Orbital elements: Difference between revisions
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We'll use the Clifford geometric algebra library but only for the vector operations. |
We'll use the Clifford geometric algebra library but only for the vector operations. |
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<lang perl6> |
<lang perl6>subset PositiveReal of Real where * >= 0; |
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subset PositiveReal of Real where * >= 0; |
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sub orbital-state-vectors( |
sub orbital-state-vectors( |
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PositiveReal :$semimajor-axis, |
PositiveReal :$semimajor-axis, |
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Real :$true-anomaly |
Real :$true-anomaly |
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) { |
) { |
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use Clifford; |
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my ($i, $j, $k) = @e[^3]; |
my ($i, $j, $k) = @e[^3]; |
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Revision as of 12:20, 7 July 2016
Orbital elements is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
The purpose of this task is to convert orbital elements into orbital state vectors. It will be assumed that µ = GM = 1.
TODO: pick an example from a reputable source.
Perl 6
We'll use the Clifford geometric algebra library but only for the vector operations.
<lang perl6>subset PositiveReal of Real where * >= 0; sub orbital-state-vectors(
PositiveReal :$semimajor-axis, PositiveReal :$eccentricity, Real :$inclination, Real :$longitude-of-ascending-node, Real :$argument-of-periapsis, Real :$true-anomaly
) {
use Clifford; my ($i, $j, $k) = @e[^3];
sub rotate($a is rw, $b is rw, Real \α) { ($a, $b) = cos(α)*$a + sin(α)*$b, -sin(α)*$a + cos(α)*$b; } rotate($i, $j, $longitude-of-ascending-node); rotate($j, $k, $inclination); rotate($i, $j, $argument-of-periapsis);
my \l = $eccentricity == 1 ?? # PARABOLIC CASE 2*$semimajor-axis !! $semimajor-axis*(1 - $eccentricity**2);
my ($c, $s) = map {.($true-anomaly)}, &cos, &sin;
my \r = l/(1 + $eccentricity*$c); my \rprime = $s*r**2/l;
my $position = r*($c*$i + $s*$j);
my $speed = (rprime*$c - r*$s)*$i + (rprime*$s + r*$c)*$j; $speed /= sqrt(($speed·$speed).Real); $speed *= sqrt(2/r - 1/$semimajor-axis);
{ :position($position X· @e[^3]), :speed($speed X· @e[^3]) }
}
say orbital-state-vectors
semimajor-axis => 1, eccentricity => 0.1, inclination => 0, longitude-of-ascending-node => pi/6, argument-of-periapsis => 0, true-anomaly => 0;
</lang>
- Output:
{position => (0.779422863405995 0.45 0), speed => (-0.552770798392567 0.957427107756338 0)}