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Scratch.hdnb
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# Scratchpad
A persistent REPL I use to help maintain my remaining sanity :)
To properly engage with this document: https://marketplace.visualstudio.com/items?itemName=jakearl.handydandy-notebook
### Utils
```ts
// important spacer :)
const entries = Object.entries as <K extends string, V>(
o: Record<K, V>
) => [K, V][];
const fromEntries = Object.fromEntries as <K extends string, V>(
e: [K, V][]
) => Record<K, V>;
const omap = <T, U, K extends string>(
source: Record<K, T>,
transform: (t: T, k: K) => U
): Record<K, U> =>
fromEntries(entries(source).map(([k, v]) => [k, transform(v, k)]));
const wrap = (degrees: number): number => ((degrees % 360) + 360) % 360;
const radToDeg = (rad: number) => (rad * 180) / Math.PI;
const degToRad = (deg: number) => (deg * Math.PI) / 180;
const sin = (deg: number) => Math.sin(degToRad(deg));
const cos = (deg: number) => Math.cos(degToRad(deg));
const tan = (deg: number) => Math.tan(degToRad(deg));
const cot = (deg: number) => 1 / tan(deg);
const acos = (x: number) => radToDeg(Math.acos(x));
const atan = (x: number) => radToDeg(Math.atan(x));
```
### Test the utils
```ts
// {{cell:utils}}
console.log(wrap(180))
console.log(wrap(0))
console.log(wrap(361))
console.log(wrap(721))
console.log(wrap(-1))
console.log(wrap(-361))
console.log(wrap(-359))
const data = omap({ hello: 1, world: 2 }, (n) => n + "!");
console.log(data)
```
### Reference Tables from Schureman
```ts
// Table 1
// h p1 s p N
// 0.04106864 0.00000196 0.54901653 0.00464183 -0.00220641
// Table 2
// C V u f
// J1 T + s + h - p - 90 -v 76
// K1 T + h - 90 -v' 227
// Lam 2T - s + p + 180 -2v + 2Xi 78
// Table 4
// Y s p h p1 N
// 1970 197.96 302.64 280.24 282.42 345.28
// 1971 327.35 343.31 280.00 282.44 325.95
// 1972 96.73 23.97 279.76 282.46 306.63
// 2000 211.74 83.29 279.97 282.94 125.07
// Table 5
// s p h p1 N
// 224.93 20.16 178.40 0.01 -9.58 <- July 1
// 13.18 0.11 0.99 0.00 -0.05 <- 2
// Table 6
// N v Xi v' 2v'' I
// 336 -4.42 -3.98 -3.15 -6.68 28.23
// 316 -7.79 -7.04 -5.52 -11.60 27.38
// 297 -10.44 -9.48 -7.34 -15.24 26.17
// 115 12.67 11.70 8.52 16.62 21.75
// Table 11
// N J1 K1 Lam
// 336 4.42 3.15 0.88
// 316 7.79 5.52 1.50
// 297 10.44 7.34 1.91
// 115 -12.67 -8.52 -1.93
// Table 15
// Y J1 K1 Lam
// 1970 270.0 13.4 285.6
// 1971 1.8 15.5 197.4
// 1972 93.1 17.1 109.1
// 2000 125.8 1.5 49.6
```
### Table 1 Data
```ts
// important spacer
type OrbitState = {
T: number;
s: number;
h: number;
p: number;
p1: number;
N: number;
};
type LunarNodeState = {
v: number;
vPrime: number;
twoVPrime: number;
Xi: number;
};
const OrbitVelocities: OrbitState = {
h: 0.04106864,
N: -0.00220641,
p1: 0.00000196,
s: 0.54901653,
p: 0.00464183,
T: 15,
};
const EpochState: OrbitState = {
h: 280.24,
N: 345.28,
p1: 282.42,
s: 197.96,
p: 302.64,
T: 180,
};
```
### Table 15 Validation
Lunar Node values hardcoded (Tables 4,5,6)
```ts
// {{cell:utils}}
// {{cell:Table 1 Data}}
const OrbitAtTime = (time: Date) => {
const deltaHours = +time / 1000 / 60 / 60;
return omap(EpochState, (t, k) =>
wrap(t + OrbitVelocities[k] * deltaHours)
);
};
const LunarNodeStateForYear = (y: number): LunarNodeState => {
const db: Record<number, LunarNodeState> = {
1970: {v: -4.42, Xi: -3.98, vPrime: -3.15, twoVPrime: -6.68 },
1971: {v: -7.79, Xi: -7.04, vPrime: -5.52, twoVPrime: -11.60 },
1972: {v: -10.44, Xi: -9.48, vPrime: -7.34, twoVPrime: -15.24 },
2000: {v: 12.67, Xi: 11.70, vPrime: 8.52, twoVPrime: 16.62 },
}
const x = db[y]
if (!x) throw Error('bad year: ' + y)
return x
}
// console.log(1970, OrbitAtTime(new Date("1970")));
// console.log(1971, OrbitAtTime(new Date("1971")));
// console.log(1972, OrbitAtTime(new Date("1972")));
// console.log(2000, OrbitAtTime(new Date("2000")));
const J1 = (o: OrbitState, l: LunarNodeState) =>
{
const V = o.T + o.s + o.h - o.p - 90
const u = -l.v;
return wrap(V + u);
}
const K1 = (o: OrbitState, l: LunarNodeState) =>
{
const V = o.T + o.h - 90
const u = -l.vPrime;
return wrap(V + u);
}
const Lam = (o: OrbitState, l: LunarNodeState) =>
{
const V = 2 * o.T - o.s + o.p + 180
const u = -2*l.v + 2*l.Xi;
return wrap(V + u);
}
const logStatsForYear = (y: number) => {
const d = new Date(''+y)
const o = OrbitAtTime(d)
const l = LunarNodeStateForYear(y)
console.log(y, {J1: J1(o, l), K1: K1(o, l), Lam: Lam(o, l)})
}
logStatsForYear(1970)
logStatsForYear(1971)
logStatsForYear(1972)
logStatsForYear(2000)
```
### Table 6 Validation
In which the angle of the lunar node is converted to `u` parameters
```ts
// {{cell:utils}}
const NtoXiNu = (
N: number
): { Xi: number; Nu: number; NuPrime: number; TwiceNuDoublePrime: number } => {
// tan 1/2 (N - Xi + Nu) = 1.01883 tan 1/2 N
// tan 1/2 (N - Xi - Nu) = 0.64412 tan 1/2 N
// Schureman, page 172
const i = atan(1.01883 * tan(N / 2));
const j = atan(0.64412 * tan(N / 2));
const Nu = i - j;
const Xi = N - i - j;
// cos(I) = 0.91370 - 0.03569 * cos(N)
// Schureman, page 172
const I = acos(0.9137 - 0.03569 * cos(N));
// Nu' = atan[ ( sin 2I sin Nu ) / ( sin 2I cos Nu + 0.3347 ) ]
// Schureman, page 51
const NuPrime = atan(
(sin(2 * I) * sin(Nu)) / (sin(2 * I) * cos(Nu) + 0.3347)
);
// 2Nu'' = atan[ ( sin^2 I * sin 2Nu ) / ( sin^2 I cos 2Nu + 0.0727 ) ]
// Schureman, page 52
const TwiceNuDoublePrime = atan(
(sin(I) ** 2 * sin(2 * Nu)) / (sin(I) ** 2 * cos(2 * Nu) + 0.0727)
);
return { Xi, Nu, NuPrime, TwiceNuDoublePrime };
};
console.log(NtoXiNu(336));
console.log(NtoXiNu(316));
console.log(NtoXiNu(297));
console.log(NtoXiNu(115));
```
```ts
// {{cell:utils}}
console.log(wrap(-3.98))
console.log(wrap(-7.04))
console.log(wrap(-9.48))
```
```ts
for (let y = 2000; y <= 2020; y++) {
console.log(new Date((+new Date(''+y) + +new Date(''+(y+1)))/2))
}
```
```ts
// {{cell:utils}}
const Ps = Array.from({ length: 361 }).map((_, i) => i);
const Is = [23.5];
for (const P of Ps) {
for (const I of Is) {
const R = atan(sin(2 * P) / (cot(I / 2) ** 2 / 6 - cos(2 * P)));
const Q =
atan(((5 * cos(I) - 1) / (7 * cos(I) + 1)) * tan(P)) +
(P > 90 ? 180 : 0) +
(P > 270 ? 180 : 0);
console.log(P, Q);
}
}
```
```ts
// {{cell:utils}}
const I = 23.5
console.log(((5 * cos(I - 1)) / (7 * cos(I + 1))))
console.log(((5 * cos(I) - 1) / (7 * cos(I) + 1)))
```
```ts
const mid = new Date(1673380582728)
console.log(mid.toString())
const offset = -8
const stationDate = new Date(+mid + (offset ?? 0) * 60*60*1000)
const stationTime = {
hours: stationDate.getUTCHours(),
minutes: stationDate.getUTCMinutes(),
day: stationDate.getUTCDate(),
month: stationDate.getUTCMonth(),
year: stationDate.getUTCFullYear(),
}
console.table(stationTime)
```
```ts
const thing = daysPerRev => {
const hoursPerRev = daysPerRev * 24
// const revsPerHour = 1 / hoursPerRev
// const distance = Math.log(1 / revsPerHour ** 2 * 16/36)
const revsPerHour = 1 / hoursPerRev
const logArg = (1 / revsPerHour ** 2) * (16 / 36)
const distance = logArg > 1 ? Math.log(logArg) : 0
console.log(daysPerRev, revsPerHour,logArg , distance)
}
thing(1/24)
thing(1/16)
thing(1/8)
thing(1/4)
thing(1)
thing(4)
thing(16)
thing(64)
thing(256)
const boop = 2.772588722239781
console.log(Array.from({length: 6}).map((_,i) => (i+1) * boop))
```
```ts
// {{cell:utils}}
// {{cell:Table 1 Data}}
// An Epoch for New Moons. Astronomical Algorithms, Jean Meeus
const FirstLunation = new Date('2000-01-06T18:14')
const LunarSpeed = OrbitVelocities.s - OrbitVelocities.h
export const MoonPhaseAtTime = (time: Date) => {
const deltaHours = (+time - +FirstLunation) / (1000 * 60 * 60)
const deltaDegrees = deltaHours * LunarSpeed
return wrap(deltaDegrees)
}
const day = 24 * 60 * 60 * 1000
const lunarCycle = 29.5 * day
for (const cycles of [-0.25, 0, 0.25, 0.5, 1, 10, 15.5]) {
console.log(cycles, MoonPhaseAtTime(new Date(+FirstLunation + cycles * lunarCycle)))
}
```