Characteristic energy

Encyclopedia

In astrodynamics

a

, is a measure of the energy required for an interplanetary mission that requires attaining an excess orbital velocity

over an escape velocity

required for additional orbital maneuver

s. The unit of the characteristic energy is km

Characteristic energy can be computed as:

where

is the orbital velocity

when the orbital distance tends to infinity. Note that, since the kinetic energy is one half m C

() of the escaping object.

(e.g. earth) on a parabolic trajectory

:

on a hyperbolic trajectory

:

where:

is standard gravitational parameter

,

is length of semi-major axis

of orbit

's hyperbola

.

Astrodynamics

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It...

a

**characteristic energy**(), a form of specific energySpecific energy

Specific energy is defined as the energy per unit mass. Common metric units are J/kg. It is an intensive property. Contrast this with energy, which is an extensive property. There are two main types of specific energy: potential energy and specific kinetic energy. Others are the gray and sievert,...

, is a measure of the energy required for an interplanetary mission that requires attaining an excess orbital velocity

Orbital velocity

Orbital velocity can refer to the following:* The orbital speed of a body in a gravitational field.* The velocity of particles due to wave motion, in particular in wind waves....

over an escape velocity

Escape velocity

In physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero gravitational potential energy is negative since gravity is an attractive force and the potential is defined to be zero at infinity...

required for additional orbital maneuver

Orbital maneuver

In spaceflight, an orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft.For spacecraft far from Earth—for example those in orbits around the Sun—an orbital maneuver is called a deep-space maneuver .-delta-v:...

s. The unit of the characteristic energy is km

Kilometre

The kilometre is a unit of length in the metric system, equal to one thousand metres and is therefore exactly equal to the distance travelled by light in free space in of a second...

^{2}sSecond

The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

^{-2}.Characteristic energy can be computed as:

where

is the orbital velocity

Orbital velocity

Orbital velocity can refer to the following:* The orbital speed of a body in a gravitational field.* The velocity of particles due to wave motion, in particular in wind waves....

when the orbital distance tends to infinity. Note that, since the kinetic energy is one half m C

_{3}is in fact equal to twice the magnitude of the specific orbital energySpecific orbital energy

In the gravitational two-body problem, the specific orbital energy \epsilon\,\! of two orbiting bodies is the constant sum of their mutual potential energy and their total kinetic energy , divided by the reduced mass...

() of the escaping object.

## Parabolic trajectory

For a spacecraft that is leaving the central bodyCentral body

In astrodynamics a central body is a body that is being orbited by an secondary body, or satellite .The central body is properly referred to as the primary body.Under standard assumptions in astrodynamics:...

(e.g. earth) on a parabolic trajectory

Parabolic trajectory

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

:

## Hyperbolic trajectory

For a spacecraft that is leaving the central bodyCentral body

In astrodynamics a central body is a body that is being orbited by an secondary body, or satellite .The central body is properly referred to as the primary body.Under standard assumptions in astrodynamics:...

on a hyperbolic trajectory

Hyperbolic trajectory

In astrodynamics or celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1. Under standard assumptions a body traveling along this trajectory will coast to infinity, arriving there with hyperbolic excess velocity relative to the central body. Similarly to...

:

where:

is standard gravitational parameter

Standard gravitational parameter

In astrodynamics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body.\mu=GM \ The SI units of the standard gravitational parameter are m3s−2....

,

is length of semi-major axis

Semi-major axis

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape...

of orbit

Orbit

In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

's hyperbola

Hyperbola

In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...

.

## See also

- Specific orbital energySpecific orbital energyIn the gravitational two-body problem, the specific orbital energy \epsilon\,\! of two orbiting bodies is the constant sum of their mutual potential energy and their total kinetic energy , divided by the reduced mass...
- OrbitOrbitIn physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
- Parabolic trajectoryParabolic trajectoryIn astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1. When moving away from the source it is called an escape orbit, otherwise a capture orbit...
- Hyperbolic trajectoryHyperbolic trajectoryIn astrodynamics or celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1. Under standard assumptions a body traveling along this trajectory will coast to infinity, arriving there with hyperbolic excess velocity relative to the central body. Similarly to...