# Orbital elements

``````func orbital_state_vectors(
semimajor_axis,
eccentricity,
inclination,
longitude_of_ascending_node,
argument_of_periapsis,
true_anomaly
) {
var (i, j, k) = (
Vector(1, 0, 0),
Vector(0, 1, 0),
Vector(0, 0, 1),
)

func muladd(v1, x1, v2, x2) {
(v1 * x1) + (v2 * x2)
}

func rotate(Ref i, Ref j, α) {
(*i, *j) = (
)
}

rotate(\i, \j, longitude_of_ascending_node)
rotate(\j, \k, inclination)
rotate(\i, \j, argument_of_periapsis)

var l = (eccentricity == 1 ? 2*semimajor_axis
: semimajor_axis*(1 - eccentricity**2))

var (c, s) = with(true_anomaly) { (.cos, .sin) }

var r = l/(1 + eccentricity*c)
var rprime = (s * r**2 / l)
var position = muladd(i, c, j, s)*r

var speed = muladd(i, rprime*c - r*s, j, rprime*s + r*c)
speed /= speed.abs
speed *= sqrt(2/r - 1/semimajor_axis)

struct Result { position, speed }
Result(position, speed)
}

for args in ([
[1, 0.1, 0, 355/(113*6), 0, 0],
[1, 0.1, Num.pi/18, Num.pi/6, Num.pi/4, 0]
]) {
var r = orbital_state_vectors(args...)

say "Arguments: #{args}:"
say "Position : #{r.position}"
say "Speed    : #{r.speed}\n"
}
``````

#### Output:

``````Arguments: [1, 1/10, 0, 355/678, 0, 0]:
Position : [0.779422843398679832042176328223663037464703527986, 0.450000034653684237432302249506712706822033851071, 0]
Speed    : [-0.552770840960443759673279062314259546277084494097, 0.957427083179761535246200368614952095349966503287, 0]

Arguments: [1, 1/10, 0.174532925199432957692369076848861271344287188854, 0.523598775598298873077107230546583814032861566563, 0.785398163397448309615660845819875721049292349844, 0]:
Position : [0.23777128398220654779107184959165027147748809404, 0.860960261697715834668966272382699039216399966872, 0.110509023572075562109405412890808505271310143909]
Speed    : [-1.06193301748006004757467368094494935655538772696, 0.275850020569249507846452830330085489348356659642, 0.135747024865598167166145512759280712986072818844]
``````