func Example() {
// Example 16.a, p. 107.
h0 := unit.AngleFromDeg(.5) // apparent lower limb of Sun
R := refraction.Bennett(h0)
fmt.Printf("R: %.3m\n", sexa.FmtAngle(R))
tL := h0 - R // true lower
fmt.Printf("L: %.3m\n", sexa.FmtAngle(tL))
tU := tL + unit.AngleFromMin(32) // add true diameter of sun
fmt.Printf("U: %.3m\n", sexa.FmtAngle(tU))
R = refraction.Saemundsson(tU)
fmt.Printf("R: %.3m\n", sexa.FmtAngle(R))
// Output:
// R: 28.754′
// L: 1.246′
// U: 33.246′
// R: 24.618′
}
import (
"errors"
"math"
"github.com/soniakeys/meeus/deltat"
"github.com/soniakeys/meeus/elliptic"
"github.com/soniakeys/meeus/globe"
"github.com/soniakeys/meeus/interp"
"github.com/soniakeys/meeus/julian"
pp "github.com/soniakeys/meeus/planetposition"
"github.com/soniakeys/meeus/sidereal"
"github.com/soniakeys/unit"
)
var meanRefraction = unit.AngleFromMin(34)
// "Standard altitudes" for various bodies.
//
// The standard altitude is the geometric altitude of the center of body
// at the time of apparent rising or setting.
var (
Stdh0Stellar = unit.AngleFromMin(-34)
Stdh0Solar = unit.AngleFromMin(-50)
Stdh0LunarMean = unit.AngleFromDeg(.125)
)
// Stdh0Lunar is the standard altitude of the Moon considering π, the
// Moon's horizontal parallax.
func Stdh0Lunar(π unit.Angle) unit.Angle {
return π.Mul(.7275) - meanRefraction
// Copyright 2013 Sonia Keys
// License MIT: http://www.opensource.org/licenses/MIT
package base
import "github.com/soniakeys/unit"
// SmallAngle is threshold used by various routines for switching between
// trigonometric functions and Pythagorean approximations.
//
// In chapter 17, p. 109, Meeus recommends 10′.
var (
SmallAngle = unit.AngleFromMin(10) // about .003 radians
CosSmallAngle = SmallAngle.Cos() // about .999996
)
// Hav implements the haversine trigonometric function.
//
// See https://en.wikipedia.org/wiki/Haversine_formula.
func Hav(a unit.Angle) float64 {
// (17.5) p. 115
return .5 * (1 - a.Cos())
}
// Horner evaluates a polynomal with coefficients c at x. The constant
// term is c[0]. The function panics with an empty coefficient list.
func Horner(x float64, c ...float64) float64 {
i := len(c) - 1
y := c[i]
for i > 0 {
i--
// Saemundsson returns refraction for obtaining apparent altitude.
//
// h must be a computed true "airless" altitude of a celestial body in radians.
//
// Result is refraction to be added to h to obtain the apparent altitude
// of the body.
//
// Results are consistent with Bennett to within 4 arc sec.
func Saemundsson(h unit.Angle) unit.Angle {
// (16.4) p. 106
hd := h.Deg()
return unit.AngleFromMin(1.02 / math.Tan((hd+10.3/(hd+5.11))*math.Pi/180))
}
// Bennett2 returns refraction for obtaining true altitude.
//
// Similar to Bennett, but a correction is applied to give a more accurate
// result.
//
// Results are accurate to .015 arc min. Result unit is radians.
func Bennett2(h0 unit.Angle) unit.Angle {
R := Bennett(h0).Min()
return unit.AngleFromMin(R - .06*math.Sin((14.7*R+13)*math.Pi/180))
}
// Bennett returns refraction for obtaining true altitude.
//
// h0 must be a measured apparent altitude of a celestial body in radians.
//
// Results are accurate to .07 arc min from horizon to zenith.
//
// Result is refraction to be subtracted from h0 to obtain the true altitude
// of the body.
func Bennett(h0 unit.Angle) unit.Angle {
// (16.3) p. 106
hd := h0.Deg()
return unit.AngleFromMin(1 / math.Tan((hd+7.31/(hd+4.4))*math.Pi/180))
}