Black moon / Lilith / Mean Apogee

[ebraminio]

As some of the local calendar books feature black moon calculations:

I wanted be able to calculate them using this library and turned out this is easy to calculate only using,

fun meanApogee(time: Time): Double {
    val t = time.tt / 36525.0
    // https://ftp.space.dtu.dk/pub/DTU10/DTU10_TIDEMODEL/SOFTWARE/test_perth3.f#:~:text=lunar%20perigee
    val meanPerigee = ((-1.249172e-5 * t - 1.032e-2) * t + 4069.0137287) * t + 83.3532465
    return (meanPerigee + 180) % 360
}

And it passes the tests brought from those calendar books with some tolerance,

    @Test
    fun `Check black moon values`() {
        listOf(
            1398 to Zodiac.AQUARIUS.with(25, 7),
            1400 to Zodiac.TAURUS.with(16, 42),
            1402 to Zodiac.LEO.with(7, 59),
            1403 to Zodiac.VIRGO.with(18, 46),
        ).map { (year, expected) ->
            val time = seasons(CivilDate(PersianDate(year, 1, 1)).year).marchEquinox
            { assertEquals(expected, meanApogee(time), .15, "$year") }
        }.run(::assertAll)
    }

However if true apogee is meant to be calculated one should go for

lunarApsidesAfter(time)
    .first { it.kind == ApsisKind.Apocenter }
    .time

Which is different from these calculations apparently.

Thought might be useful for others also 😊