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Orbital elements: Difference between revisions

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Orbital elements (view source)

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=={{header|Phix}}==
{{trans|Python}}
<!--<lang Phix>function vabs(sequence vphixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
return sqrt(sum(sq_power(v,2)))
<span style="color: #008080;">function</span> <span style="color: #000000;">vabs</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)))</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function mulAdd(sequence v1, atom x1, sequence v2, atom x2)
return sq_add(sq_mul(v1,x1),sq_mul(v2,x2))
<span style="color: #008080;">function</span> <span style="color: #000000;">mulAdd</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">v2</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">))</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function rotate(sequence i, j, atom alpha)
atom ca = cos(alpha),
<span style="color: #008080;">function</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">alpha</span><span style="color: #0000FF;">)</span>
sa = sin(alpha)
<span style="color: #004080;">atom</span> <span style="color: #000000;">ca</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">alpha</span><span style="color: #0000FF;">),</span>
return {mulAdd(i,ca,j,sa),mulAdd(i,-sa,j,ca)}
<span style="color: #000000;">sa</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">alpha</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">mulAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ca</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">),</span><span style="color: #000000;">mulAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ca</span><span style="color: #0000FF;">)}</span>
 
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
procedure orbitalStateVectors(atom semimajorAxis, eccentricity, inclination, longitudeOfAscendingNode, argumentOfPeriapsis, trueAnomaly)
sequence i = {1, 0, 0},
<span style="color: #008080;">procedure</span> <span style="color: #000000;">orbitalStateVectors</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">semimajorAxis</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">eccentricity</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">inclination</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">longitudeOfAscendingNode</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">argumentOfPeriapsis</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">trueAnomaly</span><span style="color: #0000FF;">)</span>
j = {0, 1, 0},
<span style="color: #004080;">sequence</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>
k = {0, 0, 1}
<span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
{i,j} = rotate(i, j, longitudeOfAscendingNode)
{j} = rotate(j, k, inclination)
<span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">longitudeOfAscendingNode</span><span style="color: #0000FF;">)</span>
{i,j} = rotate(i, j, argumentOfPeriapsis)
<span style="color: #0000FF;">{</span><span style="color: #000000;">j</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">inclination</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">argumentOfPeriapsis</span><span style="color: #0000FF;">)</span>
atom l = iff(eccentricity=1?2:1-eccentricity*eccentricity)*semimajorAxis,
c = cos(trueAnomaly),
<span style="color: #004080;">atom</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">eccentricity</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #000000;">2</span><span style="color: #0000FF;">:</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">eccentricity</span><span style="color: #0000FF;">*</span><span style="color: #000000;">eccentricity</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">semimajorAxis</span><span style="color: #0000FF;">,</span>
s = sin(trueAnomaly),
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">trueAnomaly</span><span style="color: #0000FF;">),</span>
r = 1 / (1+eccentricity*c),
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">trueAnomaly</span><span style="color: #0000FF;">),</span>
rprime = s * r * r / l
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">eccentricity</span><span style="color: #0000FF;">*</span><span style="color: #000000;">c</span><span style="color: #0000FF;">),</span>
sequence posn = sq_mul(mulAdd(i, c, j, s),r),
<span style="color: #000000;">rprime</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">l</span>
speed = mulAdd(i, rprime*c-r*s, j, rprime*s+r*c)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">posn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mulAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">),</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span>
speed = sq_div(speed,vabs(speed))
<span style="color: #000000;">speed</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mulAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rprime</span><span style="color: #0000FF;">*</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">r</span><span style="color: #0000FF;">*</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rprime</span><span style="color: #0000FF;">*</span><span style="color: #000000;">s</span><span style="color: #0000FF;">+</span><span style="color: #000000;">r</span><span style="color: #0000FF;">*</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
speed = sq_mul(speed,sqrt(2/r - 1/semimajorAxis))
<span style="color: #000000;">speed</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">speed</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vabs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">speed</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">speed</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">speed</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">/</span><span style="color: #000000;">r</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">semimajorAxis</span><span style="color: #0000FF;">))</span>
puts(1,"Position :") ?posn
puts(1,"Speed :") ?speed
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Position :"</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">posn</span>
end procedure
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Speed :"</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">speed</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
orbitalStateVectors(1.0, 0.1, 0.0, 355.0 / (113.0 * 6.0), 0.0, 0.0)</lang>
<span style="color: #000000;">orbitalStateVectors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">355.0</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">113.0</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">6.0</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">0.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.0</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
{{out}}
<pre>
Petelomax
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