Constants of Orbital Motion Specific Mechanical Energy To generalize this equation, we ignore the mass, so both sides of the equation are divided my “m”. Doing so defines a new flavor of mechanical energy called Specific Mechanical Energy

 = spacecraft’s specific mechanical energy V = spacecraft’s velocity  = gravitational parameter  * 10^5 km^3/s^2 for earth R = spacecraft’s distance from Earth’s center

One parameter represents a spacecraft’s mean, or average, distance from the primary focus  =-  /2a

Specific Angular Momentum In astrodynamics, the specific relative angular momentum of an orbiting body with respect to a central body is the relative angular momentum of the first body per unit mass. Specific relative angular momentum plays a pivotal role in definition of orbit equations. Specific relative angular momentum, represented by the symbol, is defined as the cross product of the position vector and velocity vector of the orbiting body relative to the central body:

r = is the orbital position vector of the orbiting body relative to the central body,orbital position vector v = is the orbital velocity vector of the orbiting body relative to the central body, p = is the linear momentum of the orbiting body relative to the central body, m = is the mass of the orbiting body, and h = is the relative angular momentum of the orbiting body with respect to the central body. Under standard assumptions for an orbiting body in a trajectory around central body at any given time the vector is perpendicular to the osculating orbital plane defined by orbital position and velocity vectors.