we see that both the larger and the smaller mass must be accelerated in the gravitational field. Relative to the center of mass the velocity of the larger mass ( , for planet) can be expressed in terms of the velocity of the smaller mass (, for rocket). We get . The 'barycentric' escape velocity now becomes : while the 'relative to the other' escape velocity becomes : . Height of lower-velocity trajectories Ignoring all factors other than the gravitational force between the body and the object, an object projected vertically at speed from the surface of a spherical body with escape velocity and radius will attain a maximum height satisfying the equation which, solving for h results in where is the ratio of the original speed to the escape velocity Unlike escape velocity, the direction (vertically up) is important to achieve maximum height. Trajectory If an object attains exactly escape velocity, but is not directed straight away from the planet, then it will follow a curved path or trajectory. Although this trajectory does not form a closed shape, it can be referred to as an orbit. Assuming that gravity is the only significant force in the system, this object's speed at any point in the trajectory 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 trajectory will be a parabola whose focus is located at the center of mass of the planet. An actual escape requires a course with a trajectory that does not intersect with the planet, or 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/2a, where a is the semi-major axis, which is infinite for parabolic trajectories. If the body has a velocity greater than escape velocity then its path will form a hyperbolic trajectory and it will have an excess hyperbolic velocity, equivalent to the extra energy the body has. A relatively small extra delta-v above that needed to accelerate to the escape speed can result in a relatively large speed at infinity. Some orbital manoeuvres make use of this fact. For example, at a