In the gravitational two-body problem, the specific orbital energy (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy () and their total kinetic energy (), divided by the reduced mass. According to the orbital energy conservation equation (also referred to as vis-viva equation), it does not vary with time:
where
is the relative orbital speed;
is the orbital distance between the bodies;
is the sum of the standard gravitational parameters of the bodies;
is the specific relative angular momentum in the sense of relative angular momentum divided by the reduced mass;
is the orbital eccentricity;
is the semi-major axis.
It is expressed in or . For an elliptic orbit the specific orbital energy is the negative of the additional energy required to accelerate a mass of one kilogram to escape velocity (parabolic orbit). For a hyperbolic orbit, it is equal to the excess energy compared to that of a parabolic orbit. In this case the specific orbital energy is also referred to as characteristic energy.
For an elliptic orbit, the specific orbital energy equation, when combined with conservation of specific angular momentum at one of the orbit's apsides, simplifies to:
where
is the standard gravitational parameter;
is semi-major axis of the orbit.
For a parabolic orbit this equation simplifies to
For a hyperbolic trajectory this specific orbital energy is either given by
or the same as for an ellipse, depending on the convention for the sign of a.
In this case the specific orbital energy is also referred to as characteristic energy (or ) and is equal to the excess specific energy compared to that for a parabolic orbit.
It is related to the hyperbolic excess velocity (the orbital velocity at infinity) by
It is relevant for interplanetary missions.
Thus, if orbital position vector () and orbital velocity vector () are known at one position, and is known, then the energy can be computed and from that, for any other position, the orbital speed.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
This course is a "concepts" course. It introduces a variety of concepts in use in the design of a space mission, manned or unmanned, and in space operations. it is partly based on the practical space
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section.
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section.
In astrodynamics, the characteristic energy () is a measure of the excess specific energy over that required to just barely escape from a massive body. The units are length2 time−2, i.e. velocity squared, or energy per mass. Every object in a 2-body ballistic trajectory has a constant specific orbital energy equal to the sum of its specific kinetic and specific potential energy: where is the standard gravitational parameter of the massive body with mass , and is the radial distance from its center.
Context. Isolated local group (LG) dwarf galaxies have evolved most or all of their life unaffected by interactions with the large LG spirals and therefore offer the opportunity to learn about the intrinsic characteristics of this class of objects. Aims. O ...
2020
, ,
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients requires solving loc ...
EPFL2020
,
A chemo-dynamical analysis of 115 metal-poor candidate stars selected from the narrow band Pristine photometric survey is presented based on CFHT high-resolution ESPaDOnS spectroscopy, We have discovered 28 new bright (V < 15) stars with I Fe/H]