Talk:Orbital state vectors
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[edit] Linear eccentricity
Linear eccentricity is redirected to eccentricity, then what is the difference? WouterVH 13:26, 8 May 2005 (UTC)
[edit] Definition of "Up" in the frame of reference
It should be made clearer how the direction of "up" is defined for the coordinate system. Is it North? A normal vector to the ecliptic plane? The local "upwards" direction of the launch site?
One unambiguous method of specifying an 'up' direction would be to use the direction of the specific angular momentum r x v - this vector is normal to the plane of the orbit. This would have several advantages, namely: [1] the z-component of linear velocity would always be zero, and the analysis could concentrate upon the determination of x and y components of the velocity vector (because by definition the orbit is a planar motion); [2] the coordinate system thus formed would obey the standard mathematical conventions for coordinate systems (the axes would be a right handed set because of the manner in which the vector cross product is defined); [3] the position vector would also have a z-coordinate that was always zero, thus reducing the analysis to a two-dimensional one. Of course, whether this choice of 'up' is the choice that is made in a given analysis is moot: one has to delve deeper into the details of a particular analysis to determine which direction is considered to be the z-direction for the purpose of that analysis. A typical (though by no means universal) choice is to define the z-axis as normal to the plane of the Earth's orbit around the Sun. There are, of course, two such possible normal directions, and the one that is usually chosen to be positive is, if I recall correctly, such that a vector in this direction makes an acute angle with a vector directed outwards from the North pole of the Earth (i.e., in the vector dot product of the two vectors, 0 < cos A <= 1). Of course, the determination of the z-direction in this instance is a geocentric one: if one is interested in planetary motions about the Sun, a heliocentric system is generally chosen (the centre of the coordinate system being fixed upon the largest gravitating mass). In this case, the z-direction would be the same. For more exotic work, involving a galactic coordinate system, the definition of the z-direction would be normal to the plane in which the bulk of the galaxy's stars reside (for a spiral galaxy such as our own). The point that needs to be stressed here is that a natural and convenient z-direction for the purpose of the analysis is chosen, and that in many cases the nature of the system being considered makes particular choices of z-direction thus natural and convenient. For a general analysis not tied to a particular set of bodies, the normal to the orbiting plane defined by r x v is probably the most natural and convenient choice for the reasons given above, but for particular systems (e.g., spacecraft orbiting the Earth) a different choice, frequently based upon the geographical coordinate system for Earth itself, makes more sense from a navigational standpoint, particularly if the intention is for the spacecraft to perform specific duties related to ground based tracking stations, or the spacecraft is a manned re-entry vehicle. Choosing a coordinate system that makes it easy for one's astronauts to arrive back home with a minimum of computational overhead determines the choice of 'z' in that case. Trouble is, unless whoever chooses the z-direction makes that choice explicit, determining it by inspection may sometimes be a nontrivial task! Calilasseia 02:56, 25 July 2006 (UTC)
