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<head>
<title>Kerbal Orbits</title>
<script type="text/javascript">
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// https://developer.mozilla.org/en/Drawing_Graphics_with_Canvas
// http://www.whatwg.org/specs/web-apps/current-work/multipage/the-canvas-element.html#the-2d-context
// http://www.w3schools.com/jsref/default.asp
var mainCanvasCtx, mainCanvas;
var mouseIsDown = false;
var mouseIsDragging = false;
var cursorClickX = 0, cursorClickY = 0;
var cursorLastX = 0, cursorLastY = 0;
var pi = Math.PI;
var phi = (1 + Math.sqrt(5))/2;
var debugDiv = null;
function writedbg(msg) {if(debugDiv) debugDiv.value += msg + "\n";}
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var regex = new RegExp(regexS);
var results = regex.exec(window.location.href);
if(results == null)
return defVal;
else
return results[1];
}
//************************************************************************************************
var KERBIN_R = 600e3
var KERBIN_GM = (9.80665*KERBIN_R*KERBIN_R);// A = M*G/r^2, M*G = A*r^2, A = 9.8665 m/s^2, r = KERBIN_R m
var infinity = 1.7976931348623157E+10308;
var periapsis = 0, apoapsis = 0;
var periapsisVel = 0, apoapsisVel = 0;// these are calculated from the above for elliptical orbits
var elliptical = true;
var lenScale = 1;
var velScale = 1;
var zooming = false;
var savedScale = 0;
var safety = false;
//************************************************************************************************
var scale = 2000e3;
var canvasMinX = -scale, canvasMinY = -scale;
var canvasSizeX = 3*scale, canvasSizeY = 2*scale;
var width = 0, height = 0;
var scaleX, scaleY;
// Screen/world coordinate transforms
function s2w_x(x) {return (x/scaleX) + canvasMinX;}
function s2w_y(y) {return ((height - y)/scaleY) + canvasMinY;}
function w2s_x(x) {return (x - canvasMinX)*scaleX;}
function w2s_y(y) {return height - (y - canvasMinY)*scaleY;}
function Circle(ctx, x, y, r) {
ctx.beginPath();
ctx.arc((x - canvasMinX)*scaleX, (y - canvasMinY)*scaleY, r, 0, 2*pi, false);
ctx.stroke();
}
function Line(ctx, x, y, x2, y2) {
ctx.beginPath();
ctx.moveTo((x - canvasMinX)*scaleX, (y - canvasMinY)*scaleY);
ctx.lineTo((x2 - canvasMinX)*scaleX, (y2 - canvasMinY)*scaleY);
ctx.stroke();
}
function DrawMainCanvas()
{
var ctx = mainCanvasCtx;
ctx.fillStyle = "#EEEEEE";
ctx.fillRect(0, 0, mainCanvas.width, mainCanvas.height);
var width = ctx.canvas.width;
var height = ctx.canvas.height;
var scale = canvasSizeX/(ctx.canvas.width + 1);
var aspect = ctx.canvas.width/ctx.canvas.height;
ctx.save();
ctx.translate(0, ctx.canvas.height);
ctx.scale(1.0, -1.0);
ctx.lineWidth = 1;
ctx.fillStyle = "#000088";
ctx.strokeStyle = "#000000";
ctx.beginPath();
ctx.arc(w2s_x(0), w2s_y(0), KERBIN_R/scale, 0, 2*pi, false);
ctx.fill();
ctx.strokeStyle = "#6666AA";
ctx.beginPath();
ctx.arc(w2s_x(0), w2s_y(0), (KERBIN_R + 35e3)/scale, 0, 2*pi, false);
ctx.stroke();
semimaj = (apoapsis + periapsis)/2;
semimin = Math.sqrt(apoapsis*periapsis);
ctx.strokeStyle = "#000000";
ctx.beginPath();
ctx.moveTo(w2s_x(apoapsis), w2s_y(0));
n = 720
for(j = 0; j <= n; ++j) {
th = Math.PI*2.0*j/n;
x = w2s_x(Math.cos(th)*semimaj + semimaj - periapsis);
y = w2s_y(Math.sin(th)*semimin);
ctx.lineTo(Math.min(2*width, Math.max(-width, x)), Math.min(2*height, Math.max(-height, y)));
}
ctx.stroke();
ctx.restore();
}
function SetFromApoapsisPeriapsisEll(peri, apo)
{
apoapsis = apo;
periapsis = peri;
// Can not make an elliptical trajectory parabolic/hyperbolic by setting apsides
if(apoapsis < periapsis) {
tmp = apoapsis;
apoapsis = periapsis;
periapsis = tmp;
}
periapsisVel = Math.sqrt(KERBIN_GM*(2.0/periapsis - 2.0/(periapsis + apoapsis)));
apoapsisVel = Math.sqrt(KERBIN_GM*(2.0/apoapsis - 2.0/(periapsis + apoapsis)));
}
function SetFromApoapsis(apo)
{
if(elliptical)
SetFromApoapsisPeriapsisEll(periapsis, apo);
else // Parabolic/hyperbolic
SetFromApoapsisApovel();
}
function SetFromPeriapsis(peri)
{
if(elliptical)
SetFromApoapsisPeriapsisEll(peri, apoapsis);
else // Parabolic/hyperbolic
SetFromPeriapsisPerivel();
}
function SetFromApovelPerivel(apovel, perivel)
{
// v = sqrt(mu*(2.0/r - 1/a));
//
// So:
// r1 = 2.0/(2.0/r0 - v0*v0/mu) - r0;
// v1 = sqrt(mu*(2.0/r1 - 2.0/(r0 + r1)));
//
// Wolfram Alpha to the rescue...
// If v0*v0 != v0*v1: (v0 != v1, false for circular orbits)
// r0 = 2*mu/(v0*v0 - v0*v1)
// If v0*(v0 + v1) != 0: (v0 > 0 and v0 + v1 > 0, which is always true for sane numbers)
// r0 = 2*mu/(v0*(v0 + v1))
if(apovel > perivel) {
tmp = apovel;
apovel = periapsisVel;
perivel = tmp;
}
periapsisVel = perivel;
apoapsisVel = apovel;
periapsis = 2*KERBIN_GM/(perivel*(perivel + apovel));
apoapsis = 2.0/(2.0/periapsis - perivel*perivel/KERBIN_GM) - periapsis;
// apoapsisVelCheck = Math.sqrt(KERBIN_GM*(2.0/apoapsis - 2.0/(periapsis + apoapsis)));
}
function SetFromPeriapsisPerivel(peri, perivel)
{
periapsis = peri;
periapsisVel = perivel;
// Can make an elliptical trajectory parabolic/hyperbolic
periEscVel = Math.sqrt(2.0*KERBIN_GM/periapsis);
if(periapsisVel > periEscVel)
{
elliptical = false;
apoapsis = infinity;
// Excess velocity
apoapsisVel = Math.sqrt(2.0*((periapsisVel*periapsisVel)/2.0 - KERBIN_GM/periapsis));
}
else
{
elliptical = true;
apoapsis = 2.0/(2.0/periapsis - periapsisVel*periapsisVel/KERBIN_GM) - periapsis;
apoapsisVel = Math.sqrt(KERBIN_GM*(2.0/apoapsis - 2.0/(periapsis + apoapsis)));
}
}
function SetFromApoapsisApovel(apo, apovel)
{
apoapsis = apo;
apoapsisVel = apovel;
// Can make an elliptical trajectory parabolic/hyperbolic, and if so, swaps periapsis/apoapsis
// V = sqrt(KERBIN_GM*(2.0/r - 2.0/(peri + apo)))
// 2.0/(2.0/apo - V^2/KERBIN_GM) - apo = peri
apoEscVel = Math.sqrt(2.0*KERBIN_GM/apoapsis);
if(apoapsisVel > apoEscVel)
{
elliptical = false;
periapsis = apoapsis;
apoapsis = infinity;
// apoapsisVel is excess velocity
periapsisVel = apoapsisVel;
apoapsisVel = Math.sqrt(2.0*((periapsisVel*periapsisVel)/2.0 - KERBIN_GM/periapsis));
}
else
{
elliptical = true;
periapsis = 2.0/(2.0/apoapsis - apoapsisVel*apoapsisVel/KERBIN_GM) - apoapsis;
periapsisVel = Math.sqrt(KERBIN_GM*(2.0/periapsis - 2.0/(periapsis + apoapsis)));
}
}
// Taylor series approximation of inverse of Kepler's equation
function InvKep(M, e)
{
// 3! = 6, 5! = 120, 7! = 540, 9! = 362880
me = 1 - e
me2 = me*me
me3 = me2*me
me4 = me2*me2
me7 = me4*me3
me10 = me7*me3
me13 = me10*me3
e2 = e*e
e3 = e2*e
e4 = e3*e
E = M*(1.0/me -
M*M*(e/(me4*6) +
M*M*((9*e2 + e)/(me7*120) -
M*M*((225*e3 + 54*e2 + e)/(me10*540) +
M*M*(11025*e4 + 4131*e3 + 243*e2 + e)/(me13*362880)))));
return E;
}
function SetFromDataPoints(data)
{
// We only have velocity, altitude,
// v = sqrt(mu*(2/r - 1/a))
// Given mu, v0, r0, v1, r1:
// v0 = sqrt(mu*(2/r0 - 1/a))
// v1 = sqrt(mu*(2/r1 - 1/a))
// r0 = 2/(v0^2/mu + 1/a)
// r1 = 2/(v1^2/mu + 1/a)
// a = 1/(2/r0 - v0^2/mu)
// a = 1/(2/r1 - v1^2/mu)
// a = (apo + peri)/2
// E = ((v*v)/2.0 - (G*m)/r)
// Period:
// P = 2*pi*sqrt(a**3/mu)
// Mean anomaly:
// M = 2*pi*t/P = t/sqrt(a**3/mu)
// M = E - e*sin(E)
// t/sqrt(a**3/mu) = E - e*sin(E)
// E = InvKep(t/sqrt(a**3/mu), e)
// tan(halftheta) = sqrt((1 + e)/(1 - e))*tan(E/2)
// r = a*(1 - e*e)/(1 + e*cos(theta))
}
// Set up ellipse from altitude, velocity, and angle
function SetFromRVA(r, v, ang)
{
// angle is of velocity vector, tangent to ellipse, to a ray from the planet
cosa = Math.cos(ang)
sina = Math.sin(ang)
//a = 1/(2/r - v^2/mu)
a = 1.0/(2.0/r - v*v/KERBIN_GM);// semimajor axis
// Only known with e:
// b = a*sqrt(1 - e*e)
// e = (apo - peri)/(apo + peri) = (apo - peri)/(2*a)
// peri = a - e*a
// apo = 2*a - peri
b = a*Math.sqrt(1 - e*e);// semiminor axis
// point and tangent on ellipse by angle from center of corresponding circle:
// ex = cos(th), ey = sin(th)*b/a
// tx = -sin(th), ty = cos(th)*b/a
// atan(-tan(ang)*b/a) = th
}
function UpdateStats()
{
debugDiv.value = ""
peri = periapsis;
apo = apoapsis;
lenprec = (lenScale <= 1)? 1 : 4;
velprec = (velScale <= 1)? 1 : 4;
document.getElementById("periInput").value = ((periapsis - KERBIN_R)/lenScale).toFixed(lenprec);
document.getElementById("apoInput").value = ((apoapsis - KERBIN_R)/lenScale).toFixed(lenprec);
document.getElementById("perivelInput").value = (periapsisVel/velScale).toFixed(velprec);
document.getElementById("apovelInput").value = (apoapsisVel/velScale).toFixed(velprec);
if(elliptical)
{
vperi = periapsisVel;
vapo = apoapsisVel;
semimaj = (apo + peri)/2;
semimin = Math.sqrt(apo*peri);
ecc = (1 - 2.0/(apo/peri + 1));
period = 2.0*Math.PI*Math.sqrt(Math.pow((peri + apo)/2.0, 3)/KERBIN_GM)
periEscVel = Math.sqrt(2.0*KERBIN_GM/periapsis)
apoEscVel = Math.sqrt(2.0*KERBIN_GM/apoapsis)
periHohDV = Math.abs(vperi - Math.sqrt(KERBIN_GM/periapsis))
apoHohDV = Math.abs(vapo - Math.sqrt(KERBIN_GM/apoapsis))
writedbg("periapsis: " + (periapsis/1e3).toFixed(4) + " km, apoapsis: " + (apoapsis/1e3).toFixed(4) + " km");
writedbg("periapsis: " + ((periapsis - KERBIN_R)/1e3).toFixed(4) + " km AMSL, " +
"apoapsis: " + ((apoapsis - KERBIN_R)/1e3).toFixed(4) + " km AMSL");
writedbg("\nvelocity at periapsis: " + vperi.toFixed(1) + " m/s, " +
"at apoapsis: " + vapo.toFixed(1) + " m/s");
writedbg("Hohmann delta-v at periapsis: " + periHohDV.toFixed(1) + " m/s, " +
"at apoapsis: " + apoHohDV.toFixed(1) + " m/s");
writedbg("Vesc at periapsis: " + periEscVel.toFixed(1) + " m/s, " +
"at apoapsis: " + apoEscVel.toFixed(1) + " m/s");
writedbg("\nperiod: " + (period/60).toFixed(1) + " minutes");
writedbg("semimajor axis: " + (semimaj/1e3).toFixed(4) + " km");
writedbg("semiminor axis: " + (semimin/1e3).toFixed(4) + " km");
writedbg("eccentricity: " + ecc.toFixed(1));
}
else
{
writedbg("periapsis: " + (periapsis/1e3).toFixed(4) + " km");
writedbg("periapsis: " + ((periapsis - KERBIN_R)/1e3).toFixed(4) + " km AMSL");
writedbg("velocity at periapsis: " + periapsisVel.toFixed(1) +
" m/s, excess velocity: " + apoapsisVel.toFixed(1) + " m/s");
}
var plotLink = document.getElementById("plotLink");
plotLink.href = "http://files.arklyffe.com/orbcalc.html?" +
"a=" + (""+apoapsis) +
"&p=" + (""+periapsis) +
"&av=" + (""+apoapsisVel) +
"&pv=" + (""+periapsisVel);
}
function PeriapsisChanged() {
paramLock = document.getElementById("paramLockSelect").value;
peri = (+document.getElementById("periInput").value + KERBIN_R)*lenScale;
if(paramLock == "apo-peri")
SetFromPeriapsis(peri);
else
SetFromPeriapsisPerivel(peri, periapsisVel);
UpdateStats();
DrawMainCanvas();
}
function ApsoapsisChanged() {
paramLock = document.getElementById("paramLockSelect").value;
apo = (+document.getElementById("apoInput").value + KERBIN_R)*lenScale;
if(paramLock == "apo-peri")
SetFromApoapsis(apo);
else
SetFromApoapsisApovel(apo, apoapsisVel);
UpdateStats();
DrawMainCanvas();
}
// Set velocity at apoapsis, recompute periapsis
function ApoVelChanged() {
paramLock = document.getElementById("paramLockSelect").value;
apovel = +document.getElementById("apovelInput").value*velScale;
if(paramLock == "apo-peri")
SetFromApovelPerivel(apovel, periapsisVel);
else
SetFromApoapsisApovel(apoapsis, apovel);
UpdateStats();
DrawMainCanvas();
}
// Set velocity at periapsis, recompute apoapsis
function PeriVelChanged() {
paramLock = document.getElementById("paramLockSelect").value;
perivel = +document.getElementById("perivelInput").value*velScale;
if(paramLock == "apo-peri")
SetFromApovelPerivel(apoapsisVel, perivel);
else
SetFromPeriapsisPerivel(periapsis, perivel);
UpdateStats();
DrawMainCanvas();
}
function ZoomIn()
{
scale /= 2;
canvasMinX = -scale;
canvasMinY = -scale;
canvasSizeX = 3*scale;
canvasSizeY = canvasSizeX*height/width;// square aspect ratio
scaleX = width/canvasSizeX;
scaleY = height/canvasSizeY;
DrawMainCanvas();
}
function ZoomOut()
{
scale *= 2;
canvasMinX = -scale;
canvasMinY = -scale;
canvasSizeX = 3*scale;
canvasSizeY = canvasSizeX*height/width;// square aspect ratio
scaleX = width/canvasSizeX;
scaleY = height/canvasSizeY;
DrawMainCanvas();
}
function MouseMoved(evt, x, y) {}
function MouseDown(evt, x, y) {
if(safety) return;
if(event.shiftKey)
{
zooming = true;
savedScale = scale;
}
else
{
zooming = false;
MouseDragging(evt, x, y, x, y);
}
}
function MouseClicked(evt, x, y) {}
function MouseDragged(evt, x, y, prevX, prevY) {}
function MouseDragging(evt, x, y, prevX, prevY) {
if(safety) return;
if(zooming)
{
width = mainCanvasCtx.canvas.width;
height = mainCanvasCtx.canvas.height;
// Zoom
scale = savedScale + (savedScale*(y - cursorClickY))/height;
canvasMinX = -scale;
canvasMinY = -scale;
canvasSizeX = 3*scale;
canvasSizeY = canvasSizeX*height/width;// square aspect ratio
scaleX = width/canvasSizeX;
scaleY = height/canvasSizeY;
DrawMainCanvas();
}
else
{
MouseDragAltitude(evt, x, y, prevX, prevY)
}
}
function MouseDragAltitude(evt, x, y, prevX, prevY) {
if(safety) return;
paramLock = document.getElementById("paramLockSelect").value;
click_wx = s2w_x(cursorClickX)
wx = s2w_x(x)
if(click_wx > 0)
{
if(wx > 0)
{
elliptical = true;
if(paramLock == "apo-peri")
{
if(wx < periapsis)
wx = periapsis;
SetFromApoapsis(wx);
}
else
{
apoapsis = savedApoapsis;
periapsis = savedPeriapsis;
apoapsisVel = savedApovel;
periapsisVel = savedPerivel;
SetFromApoapsisApovel(wx, apoapsisVel);
}
}
}
else
{
wx = -wx;
if(wx > 0)
{
if(paramLock == "apo-peri")
{
if(wx > apoapsis)
wx = apoapsis;
SetFromPeriapsis(wx);
}
else
{
apoapsis = savedApoapsis;
periapsis = savedPeriapsis;
apoapsisVel = savedApovel;
periapsisVel = savedPerivel;
SetFromPeriapsisPerivel(wx, periapsisVel);
}
}
}
UpdateStats();
DrawMainCanvas();
}
function UnitsChanged(self)
{
units = document.getElementById("unitsSelect").value;
if(units == "m_ms") {
lenScale = 1;
velScale = 1;
}
else if(units == "km_ms") {
lenScale = 1000;
velScale = 1;
}
else if(units == "m_kms") {
lenScale = 1;
velScale = 1000;
}
else if(units == "km_kms") {
lenScale = 1000;
velScale = 1000;
}
else {
lenScale = 1;
velScale = 1;
}
UpdateStats();
}
function SafetyBtnChanged(self)
{
safety = document.getElementById("safetyBtn").checked;
}
//************************************************************************************************
window.onload = function() {
apo = +getURL_Param("a", 0)
peri = +getURL_Param("p", 0)
apoV = +getURL_Param("av", 0)
periV = +getURL_Param("pv", 0)
if(apo > 0 && peri > 0)
SetFromApoapsisPeriapsisEll(apo, peri);
else if(apo > 0 && apoV > 0)
SetFromApoapsisApovel(apo, apoV);
else if(peri > 0 && periV > 0)
SetFromPeriapsisPerivel(peri, periV);
else
SetFromApoapsisPeriapsisEll(50e3 + KERBIN_R, 200e3 + KERBIN_R)
debugDiv = document.getElementById("debugDiv");
mainCanvas = document.getElementById("mainCanvas");
mainCanvasCtx = mainCanvas.getContext("2d");
width = mainCanvasCtx.canvas.width;
height = mainCanvasCtx.canvas.height;
canvasSizeY = canvasSizeX*height/width;//square the initial aspect
scaleX = width/canvasSizeX;
scaleY = height/canvasSizeY;
//Mouse events
mainCanvas.onmouseover = function(evt) {document.body.style.cursor = "crosshair"; return false;}
mainCanvas.onmouseout = function(evt) {document.body.style.cursor = "default"; return false;}
mainCanvas.onmousedown = function(evt) {
mouseIsDown = true;
cursorLastX = evt.clientX - mainCanvas.offsetLeft +
(window.pageXOffset || document.body.scrollLeft || document.documentElement.scrollLeft);
cursorLastY = evt.clientY - mainCanvas.offsetTop +
(window.pageYOffset || document.body.scrollTop || document.documentElement.scrollTop);
cursorClickX = cursorLastX;
cursorClickY = cursorLastY;
MouseDown(evt, cursorClickX, cursorClickY);
return false;
}
//if mouse is down, get mouseup events from window, not just canvas. Otherwise ignore.
onmouseup = function(evt) {
if(mouseIsDown) {
var x = evt.clientX - mainCanvas.offsetLeft +
(window.pageXOffset || document.body.scrollLeft || document.documentElement.scrollLeft);
var y = evt.clientY - mainCanvas.offsetTop +
(window.pageYOffset || document.body.scrollTop || document.documentElement.scrollTop);
mouseIsDown = false;
if(mouseIsDragging) {
//mouse dragged
mouseIsDragging = false;
MouseDragged(evt, x, y, cursorLastX, cursorLastY);
}
else {
//mouse clicked
MouseClicked(evt, x, y);
}
}
return false;
}
onmousemove = function(evt) {
var x = evt.clientX - mainCanvas.offsetLeft +
(window.pageXOffset || document.body.scrollLeft || document.documentElement.scrollLeft);
var y = evt.clientY - mainCanvas.offsetTop +
(window.pageYOffset || document.body.scrollTop || document.documentElement.scrollTop);
if(mouseIsDown) {
mouseIsDragging = true;
MouseDragging(evt, x, y, cursorLastX, cursorLastY);
cursorLastX = x;
cursorLastY = y;
}
MouseMoved(evt, x, y);
return false;
}
writedbg("Init done");
UpdateStats();
DrawMainCanvas();
}
//************************************************************************************************
</script>
</head>
<body>
<a id="plotLink" href="http://files.arklyffe.com/orbcalc.html">This Orbit</a><br>
<canvas id="mainCanvas" width="800" height="600"></canvas><br>
<table>
<tr>
<td>Periapsis AMSL: <input type="text" id="periInput" size="8" onchange="PeriapsisChanged()"></td>
<td>Velocity: <input type="text" id="perivelInput" size="8" onchange="PeriVelChanged()"></td>
<td>Parameters: <select id="paramLockSelect">
<option value="apo-peri" selected>Apoapsis-Periapsis</option>
<option value="aps-vel">Apside-Velocity</option>
</select></td>
<td><input type="button" value="Zoom -" onclick="ZoomOut()">
<input type="button" value="Zoom +" onclick="ZoomIn()"></td>
</tr>
<tr>
<td>Apoapsis AMSL: <input type="text" id="apoInput" size="8" onchange="ApsoapsisChanged()"></td>
<td>Velocity: <input type="text" id="apovelInput" size="8" onchange="ApoVelChanged()"></td>
<td>Units: <select id="unitsSelect" onchange="UnitsChanged()">
<option value="m_ms" selected>m, m/s</option>
<option value="km_ms">km, m/s</option>
<option value="m_kms">m, km/s</option>
<option value="km_kms">km, km/s</option>
</select></td>
<td><input type="checkbox" id="safetyBtn" size="8" onchange="SafetyBtnChanged()">Ignore Mouse</td>
</tr>
</table>
<div><textarea id="debugDiv" rows="20" cols="60" wrap="virtual" style="width:640px; height:250px"></textarea></div><br>
</body>
</html>