The motion track of the celestial body is a conic curve (ellipse, parabola and hyperbola), of which the elliptical curve track is a Keplerian track, and the escape parabola and hyperbola track are non Keplerian tracks.Non Kepler orbits can be divided into single center gravitational field and multi center gravitational field.
Human scientific understanding of celestial body movement is based onCopernicus(1473-1543), Kepler (1571-1630) summarized the three laws of planetary motion around the sun based on previous astronomical observation data, which is calledKepler's three laws。After Kepler and Galileo (1564-1642), Newton (1642-1727) proposedLaw of universal gravitationAnd the three laws of motion of objects (later calledNewton's three laws）Newtonian mechanics based on this is the foundation of celestial mechanicsAerospace dynamicsThe foundation of.Kepler's lawThe kinematic description of the orbital motion law of the planet (also applicable to spacecraft) is given, and Newtonian mechanics gives a dynamic explanation of this orbital motion law.Kepler's law can be strictly proved by Newtonian mechanics.From Copernicus' theory of heliocentric geodynamics to the establishment of Newtonian mechanics is the first leap in human understanding of the universe.
Two body problemIt is a basic problem in celestial mechanics. It refers to the motion law of two celestial bodies that can be regarded as particles under the unique gravitational action between them.Two body problem can be usedNewton's law of universal gravitationandNewton's law of motionTo describe and completely solve.Kepler's three laws are the solution of the two body problem.Under the assumption of the two body problem, further assuming that the mass of the main body is far greater than that of the secondary body (or spacecraft), and that the main body is inertial fixed, it becomes a restrictive two body problem.
The orbit of a spacecraft refers to the trajectory of its center of mass under the action of celestial gravity and other external forces.Due to the effect of other external forces other than the gravity of the center of the celestial body, the orbital motion of the spacecraft does not strictly follow the solution of the two body problem, which occurs when the spacecraft is subject to the perturbation of the natural environment such as the earth's non spherical and uneven mass distribution, atmospheric resistance, solar light pressure, and the gravity of other celestial bodies,It also occurs when the spacecraft is subjected to the control force generated by its initiative.In these cases, the orbit of spacecraft is no longer strict and sometimes even not ideal Kepler orbit at all, so the problem of non Kepler orbit is proposed.From the perspective of orbit dynamics and orbit control, spacecraft orbits can be divided into Kepler orbits (KO) and non Kepler orbits (NKO). Spacecraft Kepler orbits can be divided into ideal KO and deemed KO. Spacecraft non Kepler orbits can be divided into non essential NKO and essential NKO. There are natural (passive) and artificial (active) cases in these two types of NKO[1]。
Kepler orbit
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Kepler Orbital Source
As a noun term, Kepler orbits come fromKepler's three laws, originated from the study of the laws of motion of planets around the sun - planetary orbits.The term "Kepler orbit" was put forward by people after Kepler, and extended Kepler orbit to the solution of the two body problem.The English term for Keplerian orbits is Keplerian orbits, which is abbreviated as KO in this paper.Since the orbital motion of spacecraft also conforms to the three laws of Kepler, the term "Kepler orbit" also applies to spacecraft.The Kepler orbit mentioned in this paper mostly refers to the Kepler orbit of spacecraft.
definition
Kepler orbit definition includes:
The orbit of a celestial body or spacecraft that conforms to Kepler's three laws.
The orbit of a celestial body or spacecraft obtained from the solution of the two body problem.
Therefore, Kepler orbit is also calledTwo body problemTrack.Kepler orbits that meet the above definition are also called ideal Kepler orbits.
Classification and characteristics
Figure 1
The classification of Kepler orbits is shown in Figure 1.
The "treat as" in the figure means "it can be regarded as".The characteristics of deemed KO are shown in the figure.The Kepler orbit of the spacecraft can be solved by the following basic equations of the two body problem:
The above equation describes the orbital motion of spacecraft relative to celestial bodies in the inertial coordinate system.Where r is the position vector from the celestial body (mass recorded as m1) to the spacecraft (m2), μ=G (m1+m2) is the gravitational constant of the two body system, and G isUniversal gravitational constant。Since m1>>m2, only the gravity of m1 on m2 can be considered. In this case, the Kepler orbit of the spacecraft can be regarded as the solution of the restricted two body problem, that is, the trajectory of motion (with central force) in the gravitational field of the center of the inertial fixed celestial body.
The orbit equation of the spacecraft can be solved from the above equation
Kepler orbit can use the six elements of Kepler orbit (referred to as orbital elements, also known asNumber of tracks）To represent.It must be pointed out that the spacecraft Kepler orbit is an ideal orbit under certain assumptions.Artificial earth satelliteAfter appearing, just followKepler's three lawsAnd utilizationTwo body problemIt is impossible to accurately predict the position of the satellite, so the term spacecraft orbit perturbation problem and perturbation orbit was proposed, and then the term non Kepler orbit came into being.
