Orbital elements: Difference between revisions
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NB. Om: Longitude of the ascending node
NB. w: argument of Periapsis (the other "omega")
NB. f: true anomaly (varies with time)
L=. a*2:`]@.*1-*:e
'c s'=. 2{.,F=. 2 R f
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position,:speed
}}</lang>
The true anomaly, argument of Periapsis, Longitude of the ascending node and inclination are all angles. And we use the dot product of their rotation matrices (in that order) to find the orientation of the orbit and the object's position in that orbit. Here, <code>R</code> finds the rotation matrix for a given angle around a given axis. Here's an example of what R gives us for a sixty degree angle:
<lang J> 0 1 2 R&.> 60r180p1 NB. rotate around first, second or third axis
┌────────────────────┬────────────────────┬────────────────────┐
│1 0 0│ 0.5 0 _0.866025│ 0.5 0.866025 0│
│0 0.5 0.866025│ 0 1 0│_0.866025 0.5 0│
│0 _0.866025 0.5│0.866025 0 0.5│ 0 0 1│
└────────────────────┴────────────────────┴────────────────────┘</lang>
Task example:<lang J> orbitalStateVectors 1 0.1 0 355r678 0 0
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