dyad.TwoBody

class dyad.TwoBody(m_1, m_2, a, e, Omega=0.0, i=0.0, omega=0.0)[source]

A class representing the elliptical orbits of a two-body system

Represents the orbit of the secondary body with respect to the primary body as well as the orbit of the primary and secondary bodies with respect to the system’s centre of mass.

Parameters:

m_1: array-like: Mass of the primary body, \(m_{1}\).
m_2: array-like: Mass of the secondary body, \(m_{2}\).
a: array-like: Semimajor axis of the relative orbit, \(a\).
e: array-like: Eccentricity of the relative orbit, \(e\).
Omega: array-like: Longitude of the ascending node of the relative orbit, \(\Omega\).
i: array-like: Inclination of the relative orbit, \(i\).
omega: array-like: Argument of pericentre of the relative orbit, \(\omega\).

Attributes:

angular_momentum: Get the body’s specific angular momentum
angular_momentum_magnitude: Get the magnitude of the body’s specific angular momentum
apoapsis: Get the apoapsis of the orbit
area: Get the area contained by the orbit
argument_of_pericentre: Get the orbit’s argument of pericentre
central_mass: Get the central mass
eccentricity: Get the orbit’s eccentricity
eccentricity_vector: Get the eccentricity vector of the orbit
energy: Get the body’s specific total energy
inclination: Get the inclination of the orbit
longitude_of_ascending_node: Get the longitude of the ascending node of the orbit
lrl_vector: Get the Laplace-Runge-Lenz vector of the orbit
periapsis: Get the periapsis of the orbit
period: Get the orbital period
primary: Get the primary body’s orbit as an instance of Orbit
secondary: Get the secondary body’s orbit as an instance of Orbit
semilatus_rectum: Get the orbit’s semilatus rectum
semimajor_axis: Get the orbit’s semimajor axis
semiminor_axis: Get the orbit’s semiminor axis

Methods

`delaunay_elements`([theta])	Get the Delaunay elements of the orbit
`eccentric_anomaly`(theta)	Return the body's eccentric anomaly
`kinetic_energy`(theta)	Return the body's specific kinetic energy
`mean_anomaly`(theta)	Return the body's mean anomaly
`modified_delaunay_elements`([theta])	Get the modified Delaunay elements of the orbit
`orbital_elements`([theta])	Get the orbital elements of the orbit
`potential`(theta)	Return the gravitational potential at the body's position
`radius`(theta)	Return the body's radius
`speed`(theta)	Return the body's speed
`state`(theta)	Return the orbital state vector in Cartesian coordinates

Examples

Scalar parameters defining a single binary system in the perifocal plane.

>>> dyad.TwoBody(1., 1., 1., 0.)
<dyad._core.TwoBody object at 0x...>

Scalar parameters defining a single orbit in the observer’s frame.

>>> dyad.TwoBody(1., 1., 1., 0., 1., 1., 1.)
<dyad._core.TwoBody object at 0x...>

Array-like parameters defining multiple orbits.

>>> m, q, a, e = [1., 1.], [1., 1.], [1., 1.], [0., 0.]
>>> dyad.TwoBody(m, q, a, e)
<dyad._core.TwoBody object at 0x...>

The relative position and velocity of the secondary body with respect to the primary body in the form \((x, y, z, v_{x}, v_{y}, v_{z})\).

>>> dyad.TwoBody(1., 1., 1., 0.).state(1.)
array([ 0.54030231,  0.84147098,  0.        , -0.02047084,  0.01314417,
        0.        ])

The position and velocity of the primary and secondary bodies with respect to the centre-of-mass frame each again in the form \(x, y, z, v_{x}, v_{y}, v_{z}\).

>>> dyad.TwoBody(1., 1., 1., 0.).primary.state(1.)
array([ 0.27015115,  0.42073549,  0.        , -0.01023542,  0.00657209,
        0.        ])
>>> dyad.TwoBody(1., 1., 1., 0.).secondary.state(1.)
array([-0.27015115, -0.42073549, -0.        ,  0.01023542, -0.00657209,
       -0.        ])

__init__(m_1, m_2, a, e, Omega=0.0, i=0.0, omega=0.0)[source]

Methods

`__init__`(m_1, m_2, a, e[, Omega, i, omega])
`delaunay_elements`([theta])	Get the Delaunay elements of the orbit
`eccentric_anomaly`(theta)	Return the body's eccentric anomaly
`kinetic_energy`(theta)	Return the body's specific kinetic energy
`mean_anomaly`(theta)	Return the body's mean anomaly
`modified_delaunay_elements`([theta])	Get the modified Delaunay elements of the orbit
`orbital_elements`([theta])	Get the orbital elements of the orbit
`potential`(theta)	Return the gravitational potential at the body's position
`radius`(theta)	Return the body's radius
`speed`(theta)	Return the body's speed
`state`(theta)	Return the orbital state vector in Cartesian coordinates

Attributes

`angular_momentum`	Get the body's specific angular momentum
`angular_momentum_magnitude`	Get the magnitude of the body's specific angular momentum
`apoapsis`	Get the apoapsis of the orbit
`area`	Get the area contained by the orbit
`argument_of_pericentre`	Get the orbit's argument of pericentre
`central_mass`	Get the central mass
`eccentricity`	Get the orbit's eccentricity
`eccentricity_vector`	Get the eccentricity vector of the orbit
`energy`	Get the body's specific total energy
`inclination`	Get the inclination of the orbit
`longitude_of_ascending_node`	Get the longitude of the ascending node of the orbit
`lrl_vector`	Get the Laplace-Runge-Lenz vector of the orbit
`periapsis`	Get the periapsis of the orbit
`period`	Get the orbital period
`primary`	Get the primary body's orbit as an instance of `Orbit`
`secondary`	Get the secondary body's orbit as an instance of `Orbit`
`semilatus_rectum`	Get the orbit's semilatus rectum
`semimajor_axis`	Get the orbit's semimajor axis
`semiminor_axis`	Get the orbit's semiminor axis