hapsira.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.

hapsira.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.

hapsira.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.

hapsira.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

hapsira.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

Notes

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

hapsira.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

hapsira.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

hapsira.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

hapsira.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

hapsira.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

hapsira.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

hapsira.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

hapsira.twobody.angles.D_to_M(D)

Mean anomaly from eccentric anomaly.

Parameters:

D (Quantity) – Parabolic eccentric anomaly.

Returns:

M – Mean anomaly.

Return type:

Quantity

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

Flight path angle.

New in version 0.4.0.

Parameters:

• nu (Quantity) – True anomaly.

• ecc (Quantity) – Eccentricity.

Notes

Algorithm taken from Vallado 2007, pp. 113.