Hyperbolic Trajectory - Velocity

Velocity

Under standard assumptions the orbital velocity of a body traveling along a hyperbolic trajectory can be computed as (Vallado):

where:

• is standard gravitational parameter,
• is radial distance of orbiting body from central body,
• is the negative semi-major axis.

Under standard assumptions, at any position in the orbit the following relation holds for orbital velocity, local escape velocity and hyperbolic excess velocity :

Note that this means that a relatively small extra delta-v above that needed to accelerate to the escape speed, results in a relatively large speed at infinity.