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.