Angles¶

Angles and anomalies.

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, ecc)¶

Parabolic eccentric anomaly from mean anomaly.

Parameters:	M (Quantity) – Mean anomaly. ecc (Quantity) – Eccentricity (>1).
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, ecc)¶

Mean anomaly from eccentric anomaly.

Parameters:	D (Quantity) – Parabolic eccentric anomaly. ecc (Quantity) – Eccentricity.
Returns:	M – Mean anomaly.
Return type:	Quantity

poliastro.twobody.angles.M_to_nu(M, ecc, delta=0.01)¶

True anomaly from mean anomaly.

New in version 0.4.0.

Parameters:	M (Quantity) – Mean anomaly. ecc (Quantity) – Eccentricity. delta (float (optional)) – threshold of near-parabolic regime definition (from Davide Farnocchia et al)
Returns:	nu – True anomaly.
Return type:	Quantity

Examples

>>> M_to_nu(30.0 * u.deg, 0.06 * u.one)
<Quantity 33.67328493 deg>

poliastro.twobody.angles.nu_to_M(nu, ecc, delta=0.01)¶

Mean anomaly from true anomaly.

New in version 0.4.0.

Parameters:	nu (Quantity) – True anomaly. ecc (Quantity) – Eccentricity. delta (float (optional)) – threshold of near-parabolic regime definition (from Davide Farnocchia et al)
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.