth in a circular path. Both depend on $\sqrt{GM/r}$, but escape velocity needs twice the kinetic energy, so their ratio is a clean, memorable constant you can derive from energy conservation.