The specific orbital energy (ϵ) of a hyperbolic trajectory is greater than zero.

The orbital energy conservation equation for hyperbolic trajectory is given as,

∈ = µ / -2a

∈ = specific orbital energy

µ= is the standard gravitational parameter

a = the length of the semi-major axis (a > 0 for ellipses, a = ∞ or 1/a = 0 for parabolas,

                                                            and a < 0 for hyperbolas)

In astrodynamics or celestial mechanics a hyperbolic trajectory is a Kepler orbit with eccentricity greater than 1.
The orbit formula Hyperbolic orbits is,

r = the radial distance of the orbiting body from the mass center of the central body

h = specific angular momentum of the orbiting body

µ  = is the standard gravitational parameter

Ɵ = the true anomaly of the orbiting body

e = eccentricity

In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit. It eccentricity is equal to 1. When moving away from the source it is referred to as an escape orbit, otherwise a capture orbit.

The equation or formula for Parabolic orbits is,

r = the radial distance of the orbiting body from the mass center of the central body

h = specific angular momentum of the orbiting body

µ = is the standard gravitational parameter

Ɵ = the true anomaly of the orbiting body.

In astrodynamics, the orbital-energy-invariance law or vis-viva equation, is one of the equations that model the motion of orbiting bodies.

It represents the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva (Latin meaning – living force) accumulated or lost in the system while the work is being done.

The formula for orbital-energy-invariance law or Vis-viva equation is given as,

v = the relative speed of the two bodies

G = the gravitational constant

M = mass of the central body

r = the distance between the orbiting bodies

a = the length of the semi-major axis(a > 0 for ellipses, a = ∞ or 1/a = 0 for parabolas,

                                                            and a < 0 for hyperbolas)

The specific energy (energy per unit mass) of a space vehicle is composed of two components, the specific potential energy and the specific kinetic energy.

The specific orbital energy of two orbiting bodies is the constant sum of their mutual potential energy and their total kinetic energy, divided by the reduced mass.

Under standard assumptions, specific orbital energy (ϵ) of elliptic orbit is negative and the orbital energy conservation equation, also known as the Vis-viva equation, for this orbit can take the form as,

ϵ = -μ /2a

ϵ = <0

v =  Orbital speed of body traveling along an elliptical orbit.

μ  = is the standard gravitational parameter

r = the distance between the orbiting bodies

a = the length of the semi-major axis