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utilities.elements_from_state_vector: fix nan values for f #49

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2eaa444
from_state_vector: Fixed arg_pe incorrect when it should be > 180°.
mgiuca Sep 16, 2025
b52ac6c
from_state_vector: Fix some angular values returning 2*pi instead of 0.
mgiuca Sep 16, 2025
d338690
from_state_vector: Fixed circular inclined orbits having arg_pe = nan.
mgiuca Sep 16, 2025
0b37473
from_state_vector: Fixed assertion error for retrograde non-inclined …
mgiuca Sep 16, 2025
cbd925e
utilities.elements_from_state_vector: Abstract vector_angle to a func…
mgiuca Sep 16, 2025
9b81167
utilities.elements_from_state_vector: fix nan values for f.
mgiuca Sep 16, 2025
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48 changes: 35 additions & 13 deletions src/orbital/utilities.py
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Original file line number Diff line number Diff line change
Expand Up @@ -271,8 +271,9 @@ def elements_from_state_vector(r, v, mu):
# Inclination is the angle between the angular
# momentum vector and its z component.
i = acos(h.z / norm(h))
i_small = abs(i) < SMALL_NUMBER or abs(i - pi) < SMALL_NUMBER

if abs(i) < SMALL_NUMBER:
if i_small:
# For non-inclined orbits, raan is undefined;
# set to zero by convention
raan = 0
Expand All @@ -284,40 +285,50 @@ def elements_from_state_vector(r, v, mu):
# Argument of periapsis is the angle between
# eccentricity vector and its x component.
arg_pe = acos(ev.x / norm(ev))
if ev.y < 0:
arg_pe = -arg_pe
# If plane is upside down, arg_pe needs to be inverted.
if abs(i) > pi * 0.5:
arg_pe = -arg_pe
arg_pe = mod(arg_pe, 2 * pi)
else:
# Right ascension of ascending node is the angle
# between the node vector and its x component.
raan = acos(n.x / norm(n))
if n.y < 0:
raan = 2 * pi - raan
raan = mod(-raan, 2 * pi)

# Argument of periapsis is angle between
# node and eccentricity vectors.
arg_pe = acos(dot(n, ev) / (norm(n) * norm(ev)))
if abs(e) < SMALL_NUMBER:
# For circular orbits, place periapsis
# at ascending node by convention
arg_pe = 0
else:
# Argument of periapsis is angle between
# node and eccentricity vectors.
arg_pe = vector_angle(n, ev)

if abs(e) < SMALL_NUMBER:
if abs(i) < SMALL_NUMBER:
if i_small:
# True anomaly is angle between position
# vector and its x component.
f = acos(r.x / norm(r))
if v.x > 0:
f = 2 * pi - f
f = mod(-f, 2 * pi)
else:
# True anomaly is angle between node
# vector and position vector.
f = acos(dot(n, r) / (norm(n) * norm(r)))
f = vector_angle(n, r)
if dot(n, v) > 0:
f = 2 * pi - f
f = mod(-f, 2 * pi)
else:
if ev.z < 0:
arg_pe = 2 * pi - arg_pe
arg_pe = mod(-arg_pe, 2 * pi)

# True anomaly is angle between eccentricity
# vector and position vector.
f = acos(dot(ev, r) / (norm(ev) * norm(r)))

f = vector_angle(ev, r)
if dot(r, v) < 0:
f = 2 * pi - f
f = mod(-f, 2 * pi)

return OrbitalElements(a=a, e=e, i=i, raan=raan, arg_pe=arg_pe, f=f)

Expand Down Expand Up @@ -373,6 +384,17 @@ def divmod(x, y):
return (floor(x / y), mod(x, y))


def vector_angle(v1, v2):
"""Return the unsigned minimum angle between two XyzVectors [rad].

The result will always be between 0 and pi inclusive.
"""
# The parameter to acos is clamped to the range [-1.0, 1.0]. If this is not
# done, rounding errors can make the value slightly below -1.0 or above 1.0,
# resulting in nan. These should simply result in pi and 0.0, respectively.
return acos(np.clip(dot(v1, v2) / (norm(v1) * norm(v2)), -1.0, 1.0))


# Objects for package


Expand Down
138 changes: 65 additions & 73 deletions tests/test_orbital.py
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Original file line number Diff line number Diff line change
Expand Up @@ -672,26 +672,19 @@ def test_from_state_vector_circular_retrograde(self):
R = Position(RADIUS, 0, 0)
V = Velocity(0, -sqrt(earth.mu / RADIUS), 0)

# XXX This erroneously generates warnings and raises an assertion, due
# to internal values being NaN.
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
self.assertRaises(
AssertionError, KeplerianElements.from_state_vector, R, V, body=earth
)
# The expected values, after this bug is fixed:
# numpy.testing.assert_almost_equal(orbit.r, R)
# numpy.testing.assert_almost_equal(orbit.v, V)
# self.assertAlmostEqual(orbit.a, RADIUS)
# self.assertAlmostEqual(orbit.e, 0.0)
# self.assertAlmostEqual(orbit.i, radians(180))
# self.assertAlmostEqual(orbit.raan, 0.0)
# self.assertAlmostEqual(orbit.arg_pe, 0.0)
# self.assertAlmostEqual(orbit.M0, 0.0)

# self.assertAlmostEqual(orbit.ref_epoch, J2000)
# self.assertEqual(orbit.body, earth)
# self.assertAlmostEqual(orbit.t, 0.0)
orbit = KeplerianElements.from_state_vector(R, V, body=earth)
numpy.testing.assert_almost_equal(orbit.r, R)
numpy.testing.assert_almost_equal(orbit.v, V)
self.assertAlmostEqual(orbit.a, RADIUS)
self.assertAlmostEqual(orbit.e, 0.0)
self.assertAlmostEqual(orbit.i, radians(180))
self.assertAlmostEqual(orbit.raan, 0.0)
self.assertAlmostEqual(orbit.arg_pe, 0.0)
self.assertAlmostEqual(orbit.M0, 0.0)

self.assertAlmostEqual(orbit.ref_epoch, J2000)
self.assertEqual(orbit.body, earth)
self.assertAlmostEqual(orbit.t, 0.0)

def test_from_state_vector_inclined(self):
# Inclined circular orbit, 1/4 of the way around.
Expand All @@ -700,20 +693,14 @@ def test_from_state_vector_inclined(self):
R = Position(-RADIUS * 0.5 * sqrt(2), 0, RADIUS * 0.5 * sqrt(2))
V = Velocity(0, -sqrt(earth.mu / RADIUS), 0)

with warnings.catch_warnings():
# XXX This has a warning for dividing by zero.
warnings.simplefilter("ignore", category=RuntimeWarning)
orbit = KeplerianElements.from_state_vector(R, V, body=earth)
# XXX: r, v and arg_pe are nan due to a bug in from_state_vector.
# This happens for a perfect circle, but doesn't happen in
# test_from_state_vector_circular for some reason.
# numpy.testing.assert_almost_equal(orbit.r, R)
# numpy.testing.assert_almost_equal(orbit.v, V)
orbit = KeplerianElements.from_state_vector(R, V, body=earth)
numpy.testing.assert_almost_equal(orbit.r, R)
numpy.testing.assert_almost_equal(orbit.v, V)
self.assertAlmostEqual(orbit.a, RADIUS)
self.assertAlmostEqual(orbit.e, 0.0)
self.assertAlmostEqual(orbit.i, radians(45))
self.assertAlmostEqual(orbit.raan, radians(90))
# self.assertAlmostEqual(orbit.arg_pe, 0.0)
self.assertAlmostEqual(orbit.arg_pe, 0.0)
self.assertAlmostEqual(orbit.M0, radians(90))

self.assertAlmostEqual(orbit.ref_epoch, J2000)
Expand Down Expand Up @@ -761,15 +748,13 @@ def test_from_state_vector_elliptical_arg_pe_gt_180(self):
V = Velocity(16703.9010129, 0, 0)

orbit = KeplerianElements.from_state_vector(R, V, body=earth)
# XXX These do not match (they are 180° out, due to arg_pe).
# numpy.testing.assert_almost_equal(orbit.r, R)
# numpy.testing.assert_almost_equal(orbit.v, V)
numpy.testing.assert_almost_equal(orbit.r, R)
numpy.testing.assert_almost_equal(orbit.v, V)
self.assertAlmostEqual(orbit.a, 10000000.0, places=3)
self.assertAlmostEqual(orbit.e, 0.75)
self.assertAlmostEqual(orbit.i, 0.0)
self.assertAlmostEqual(orbit.raan, 0.0)
# XXX This is incorrectly calculated as 90°.
# self.assertAlmostEqual(orbit.arg_pe, radians(270.0))
self.assertAlmostEqual(orbit.arg_pe, radians(270.0))
self.assertAlmostEqual(orbit.M0, 0.0)

self.assertAlmostEqual(orbit.ref_epoch, J2000)
Expand All @@ -784,24 +769,19 @@ def test_from_state_vector_f_at_periapsis(self):
R = Position(0, -1767766.952966369, -1767766.952966369)
V = Velocity(16703.901013, 0, 0)

# XXX Currently crashes due to the above bug.
with warnings.catch_warnings():
warnings.simplefilter("ignore", category=RuntimeWarning)
self.assertRaises(
AssertionError, KeplerianElements.from_state_vector, R, V, body=earth
)
# numpy.testing.assert_almost_equal(orbit.r, R)
# numpy.testing.assert_almost_equal(orbit.v, V)
# self.assertAlmostEqual(orbit.a, 10000000.0, places=2)
# self.assertAlmostEqual(orbit.e, 0.75)
# self.assertAlmostEqual(orbit.i, radians(45))
# self.assertAlmostEqual(orbit.raan, 0.0)
# self.assertAlmostEqual(orbit.arg_pe, radians(270.0))
# self.assertAlmostEqual(orbit.M0, 0.0)

# self.assertAlmostEqual(orbit.ref_epoch, J2000)
# self.assertEqual(orbit.body, earth)
# self.assertAlmostEqual(orbit.t, 0.0)
orbit = KeplerianElements.from_state_vector(R, V, body=earth)
numpy.testing.assert_almost_equal(orbit.r, R)
numpy.testing.assert_almost_equal(orbit.v, V)
self.assertAlmostEqual(orbit.a, 10000000.0, places=2)
self.assertAlmostEqual(orbit.e, 0.75)
self.assertAlmostEqual(orbit.i, radians(45))
self.assertAlmostEqual(orbit.raan, 0.0)
self.assertAlmostEqual(orbit.arg_pe, radians(270.0))
self.assertAlmostEqual(orbit.M0, 0.0)

self.assertAlmostEqual(orbit.ref_epoch, J2000)
self.assertEqual(orbit.body, earth)
self.assertAlmostEqual(orbit.t, 0.0)

def test_from_state_vector_iss(self):
# ISS (Zarya) from 2008-09-20 12:25:40
Expand Down Expand Up @@ -832,23 +812,39 @@ def test_from_state_vector_roundtrips(self):
# Circular flat, f > 180°.
(Position(0, -10000000, 0), Velocity(6313.4811435530555, 0, 0)),
# Circular flat, retrograde.
# (Position(10000000, 0, 0), Velocity(0, -6313.4811435530555, 0)),
(Position(10000000, 0, 0), Velocity(0, -6313.4811435530555, 0)),
# Circular inclined, prograde.
# (Position(10000000, 0, 0), Velocity(0, 4464.305329499764, 4464.305329499764)),
(
Position(10000000, 0, 0),
Velocity(0, 4464.305329499764, 4464.305329499764),
),
# Circular inclined, prograde (raan 90°, M0 90°).
# (Position(-7071067.811865476, 0, 7071067.811865476), Velocity(0, -6313.4811435530555, 0)),
(
Position(-7071067.811865476, 0, 7071067.811865476),
Velocity(0, -6313.4811435530555, 0),
),
# Circular inclined, raan > 180°.
# (Position(0, -10000000, 0), Velocity(4464.305329499764, 0, 4464.305329499764)),
(
Position(0, -10000000, 0),
Velocity(4464.305329499764, 0, 4464.305329499764),
),
# Circular inclined, f > 180°.
# (Position(0, -7071067.811865476, -7071067.811865476), Velocity(6313.4811435530555, 0, 0)),
(
Position(0, -7071067.811865476, -7071067.811865476),
Velocity(6313.4811435530555, 0, 0),
),
# Circular polar.
# (Position(10000000, 0, 0), Velocity(0, 0, 6313.4811435530555)),
(Position(10000000, 0, 0), Velocity(0, 0, 6313.4811435530555)),
# Elliptical flat (e=0.75), prograde.
(Position(2500000, 0, 0), Velocity(0, 16703.901013, 0)),
# Elliptical flat (e=0.75), arg_pe > 180°.
# (Position(0, -2500000, 0), Velocity(16703.901013, 0, 0)),
(Position(0, -2500000, 0), Velocity(16703.901013, 0, 0)),
# Elliptical flat (e=0.75), retrograde.
# (Position(2500000, 0, 0), Velocity(0, -16703.901013, 0)),
(Position(2500000, 0, 0), Velocity(0, -16703.901013, 0)),
# Elliptical flat (e=0.75), retrograde, arg_pe = 90°, at periapsis.
(Position(0, -2500000, 0), Velocity(-16703.901013, 0, 0)),
# Elliptical flat, retrograde, arg_pe = 90°, at apoapsis.
(Position(0, -2500000, 0), Velocity(-10000.0, 0, 0)),
# Elliptical flat (e=0.75), f > 180°.
(
Position(-13255776.4031414, -5408888.899183, 0),
Expand All @@ -860,7 +856,10 @@ def test_from_state_vector_roundtrips(self):
Velocity(0, 11811.441678561141, 11811.441678561141),
),
# Elliptical inclined, arg_pe > 180°.
# (Position(0, -1767766.952966369, -1767766.952966369), Velocity(16703.901013, 0, 0)),
(
Position(0, -1767766.952966369, -1767766.952966369),
Velocity(16703.901013, 0, 0),
),
]

for i, (r, v) in enumerate(CASES):
Expand Down Expand Up @@ -1077,19 +1076,12 @@ def test_set_v_arg_pe_gt_180(self):
# arg_pe = 270°.
V = Velocity(-10000, 0, 0)

def set_v(value):
orbit.v = value

# XXX The 'r and v changed' detection logic is triggered in this case,
# causing a RuntimeError to be raised. If this was not raised, the
# following asserts would be wildly off.
self.assertRaises(RuntimeError, set_v, V)
# numpy.testing.assert_almost_equal(orbit.r, R)
# numpy.testing.assert_almost_equal(orbit.v, V)
orbit.v = V
numpy.testing.assert_almost_equal(orbit.r, R)
numpy.testing.assert_almost_equal(orbit.v, V)
# arg_pe should have rotated around 180°, and M0 to match (so r is in
# the same spot as it was before).
# XXX This is incorrectly calculated as 90°.
# self.assertAlmostEqual(orbit.arg_pe, radians(270.0))
self.assertAlmostEqual(orbit.arg_pe, radians(270.0))
self.assertAlmostEqual(orbit.M0, radians(180.0))

def test_set_n(self):
Expand Down
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