
In
astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
, and in particular in
astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational
Kepler orbit (i.e. an
elliptic or other conic one) that it would have around its
central body if
perturbations were absent. That is, it is the orbit that coincides with the current
orbital state vectors
In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are
cartesian coordinate system, Cartesian vectors of position (vector), position (\mathbf) and velocity (\mathbf) that together with their t ...
(position and
velocity
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...
).
Etymology
The word ''
osculate'' is
Latin
Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
for "kiss". In mathematics, two curves osculate when they just touch, without (necessarily) crossing, at a point, where both have the same position and slope, i.e. the two curves "kiss".
Kepler elements
An osculating orbit and the object's position upon it can be fully described by the six standard Kepler
orbital elements (osculating elements), which are easy to calculate as long as one knows the object's position and velocity relative to the central body. The osculating elements would remain constant in the absence of
perturbations. Real astronomical orbits experience perturbations that cause the osculating elements to evolve, sometimes very quickly. In cases where general celestial mechanical analyses of the motion have been carried out (as they have been for the major planets, the Moon, and other
planetary satellites), the orbit can be described by a set of mean elements with secular and periodic terms. In the case of
minor planet
According to the International Astronomical Union (IAU), a minor planet is an astronomical object in direct orbit around the Sun that is exclusively classified as neither a planet nor a comet. Before 2006, the IAU officially used the term ''minor ...
s, a system of
proper orbital elements has been devised to enable representation of the most important aspects of their orbits.
Perturbations
Perturbations that cause an object's osculating orbit to change can arise from:
* A non-spherical component to the central body (when the central body can be modeled neither with a
point mass nor with a spherically symmetrical mass distribution, e.g. when it is an
oblate spheroid).
* A third body or multiple other bodies whose gravity perturbs the object's orbit, for example the effect of the
Moon
The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...
's gravity on objects orbiting Earth.
* A relativistic correction.
* A non-
gravitational force acting on the body, for example force arising from:
** Thrust from a
rocket engine
A rocket engine is a reaction engine, producing thrust in accordance with Newton's third law by ejecting reaction mass rearward, usually a high-speed Jet (fluid), jet of high-temperature gas produced by the combustion of rocket propellants stor ...
** Releasing, leaking, venting or
ablation of a material
** Collisions with other objects
**
Atmospheric drag
In fluid dynamics, drag, sometimes referred to as fluid resistance, is a force acting opposite to the direction of motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers, two solid surfaces, or b ...
**
Radiation pressure
**
Solar wind
The solar wind is a stream of charged particles released from the Sun's outermost atmospheric layer, the Stellar corona, corona. This Plasma (physics), plasma mostly consists of electrons, protons and alpha particles with kinetic energy betwee ...
pressure
** Switch to a non-inertial reference frame (e.g. when a satellite's orbit is described in a reference frame associated with the
precessing equator of the planet).
Parameters
An object's orbital parameters will be different if they are expressed with respect to a
non-inertial reference frame (for example, a frame co-precessing with the primary's equator), than if it is expressed with respect to a (non-rotating)
inertial reference frame.
Put in more general terms, a perturbed trajectory can be analysed as if assembled of points, each of which is contributed by a curve out of a sequence of curves. Variables parameterising the curves within this family can be called ''
orbital elements''. Typically (though not necessarily), these curves are chosen as Keplerian conics, all of which share one focus. In most situations, it is convenient to set each of these curves tangent to the trajectory at the point of intersection. Curves that obey this condition (and also the further condition that they have the same curvature at the point of tangency as would be produced by the object's gravity towards the central body in the absence of perturbing forces) are called osculating, while the variables parameterising these curves are called osculating elements. In some situations, description of orbital motion can be simplified and approximated by choosing orbital elements that are not osculating. Also, in some situations, the standard (Lagrange-type or Delaunay-type) equations furnish orbital elements that turn out to be non-osculating.
[For details see: ;
]
References
External links
* Diagram of a sequence of osculating orbits for the escape from Earth orbit by the ion-driven
SMART-1 spacecraft
ESA Science & Technology - SMART-1 Osculating Orbit up to 25.08.04* A sequence of osculating orbits for the approach to the Moon by the
SMART-1 spacecraft
ESA Science & Technology - SMART-1 Osculating Orbit up to 09.01.05
; Videos
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{{Authority control
Astrodynamics
Orbital perturbations