poliastro.twobody.angles

Angles and anomalies.

Module Contents

Functions

D_to_nu(D)	True anomaly from parabolic eccentric anomaly.
nu_to_D(nu)	Parabolic eccentric anomaly from true anomaly.
nu_to_E(nu, ecc)	Eccentric anomaly from true anomaly.
nu_to_F(nu, ecc)	Hyperbolic eccentric anomaly from true anomaly.
E_to_nu(E, ecc)	True anomaly from eccentric anomaly.
F_to_nu(F, ecc)	True anomaly from hyperbolic eccentric anomaly.
M_to_E(M, ecc)	Eccentric anomaly from mean anomaly.
M_to_F(M, ecc)	Hyperbolic eccentric anomaly from mean anomaly.
M_to_D(M)	Parabolic eccentric anomaly from mean anomaly.
E_to_M(E, ecc)	Mean anomaly from eccentric anomaly.
F_to_M(F, ecc)	Mean anomaly from eccentric anomaly.
D_to_M(D)	Mean anomaly from eccentric anomaly.
fp_angle(nu, ecc)	Flight path angle.
raan_from_ltan(epoch, ltan=12.0)	RAAN angle from LTAN for SSO around the earth

poliastro.twobody.angles.D_to_nu(D)

True anomaly from parabolic eccentric anomaly.

Parameters

D (Quantity) – Eccentric anomaly.

Returns

nu – True anomaly.

Return type

Quantity

Notes

Taken from Farnocchia, Davide, Davide Bracali Cioci, and Andrea Milani. “Robust resolution of Kepler’s equation in all eccentricity regimes.” Celestial Mechanics and Dynamical Astronomy 116, no. 1 (2013): 21-34.

poliastro.twobody.angles.nu_to_D(nu)

Parabolic eccentric anomaly from true anomaly.

Parameters

nu (Quantity) – True anomaly.

Returns

D – Hyperbolic eccentric anomaly.

Return type

Quantity

Notes

Taken from Farnocchia, Davide, Davide Bracali Cioci, and Andrea Milani. “Robust resolution of Kepler’s equation in all eccentricity regimes.” Celestial Mechanics and Dynamical Astronomy 116, no. 1 (2013): 21-34.

poliastro.twobody.angles.nu_to_E(nu, ecc)

Eccentric anomaly from true anomaly.

New in version 0.4.0.

Parameters

• nu (Quantity) – True anomaly.

• ecc (Quantity) – Eccentricity.

Returns

E – Eccentric anomaly.

Return type

Quantity

poliastro.twobody.angles.nu_to_F(nu, ecc)

Hyperbolic eccentric anomaly from true anomaly.

Parameters

• nu (Quantity) – True anomaly.

• ecc (Quantity) – Eccentricity (>1).

Returns

F – Hyperbolic eccentric anomaly.

Return type

Quantity

Note

Taken from Curtis, H. (2013). Orbital mechanics for engineering students. 167

poliastro.twobody.angles.E_to_nu(E, ecc)

True anomaly from eccentric anomaly.

New in version 0.4.0.

Parameters

• E (Quantity) – Eccentric anomaly.

• ecc (Quantity) – Eccentricity.

Returns

nu – True anomaly.

Return type

Quantity

poliastro.twobody.angles.F_to_nu(F, ecc)

True anomaly from hyperbolic eccentric anomaly.

Parameters

• F (Quantity) – Hyperbolic eccentric anomaly.

• ecc (Quantity) – Eccentricity (>1).

Returns

nu – True anomaly.

Return type

Quantity

poliastro.twobody.angles.M_to_E(M, ecc)

Eccentric anomaly from mean anomaly.

New in version 0.4.0.

Parameters

• M (Quantity) – Mean anomaly.

• ecc (Quantity) – Eccentricity.

Returns

E – Eccentric anomaly.

Return type

Quantity

poliastro.twobody.angles.M_to_F(M, ecc)

Hyperbolic eccentric anomaly from mean anomaly.

Parameters

• M (Quantity) – Mean anomaly.

• ecc (Quantity) – Eccentricity (>1).

Returns

F – Hyperbolic eccentric anomaly.

Return type

Quantity

poliastro.twobody.angles.M_to_D(M)

Parabolic eccentric anomaly from mean anomaly.

Parameters

M (Quantity) – Mean anomaly.

Returns

D – Parabolic eccentric anomaly.

Return type

Quantity

poliastro.twobody.angles.E_to_M(E, ecc)

Mean anomaly from eccentric anomaly.

New in version 0.4.0.

Parameters

• E (Quantity) – Eccentric anomaly.

• ecc (Quantity) – Eccentricity.

Returns

M – Mean anomaly.

Return type

Quantity

poliastro.twobody.angles.F_to_M(F, ecc)

Mean anomaly from eccentric anomaly.

Parameters

• F (Quantity) – Hyperbolic eccentric anomaly.

• ecc (Quantity) – Eccentricity (>1).

Returns

M – Mean anomaly.

Return type

Quantity

poliastro.twobody.angles.D_to_M(D)

Mean anomaly from eccentric anomaly.

Parameters

D (Quantity) – Parabolic eccentric anomaly.

Returns

M – Mean anomaly.

Return type

Quantity

poliastro.twobody.angles.fp_angle(nu, ecc)

Flight path angle.

New in version 0.4.0.

Parameters

• nu (Quantity) – True anomaly.

• ecc (Quantity) – Eccentricity.

Note

Algorithm taken from Vallado 2007, pp. 113.

poliastro.twobody.angles.raan_from_ltan(epoch, ltan=12.0)

RAAN angle from LTAN for SSO around the earth

Parameters

• epoch (Time) – Value of time to calculate the RAAN for

• ltan (Quantity) – Decimal hour between 0 and 24

Returns

RAAN – Right ascension of the ascending node angle in GCRS

Return type

Quantity

Note

Calculations of the sun mean longitude and equation of time follow “Fundamentals of Astrodynamics and Applications” Fourth edition by Vallado, David A.