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saturnmoons, jupitermoons - add Z-coord output #40

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commenthol merged 1 commit into from
Aug 30, 2025
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saturnmoons, jupitermoons - add Z-coord output #40

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2 changes: 1 addition & 1 deletion src/base.js
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Expand Up @@ -58,7 +58,7 @@ export const COblJ2000 = 0.917482062
* `dist` is distance in to earth in AU. √(x² + y² + z²)
* Result in seconds of time.
* @param {Number} dist - distance in to earth in AU
* @returns {Number} time for light to travel a given distance in seconds
* @returns {Number} time for light to travel a given distance in days
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@dobriai dobriai Aug 18, 2025

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This is unrelated to the rest of the PR, of course. Just caught my eye. Somehow.

*/
export function lightTime (dist) {
// Formula given as (33.3) p. 224.
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15 changes: 9 additions & 6 deletions src/jupitermoons.js
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Expand Up @@ -22,13 +22,15 @@ export const callisto = 3
const k = [17295, 21819, 27558, 36548]

/**
* XY used for returning coordinates of moons.
* XYZ used for returning coordinates of moons.
* @param {number} x - in units of Jupiter radii
* @param {number} y - in units of Jupiter radii
* @param {number} z - in units of Jupiter radii
*/
function XY (x, y) {
function XYZ (x, y, z) {
this.x = x
this.y = y
this.z = z
}

/**
Expand All @@ -37,7 +39,7 @@ function XY (x, y) {
* Returned coordinates are in units of Jupiter radii.
*
* @param {Number} jde - Julian ephemeris day
* @return {Array} x, y - coordinates of the 4 Satellites of jupiter
* @return {Array} x, y, z - coordinates of the 4 Satellites of jupiter
*/
export function positions (jde) {
const d = jde - base.J2000
Expand Down Expand Up @@ -83,9 +85,10 @@ export function positions (jde) {
const r3 = 14.9883 - 0.0216 * cG
const r4 = 26.3627 - 0.1939 * cH
const sDE = Math.sin(DE)
const cDE = Math.cos(DE)
const xy = function (u, r) {
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@dobriai dobriai Aug 18, 2025

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This local function could also be renamed, but I decided to minimize the diffs, to make the PR easier to review. Cleanup could be done later. Or now, if you prefer.

const [su, cu] = base.sincos(u)
return new XY(r * su, -r * cu * sDE)
return new XYZ(r * su, -r * cu * sDE, -r * cu * cDE)
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@dobriai dobriai Aug 18, 2025

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Z does not come entirely "for free" here. This is what I think that it should be based on the X and Y formulas on p.303, namely:

X = r * sin(u),   Y = -r * cos(u) * sin(D_e)

thus Z = -r * cos(u) * cos(D_e).

We have X^2 + Y^2 + Z^2 = r^2, which is good.

The sign should be negative, based on the statements "...Z is negative if the satellite is closer to Earth...", on pp.313 and 333.

Finally the values appear quite close to the high-precision ones, from the e5 calculations, which gives me the greatest comfort.

}
return [xy(u1 + c1, r1), xy(u2 + c2, r2), xy(u3 + c3, r3), xy(u4 + c4, r4)]
}
Expand All @@ -101,7 +104,7 @@ export function positions (jde) {
* @param {Planet} earth - VSOP87 Planet earth
* @param {Planet} jupiter - VSOP87 Planet jupiter
* @param {Array} [pos] - reference to array of positions (same as return value)
* @return {Array} x, y - coordinates of the 4 Satellites of jupiter
* @return {Array} x, y, z - coordinates of the 4 Satellites of jupiter
*/
export function e5 (jde, earth, jupiter, pos) {
pos = pos || new Array(4)
Expand Down Expand Up @@ -481,7 +484,7 @@ export function e5 (jde, earth, jupiter, pos) {
x += Math.abs(z) / k[i] * Math.sqrt(1 - d * d)
// perspective effect
const W = Δ / (Δ + z / 2095)
pos[i] = new XY(x * W, y * W)
pos[i] = new XYZ(x * W, y * W, z)
}
return pos
}
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9 changes: 5 additions & 4 deletions src/saturnmoons.js
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Expand Up @@ -25,11 +25,12 @@ export const hyperion = 6
export const iapetus = 7

/**
* XY holds coordinates returned from positions().
* XYZ holds coordinates returned from positions().
*/
function XY (x, y) {
function XYZ (x, y, z) {
this.x = x
this.y = y
this.z = z
}

const d = Math.PI / 180
Expand All @@ -44,7 +45,7 @@ const d = Math.PI / 180
* @param {number} jde - Julian ephemeris day
* @param {Planet} earth - VSOP87 planet Earth // eslint-disable-line no-unused-vars
* @param {Planet} saturn - VSOP87 planet Saturn // eslint-disable-line no-unused-vars
* @return {XY[]} Array of Moon Positions in `XY`
* @return {XYZ[]} Array of Moon Positions in `XYZ`
* Use `M.mimas ... M.iapetus` to resolve to Moon and its position at `jde`
*/
export function positions (jde, earth, saturn) {
Expand Down Expand Up @@ -138,7 +139,7 @@ export function positions (jde, earth, saturn) {
const d = X[j] / s4[j].r
X[j] += Math.abs(Z[j]) / k[j] * Math.sqrt(1 - d * d)
const W = Δ / (Δ + Z[j] / 2475)
pos[j - 1] = new XY(X[j] * W, Y[j] * W)
pos[j - 1] = new XYZ(X[j] * W, Y[j] * W, Z[j])
}
return pos
}
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25 changes: 20 additions & 5 deletions test/jupitermoons.test.js
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Expand Up @@ -18,6 +18,11 @@ describe('#jupitermoons', function () {
assert.strictEqual(float(pos[2].y).toFixed(2), +0.65)
assert.strictEqual(float(pos[3].y).toFixed(2), +1.10)

assert.strictEqual(float(pos[0].z).toFixed(2), -4.82)
assert.strictEqual(float(pos[1].z).toFixed(2), -5.74)
assert.strictEqual(float(pos[2].z).toFixed(2), -14.94)
assert.strictEqual(float(pos[3].z).toFixed(2), -25.22)

// Output:
// X -3.44 +7.44 +1.24 +7.08
// Y +0.21 +0.25 +0.65 +1.10
Expand All @@ -38,11 +43,13 @@ describe('#jupitermoons', function () {

assert.deepStrictEqual(xyToFixed(pos3[2]), {
x: -0.0016,
y: -0.8424
y: -0.8424,
z: -14.9444
})
assert.deepStrictEqual(xyToFixed(pos4[3]), {
x: +0.0555,
y: +1.4811
y: +1.4811,
z: +26.2743
})

// Output:
Expand All @@ -67,6 +74,11 @@ describe('#jupitermoons', function () {
assert.strictEqual(float(pos[2].y).toFixed(4), +0.5900)
assert.strictEqual(float(pos[3].y).toFixed(4), +1.0290)

assert.strictEqual(float(pos[0].z).toFixed(4), -4.8189)
assert.strictEqual(float(pos[1].z).toFixed(4), -5.7472)
assert.strictEqual(float(pos[2].z).toFixed(4), -14.9406)
assert.strictEqual(float(pos[3].z).toFixed(4), -25.2244)

// Output:
// X -3.4503 +7.4418 +1.2010 +7.0720
// Y +0.2137 +0.2752 +0.5900 +1.0290
Expand All @@ -90,11 +102,13 @@ describe('#jupitermoons', function () {

assert.deepStrictEqual(xyToFixed(pos3[2]), {
x: +0.0032,
y: -0.8042
y: -0.8042,
z: -14.9433
})
assert.deepStrictEqual(xyToFixed(pos4[3]), {
x: +0.0002,
y: +1.3990
y: +1.3990,
z: +26.2732
})

// Output:
Expand All @@ -108,6 +122,7 @@ function xyToFixed (xy, n) {
n = n || 4
return {
x: float(xy.x).toFixed(n),
y: float(xy.y).toFixed(n)
y: float(xy.y).toFixed(n),
z: float(xy.z).toFixed(n)
}
}
17 changes: 9 additions & 8 deletions test/saturnmoons.test.js
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Expand Up @@ -9,6 +9,7 @@ describe('#saturnmoons', function () {
function comp (res, exp) {
assert.strictEqual(float(res.x).toFixed(3), exp.x)
assert.strictEqual(float(res.y).toFixed(3), exp.y)
assert.strictEqual(float(res.z).toFixed(3), exp.z)
}

describe('positions()', function () {
Expand All @@ -17,14 +18,14 @@ describe('#saturnmoons', function () {
const saturn = new planetposition.Planet(data.vsop87Bsaturn)
const pos = saturnmoons.positions(2451439.50074, earth, saturn)
const exp = [
{ x: +3.102, y: -0.204 },
{ x: +3.823, y: +0.318 },
{ x: +4.027, y: -1.061 },
{ x: -5.365, y: -1.148 },
{ x: -0.972, y: -3.136 },
{ x: +14.568, y: +4.738 },
{ x: -18.001, y: -5.328 },
{ x: -48.760, y: +4.137 }
{ x: +3.102, y: -0.204, z: +0.295 },
{ x: +3.823, y: +0.318, z: -0.833 },
{ x: +4.027, y: -1.061, z: +2.545 },
{ x: -5.365, y: -1.148, z: +3.004 },
{ x: -0.972, y: -3.136, z: +8.080 },
{ x: +14.568, y: +4.738, z: -12.755 },
{ x: -18.001, y: -5.328, z: +15.121 },
{ x: -48.760, y: +4.137, z: +32.738 }
]

pos.forEach(function (p, i) {
Expand Down