relative to the departure planet at periapsis is: The excess velocity vector for a hyperbola is displaced from the periapsis tangent by a characteristic angle, therefore the periapsis injection burn must lead the planetary departure point by the same angle: The geometric equation for eccentricity of an ellipse cannot be used for a hyperbola. But the eccentricity can be calculated from dynamics formulations as: where h is the specific angular momentum as given above in the Orbital flight section, calculated at the periapsis: and ε is the specific energy: Also, the equations for r and v given in Orbital flight depend on the semi-major axis, and thus are unusable for an escape trajectory. But setting radius at periapsis equal to the r equation at zero anomaly gives an alternate expression for the semi-latus rectum: which gives a more general equation for radius versus anomaly which is usable at any eccentricity: Substituting the alternate expression for p also gives an alternate expression for a (which is defined for a hyperbola, but no longer represents the semi-major axis). This gives an equation for velocity versus radius which is likewise usable at any eccentricity: The equations for flight path angle and anomaly versus time given in Orbital flight are also usable for hyperbolic trajectories. Launch windows There is a great deal of variation with time of the velocity change required for a mission, because of the constantly varying relative positions of the planets. Therefore, optimum launch windows are often chosen from the results of porkchop plots that show contours of characteristic energy (v∞2) plotted versus departure and arrival time. Atmospheric entry Controlled entry, descent, and landing of a vehicle is achieved by shedding the excess kinetic energy through aerodynamic heating from drag, which requires some means of heat shielding, and/or retrograde thrust. Terminal descent is usually achieved by means of parachutes and/or air brakes. Attitude control Since spacecraft spend most of their flight time coasting unpowered through the vacuum of space, they are unlike aircraft in that their flight trajectory is not determined by their attitude (orientation), except during atmospheric flight to control the forces of lift and drag, and during powered flight to align the thrust vector. Nonetheless, attitude control is often maintained in unpowered flight to keep the spacecraft in a fixed orientation for purposes of astronomical observation, communications, or for solar power generation; or to place it into a controlled