func conj(t1, t5 float64, dr, dd []float64) (t, Δd float64, err error) {
var l5 *interp.Len5
if l5, err = interp.NewLen5(t1, t5, dr); err != nil {
return
}
if t, err = l5.Zero(true); err != nil {
return
}
if l5, err = interp.NewLen5(t1, t5, dd); err != nil {
return
}
Δd, err = l5.InterpolateXStrict(t)
return
}
func conj(t1, t5 float64, dr, dd []float64) (t float64, Δd unit.Angle, err error) {
var l5 *interp.Len5
if l5, err = interp.NewLen5(t1, t5, dr); err != nil {
return
}
if t, err = l5.Zero(true); err != nil {
return
}
if l5, err = interp.NewLen5(t1, t5, dd); err != nil {
return
}
ΔdRad, err := l5.InterpolateXStrict(t)
return t, unit.Angle(ΔdRad), err
}
// Time computes the time at which a moving body is on a straight line (great
// circle) between two fixed points, such as stars.
//
// Coordinates may be right ascensions and declinations or longitudes and
// latitudes. Fixed points are r1, d1, r2, d2. Moving body is an ephemeris
// of 5 rows, r3, d3, starting at time t1 and ending at time t5. Time scale
// is arbitrary.
//
// Result is time of alignment.
func Time(r1, d1, r2, d2 float64, r3, d3 []float64, t1, t5 float64) (float64, error) {
if len(r3) != 5 || len(d3) != 5 {
return 0, errors.New("r3, d3 must be length 5")
}
gc := make([]float64, 5)
for i, r3i := range r3 {
// (19.1) p. 121
gc[i] = math.Tan(d1)*math.Sin(r2-r3i) +
math.Tan(d2)*math.Sin(r3i-r1) +
math.Tan(d3[i])*math.Sin(r1-r2)
}
l5, err := interp.NewLen5(t1, t5, gc)
if err != nil {
return 0, err
}
return l5.Zero(false)
}
func ExampleLen5_Zero() {
// Exercise, p. 30.
x1 := 25.
x5 := 29.
yTable := []float64{
base.DMSToDeg(true, 1, 11, 21.23),
base.DMSToDeg(true, 0, 28, 12.31),
base.DMSToDeg(false, 0, 16, 07.02),
base.DMSToDeg(false, 1, 01, 00.13),
base.DMSToDeg(false, 1, 45, 46.33),
}
d5, err := interp.NewLen5(x1, x5, yTable)
if err != nil {
fmt.Println(err)
return
}
z, err := d5.Zero(false)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("1988 January %.6f\n", z)
zInt, zFrac := math.Modf(z)
fmt.Printf("1988 January %d at %.62s TD\n", int(zInt),
base.NewFmtTime(zFrac*24*3600))
// compare result to that from just three central values
d3, err := interp.NewLen3(26, 28, yTable[1:4])
if err != nil {
fmt.Println(err)
return
}
z3, err := d3.Zero(false)
if err != nil {
fmt.Println(err)
return
}
dz := z - z3
fmt.Printf("%.6f day\n", dz)
fmt.Printf("%.1f minute\n", dz*24*60)
// Output:
// 1988 January 26.638587
// 1988 January 26 at 15ʰ20ᵐ TD
// 0.000753 day
// 1.1 minute
}
// Time computes the time at which a moving body is on a straight line (great
// circle) between two fixed points, such as stars.
//
// Coordinates may be right ascensions and declinations or longitudes and
// latitudes. Fixed points are r1, d1, r2, d2. Moving body is an ephemeris
// of 5 rows, r3, d3, starting at time t1 and ending at time t5. Time scale
// is arbitrary.
//
// Result is time of alignment.
func Time(r1, d1, r2, d2 unit.Angle, r3, d3 []unit.Angle, t1, t5 float64) (float64, error) {
if len(r3) != 5 || len(d3) != 5 {
return 0, errors.New("r3, d3 must be length 5")
}
gc := make([]float64, 5)
for i, r3i := range r3 {
// (19.1) p. 121
gc[i] = d1.Tan()*(r2-r3i).Sin() +
d2.Tan()*(r3i-r1).Sin() +
d3[i].Tan()*(r1-r2).Sin()
}
l5, err := interp.NewLen5(t1, t5, gc)
if err != nil {
return 0, err
}
return l5.Zero(false)
}
func ExampleLen5_InterpolateX() {
// Example 3.e, p. 28.
x1 := 27.
x5 := 29.
// work in radians to get answer in radians
yTable := []float64{
base.NewAngle(false, 0, 54, 36.125).Rad(),
base.NewAngle(false, 0, 54, 24.606).Rad(),
base.NewAngle(false, 0, 54, 15.486).Rad(),
base.NewAngle(false, 0, 54, 08.694).Rad(),
base.NewAngle(false, 0, 54, 04.133).Rad(),
}
x := 28 + (3+20./60)/24
d5, err := interp.NewLen5(x1, x5, yTable)
if err != nil {
fmt.Println(err)
return
}
y := d5.InterpolateX(x)
// radians easy to format
fmt.Printf("%.3d", base.NewFmtAngle(y))
// Output:
// 54′13″.369
}
func ExampleLen5_InterpolateX() {
// Example 3.e, p. 28.
x1 := 27.
x5 := 29.
// work in degrees
yTable := []float64{
unit.FromSexa(' ', 0, 54, 36.125),
unit.FromSexa(' ', 0, 54, 24.606),
unit.FromSexa(' ', 0, 54, 15.486),
unit.FromSexa(' ', 0, 54, 08.694),
unit.FromSexa(' ', 0, 54, 04.133),
}
d5, err := interp.NewLen5(x1, x5, yTable)
if err != nil {
fmt.Println(err)
return
}
n := (3 + 20./60) / 24
x := 28 + n
y := d5.InterpolateX(x)
fmt.Printf("%.3d", sexa.FmtAngle(unit.AngleFromDeg(y)))
// Output:
// 54′13″.369
}
