// Kepler3 solves Kepler's equation by binary search.
//
// Argument e is eccentricity, M is mean anomaly.
//
// Result E is eccentric anomaly.
func Kepler3(e float64, M unit.Angle) (E unit.Angle) {
// adapted from BASIC, p. 206
MR := M.Mod1().Rad()
f := 1
if MR > math.Pi {
f = -1
MR = 2*math.Pi - MR
}
E0 := math.Pi * .5
d := math.Pi * .25
for i := 0; i < 53; i++ {
M1 := E0 - e*math.Sin(E0)
if MR-M1 < 0 {
E0 -= d
} else {
E0 += d
}
d *= .5
}
if f < 0 {
E0 = -E0
}
return unit.Angle(E0)
}