Standard assumptions in astrodynamics

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• A1: and are the only objects in the universe
  Universe
  
  The universe is defined as everything that physically exists: the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and physical constants that govern them....
   and thus influence of other objects is disregarded,
• A2: The mass of the orbiting body
  Orbiting body
  
  In astrodynamics, an orbiting body is a body that orbits central body . Under standard assumptions in astrodynamics:* it is less massive than the central body by several orders of magnitude ....
    is far smaller than central body
  Central body
  
  In astrodynamics a central body is a body that is being orbited by an orbiting body . Under standard assumptions in astrodynamics:* it is more massive than the orbiting body by several orders of magnitude ,...
   , i.e.:

• A3: As the disparities in masses between and are so great, standard gravitational parameter
  Standard gravitational parameter
  
  In astrodynamics, the standard gravitational parameter of a celestial body is the product of the gravitational constant and the mass :The units of the standard gravitational parameter are km3s-2...
    includes only the mass of the central body
  Central body
  
  In astrodynamics a central body is a body that is being orbited by an orbiting body . Under standard assumptions in astrodynamics:* it is more massive than the orbiting body by several orders of magnitude ,...
  , in each case i.e.:

• A4: Orbit
  ORBit
  
  ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
   of orbiting body is not perturbed in any way and the effects of general relativity are so small that they can be ignored, so the only orbits allowed are the circular
  Circular orbit
  
  In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. It is an example of a rotation around a fixed axis: this axis is the line through the center of mass perpendicular to the plane of motion....
  , elliptic
  Elliptic orbit
  
  In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1. In a gravitational two-body problem with the eccentricity in this range both bodies follow Similarity elliptic orbits with the same orbital period around their common barycenter....
  , parabolic
  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....
   and hyperbolic
  Hyperbolic trajectory
  
  In astrodynamics or celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1. Under standard assumptions in astrodynamics a body traveling along this trajectory will orbital coast to infinity, arriving there with hyperbolic excess velocity relative to the central body....
   orbits of classical Newtonian theory.
• A5: One focus
  Focus (geometry)
  
  In geometry, the foci, , are a pair of special points used in describing conic sections. The four types of conic sections are the circle, parabola, ellipse, and hyperbola....
   of orbiting body's orbit
  ORBit
  
  ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
   coincides with the center of the central body,

Examples where those assumptions do not hold

• A1:
• Although escape velocity
  Escape velocity
  
  In physics, escape velocity is the speed where the kinetic energy of an object is equal to the magnitude of its gravitational potential energy, as calculated by the equation,...
   is described as a velocity that should allow an orbiting body to coast to infinity and arrive there with zero velocity, for most cases this will not be true. E.g. If a spacecraft were launched from the ground, achieving escape velocity with respect to Earth, it will not escape to infinity (e.g. leave the Solar System) because it will eventually succumb to the gravitational influence of the Sun.
• A rocket
  Rocket
  
  A rocket or rocket vehicle is a missile, aircraft or other vehicle which obtains thrust by the Reaction of the rocket to the ejection of fast moving fluid exhaust from a rocket engine....
   applying thrust
  Thrust
  
  Thrust is a reaction force described quantitatively by Isaac Newton's Newton's laws of motion. When a system expels or acceleration mass in one direction the accelerated mass will cause a proportional but opposite force on that system....
  
• An object experiencing atmospheric drag
• A2: Orbital motion within a binary star
  Binary star
  
  A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star or secondary....
   system

Two bodies orbiting each other

See also

• n-body problem
  N-body problem
  
  The n-body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i.e., Newton's laws of motion and gravity....