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:
Returns:

E – Eccentric anomaly.

Return type:

Quantity

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

Hyperbolic eccentric anomaly from true anomaly.

Parameters:
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:
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:
Returns:

E – Eccentric anomaly.

Return type:

Quantity

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

Hyperbolic eccentric anomaly from mean anomaly.

Parameters:
Returns:

F – Hyperbolic eccentric anomaly.

Return type:

Quantity

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

Parabolic eccentric anomaly from mean anomaly.

Parameters:
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:
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:

Note

Algorithm taken from Vallado 2007, pp. 113.