More accurate look angles

README.md

@@ -45,15 +45,15 @@ Calc GST given year, month, day, hour, minute and second
 #### func  JDay
 
 ```go
-func JDay(year, mon, day, hr, min, sec int) float64
+func JDay(year, mon, day, hr, min int, sec float64) (float64, float64)
 ```
 Calc julian date given year, month, day, hour, minute and second the julian date
 is defined by each elapsed day since noon, jan 1, 4713 bc.
 
 #### func  Propagate
 
 ```go
-func Propagate(sat Satellite, year int, month int, day, hours, minutes, seconds int) (position, velocity Vector3)
+func Propagate(sat Satellite, jDay, jF float64) (position, velocity Vector3)
 ```
 Calculates position and velocity vectors for given time
 
@@ -96,7 +96,7 @@ Holds an azimuth, elevation and range
 #### func  ECIToLookAngles
 
 ```go
-func ECIToLookAngles(eciSat Vector3, obsCoords LatLong, obsAlt, jday float64) (lookAngles LookAngles)
+func ECIToLookAngles(eciSat Vector3, obsCoords LatLong, obsAlt, jday float64, gravConst GravConst) (lookAngles LookAngles)
 ```
 Calculate look angles for given satellite position and observer position obsAlt
 in km Reference: http://celestrak.com/columns/v02n02/

conversions.go

@@ -39,8 +39,10 @@ func days2mdhms(year int64, epochDays float64) (mon, day, hr, min, sec float64)
 
 // Calc julian date given year, month, day, hour, minute and second
 // the julian date is defined by each elapsed day since noon, jan 1, 4713 bc.
-func JDay(year, mon, day, hr, min, sec int) float64 {
-	return (367.0*float64(year) - math.Floor((7*(float64(year)+math.Floor((float64(mon)+9)/12.0)))*0.25) + math.Floor(275*float64(mon)/9.0) + float64(day) + 1721013.5 + ((float64(sec)/60.0+float64(min))/60.0+float64(hr))/24.0)
+func JDay(year, mon, day, hr, minute int, sec float64) (float64, float64) {
+	jd := (367.0*float64(year) - math.Floor(7*(float64(year)+math.Floor((float64(mon)+9)/12.0))*0.25) + math.Floor(275*float64(mon)/9.0) + float64(day) + 1721013.5)
+	fr := (sec + float64(minute)*60.0 + float64(hr)*3600.0) / 86400.0
+	return jd, fr
 }
 
 // this function finds the greenwich sidereal time (iau-82)
@@ -57,9 +59,9 @@ func gstime(jdut1 float64) (temp float64) {
 }
 
 // Calc GST given year, month, day, hour, minute and second
-func GSTimeFromDate(year, mon, day, hr, min, sec int) float64 {
-	jDay := JDay(year, mon, day, hr, min, sec)
-	return gstime(jDay)
+func GSTimeFromDate(year, mon, day, hr, min int, sec float64) float64 {
+	jDay, jf := JDay(year, mon, day, hr, min, sec)
+	return gstime(jDay + jf)
 }
 
 // Convert Earth Centered Inertial coordinated into equivalent latitude, longitude, altitude and velocity.
@@ -125,13 +127,17 @@ func ThetaG_JD(jday float64) (ret float64) {
 
 // Convert latitude, longitude and altitude into equivalent Earth Centered Intertial coordinates
 // Reference: The 1992 Astronomical Almanac, page K11.
-func LLAToECI(obsCoords LatLong, alt, jday float64) (eciObs Vector3) {
-	re := 6378.137
+func LLAToECI(obsCoords LatLong, alt, jday float64, gravConst GravConst) (eciObs Vector3) {
 	theta := math.Mod(ThetaG_JD(jday)+obsCoords.Longitude, TWOPI)
-	r := (re + alt) * math.Cos(obsCoords.Latitude)
-	eciObs.X = r * math.Cos(theta)
-	eciObs.Y = r * math.Sin(theta)
-	eciObs.Z = (re + alt) * math.Sin(obsCoords.Latitude)
+	latSin := math.Sin(obsCoords.Latitude)
+	latCos := math.Cos(obsCoords.Latitude)
+	c := 1 / math.Sqrt(1+gravConst.f*(gravConst.f-2)*latSin*latSin)
+	sq := c * (1 - gravConst.f) * (1 - gravConst.f)
+	achcp := (gravConst.radiusearthkm*c + alt) * latCos
+
+	eciObs.X = achcp * math.Cos(theta)
+	eciObs.Y = achcp * math.Sin(theta)
+	eciObs.Z = (gravConst.radiusearthkm*sq + alt) * latSin
 	return
 }
 
@@ -147,27 +153,32 @@ func ECIToECEF(eciCoords Vector3, gmst float64) (ecfCoords Vector3) {
 // Calculate look angles for given satellite position and observer position
 // obsAlt in km
 // Reference: http://celestrak.com/columns/v02n02/
-func ECIToLookAngles(eciSat Vector3, obsCoords LatLong, obsAlt, jday float64) (lookAngles LookAngles) {
+func ECIToLookAngles(eciSat Vector3, obsCoords LatLong, obsAlt, jday float64, gravConst GravConst) (lookAngles LookAngles) {
 	theta := math.Mod(ThetaG_JD(jday)+obsCoords.Longitude, 2*math.Pi)
-	obsPos := LLAToECI(obsCoords, obsAlt, jday)
+	obsPos := LLAToECI(obsCoords, obsAlt, jday, gravConst)
 
 	rx := eciSat.X - obsPos.X
 	ry := eciSat.Y - obsPos.Y
 	rz := eciSat.Z - obsPos.Z
 
-	top_s := math.Sin(obsCoords.Latitude)*math.Cos(theta)*rx + math.Sin(obsCoords.Latitude)*math.Sin(theta)*ry - math.Cos(obsCoords.Latitude)*rz
-	top_e := -math.Sin(theta)*rx + math.Cos(theta)*ry
-	top_z := math.Cos(obsCoords.Latitude)*math.Cos(theta)*rx + math.Cos(obsCoords.Latitude)*math.Sin(theta)*ry + math.Sin(obsCoords.Latitude)*rz
+	latSin := math.Sin(obsCoords.Latitude)
+	latCos := math.Cos(obsCoords.Latitude)
+	thetaSin := math.Sin(theta)
+	thetaCos := math.Cos(theta)
 
-	lookAngles.Az = math.Atan(-top_e / top_s)
-	if top_s > 0 {
+	topS := latSin*thetaCos*rx + latSin*thetaSin*ry - latCos*rz
+	topE := -thetaSin*rx + thetaCos*ry
+	topZ := latCos*thetaCos*rx + latCos*thetaSin*ry + latSin*rz
+
+	lookAngles.Az = math.Atan(-topE / topS)
+	if topS > 0 {
 		lookAngles.Az = lookAngles.Az + math.Pi
 	}
 	if lookAngles.Az < 0 {
 		lookAngles.Az = lookAngles.Az + 2*math.Pi
 	}
 	lookAngles.Rg = math.Sqrt(rx*rx + ry*ry + rz*rz)
-	lookAngles.El = math.Asin(top_z / lookAngles.Rg)
+	lookAngles.El = math.Asin(topZ / lookAngles.Rg)
 
 	return
 }

gravity.go

@@ -7,7 +7,7 @@ import (
 
 // Holds variables that are dependent upon selected gravity model
 type GravConst struct {
-	mu, radiusearthkm, xke, tumin, j2, j3, j4, j3oj2 float64
+	mu, radiusearthkm, xke, tumin, j2, j3, j4, j3oj2, f float64
 }
 
 // Returns a GravConst with correct information on requested model provided through the name parameter
@@ -22,6 +22,7 @@ func getGravConst(name string) (grav GravConst) {
 		grav.j3 = -0.00000253881
 		grav.j4 = -0.00000165597
 		grav.j3oj2 = grav.j3 / grav.j2
+		grav.f = 1 / 298.26
 	case "wgs72":
 		grav.mu = 398600.8
 		grav.radiusearthkm = 6378.135
@@ -31,6 +32,7 @@ func getGravConst(name string) (grav GravConst) {
 		grav.j3 = -0.00000253881
 		grav.j4 = -0.00000165597
 		grav.j3oj2 = grav.j3 / grav.j2
+		grav.f = 1 / 298.26
 	case "wgs84":
 		grav.mu = 398600.5
 		grav.radiusearthkm = 6378.137
@@ -40,6 +42,7 @@ func getGravConst(name string) (grav GravConst) {
 		grav.j3 = -0.00000253215306
 		grav.j4 = -0.00000161098761
 		grav.j3oj2 = grav.j3 / grav.j2
+		grav.f = 1 / 298.257223563
 	default:
 		log.Fatal(name, "is not a valid gravity model")
 	}

helpers.go

@@ -83,9 +83,9 @@ func TLEToSat(line1, line2 string, gravconst string) Satellite {
 
 	mon, day, hr, min, sec := days2mdhms(year, sat.epochdays)
 
-	sat.jdsatepoch = JDay(int(year), int(mon), int(day), int(hr), int(min), int(sec))
+	sat.jdsatepoch, sat.jdsatepochF = JDay(int(year), int(mon), int(day), int(hr), int(min), sec)
 
-	sgp4init(&opsmode, sat.jdsatepoch-2433281.5, &sat)
+	sgp4init(&opsmode, sat.jdsatepoch+sat.jdsatepochF-2433281.5, &sat)
 
 	return sat
 }

satellite.go

@@ -11,9 +11,10 @@ type Satellite struct {
 	ErrorStr   string
 	whichconst GravConst
 
-	epochyr    int64
-	epochdays  float64
-	jdsatepoch float64
+	epochyr     int64
+	epochdays   float64
+	jdsatepoch  float64
+	jdsatepochF float64
 
 	ndot  float64
 	nddot float64

satellite_suite_test.go

@@ -7,6 +7,7 @@ import (
 	"strconv"
 	"strings"
 	"testing"
+	"time"
 )
 
 func TestSatellite(t *testing.T) {
@@ -20,6 +21,31 @@ type Result struct {
 }
 
 var _ = Describe("go-satellite", func() {
+
+	Describe("LookAngles", func() {
+
+		It("should return correct observer look angles for given ISS#22825 at 2020-05-23T20:23:37", func() {
+			sat := TLEToSat("1 25544U 98067A   20140.34419374 -.00000374  00000-0  13653-5 0  9990", "2 25544  51.6433 131.2277 0001338 330.3524 173.1622 15.49372617227549", "wgs72")
+
+			time := time.Date(2020, 5, 23, 20, 23, 37, 0, time.UTC)
+			year, month, day := time.Date()
+			hour, min, sec := time.Clock()
+
+			jDay, jF := JDay(year, int(month), day, hour, min, float64(sec))
+			pos, _ := Propagate(sat, jDay, jF)
+
+			latLong := LatLong{
+				Latitude:  DEG2RAD * 55.6167,
+				Longitude: DEG2RAD * 12.6500}
+			alt := 0.005
+
+			angles := ECIToLookAngles(pos, latLong, alt, jDay+jF, sat.whichconst)
+
+			Expect(angles.El * RAD2DEG).To(Equal(42.06164214709452))
+			Expect(angles.Az * RAD2DEG).To(Equal(181.2902281625632))
+		})
+	})
+
 	Describe("ParseTLE", func() {
 		It("should return correctly parsed values for given ISS#25544", func() {
 			sat := ParseTLE("1 25544U 98067A   08264.51782528 -.00002182  00000-0 -11606-4 0  2927", "2 25544  51.6416 247.4627 0006703 130.5360 325.0288 15.72125391563537", "wgs84")
@@ -221,7 +247,7 @@ var _ = Describe("go-satellite", func() {
 			PropagationTestCase{
 				line1: "1 23599U 95029B   06171.76535463  .00085586  12891-6  12956-2 0  2905",
 				line2: "2 23599   6.9327   0.2849 5782022 274.4436  25.2425  4.47796565123555",
-				grav: "wgs72",
+				grav:  "wgs72",
 				testData: `0.00000000 9892.63794341 35.76144969 -1.08228838 3.556643237 6.456009375 0.783610890       
 20.00000000 11931.95642997 7340.74973750 886.46365987 0.308329116 5.532328972 0.672887281
 40.00000000 11321.71039205 13222.84749156 1602.40119049 -1.151973982 4.285810871 0.521919425
@@ -296,4 +322,4 @@ func propagationTest(testCase PropagationTestCase) {
 			})
 		})
 	}
-}
+}

sgp4.go

@@ -292,10 +292,9 @@ func initl(satn int64, grav GravConst, ecco, epoch, inclo, noIn float64, methodI
 }
 
 // Calculates position and velocity vectors for given time
-func Propagate(sat Satellite, year int, month int, day, hours, minutes, seconds int) (position, velocity Vector3) {
-	j := JDay(year, month, day, hours, minutes, seconds)
-	m := (j - sat.jdsatepoch) * 1440
-	return sgp4(&sat, m)
+func Propagate(sat Satellite, jDay, jF float64) (position, velocity Vector3) {
+	tsince := (jDay-sat.jdsatepoch)*1440 + (jF-sat.jdsatepochF)*1440
+	return sgp4(&sat, tsince)
 }
 
 // this procedure is the sgp4 prediction model from space command. this is an updated and combined version of sgp4 and sdp4, which were originally published separately in spacetrack report #3. this version follows the methodology from the aiaa paper (2006) describing the history and development of the code.