Angles module

digraph {
   "poliastro.core.angles" -> "D_to_nu", "nu_to_D", "nu_to_E", "nu_to_F", "E_to_nu", "F_to_nu",
                              "M_to_E", "M_to_F", "M_to_D", "E_to_M", "F_to_M", "D_to_M", "M_to_nu",
                              "nu_to_M", "fp_angle";
}

The poliastro.core.angles module contains functions related to conversion between different angles used to define different orbital elements.

poliastro.core.angles.D_to_nu

True anomaly from parabolic eccentric anomaly.

\[\nu = 2 \cdot \arctan{(D)}\]
Parameters

D (Quantity) – Eccentric anomaly.

Returns

nu – True anomaly.

Return type

Quantity

Note

Taken from Farnocchia, Davide, Davide Bracali Cioci, and Andrea Milani. “Robust resolution of Kepler’s equation in all eccentricity regimes.” Celes

poliastro.core.angles.nu_to_D

Parabolic eccentric anomaly from true anomaly.

\[D = \tan{\frac{\nu}{2}}\]
Parameters

nu (Quantity) – True anomaly.

Returns

D – Hyperbolic eccentric anomaly.

Return type

Quantity

Note

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.core.angles.nu_to_E

Eccentric anomaly from true anomaly.

New in version 0.4.0.

\[E = 2\arctan{\sqrt{\frac{1-e}{1+e}}\tan{\frac{\nu}{2}}}\]
Parameters
Returns

E – Eccentric anomaly.

Return type

Quantity

poliastro.core.angles.nu_to_F

Hyperbolic eccentric anomaly from true anomaly.

\[F = ln{\left ( \frac{\sin{(\nu)}\sqrt{e^{2}-1} + \cos{\nu} + e}{1+e\cos{(\nu)}} \right )}\]
Parameters
Returns

F – Hyperbolic eccentric anomaly.

Return type

Quantity

Note

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

poliastro.core.angles.E_to_nu

True anomaly from eccentric anomaly.

New in version 0.4.0.

\[\nu = 2\arctan{\left ( \sqrt{\frac{1+e}{1-e}}\tan{\frac{E}{2}} \right )}\]
Parameters
Returns

nu – True anomaly.

Return type

Quantity

poliastro.core.angles.F_to_nu

True anomaly from hyperbolic eccentric anomaly.

Parameters
  • F (Quantity) – Hyperbolic eccentric anomaly.

  • ecc (Quantity) – Eccentricity (>1).

Returns

nu – True anomaly.

Return type

Quantity

poliastro.core.angles.M_to_E

Eccentric anomaly from mean anomaly.

New in version 0.4.0.

Parameters
Returns

E – Eccentric anomaly.

Return type

Quantity

poliastro.core.angles.M_to_F

Hyperbolic eccentric anomaly from mean anomaly.

Parameters
Returns

F – Hyperbolic eccentric anomaly.

Return type

Quantity

poliastro.core.angles.M_to_D

Parabolic eccentric anomaly from mean anomaly.

Parameters
Returns

D – Parabolic eccentric anomaly.

Return type

Quantity

poliastro.core.angles.E_to_M

Mean anomaly from eccentric anomaly.

New in version 0.4.0.

Parameters
Returns

M – Mean anomaly.

Return type

Quantity

poliastro.core.angles.F_to_M

Mean anomaly from eccentric anomaly.

Parameters
  • F (Quantity) – Hyperbolic eccentric anomaly.

  • ecc (Quantity) – Eccentricity (>1).

Returns

M – Mean anomaly.

Return type

Quantity

poliastro.core.angles.D_to_M

Mean anomaly from eccentric anomaly.

Parameters
  • D (Quantity) – Parabolic eccentric anomaly.

  • ecc (Quantity) – Eccentricity.

Returns

M – Mean anomaly.

Return type

Quantity

poliastro.core.angles.M_to_nu

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

>>> from numpy import radians, degrees
>>> degrees(M_to_nu(radians(30.0), 0.06))
33.67328493021166
poliastro.core.angles.nu_to_M

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.core.angles.fp_angle

Returns the flight path angle.

\[\gamma = \arctan{\frac{e\sin{\theta}}{1 + e\cos{\theta}}}\]
Parameters

Note

Algorithm taken from Vallado 2007, pp. 113.