Escape Velocity - Orbit

Orbit

If an object attains escape velocity, but is not directed straight away from the planet, then it will follow a curved path. Although this path does not form a closed shape, it is still considered an orbit. Assuming that gravity is the only significant force in the system, this object's speed at any point in the orbit will be equal to the escape velocity at that point (due to the conservation of energy, its total energy must always be 0, which implies that it always has escape velocity; see the derivation above). The shape of the orbit will be a parabola whose focus is located at the center of mass of the planet. An actual escape requires of course that the orbit not intersect the planet nor its atmosphere, since this would cause the object to crash. When moving away from the source, this path is called an escape orbit. Escape orbits are known as C3 = 0 orbits. C3 is the characteristic energy, = −GM/a, where a is the semi-major axis, which is infinite for parabolic orbits.

When there are many gravitating bodies, such as in the solar system, a rocket that travels at escape velocity from one body, say Earth, will not travel to an infinite distance because it needs an even higher speed to escape the Sun's gravity. Near the Earth, the rocket's orbit will appear parabolic, but will become an ellipse around the Sun, except when it is perturbed by the Earth, whose orbit it must still intersect, and other bodies.