# KeplerOrbit¶

class twobody.KeplerOrbit(elements=None, elements_type='kepler', barycenter=None, **kwargs)[source]

Bases: object

Represents a bound Kepler orbit.

Parameters
elementstwobody.OrbitalElements subclass instance

Either pass in an OrbitalElements object, e.g., an instance of twobody.KeplerElements, or pass in the element names themselves. If the latter, anything passed in as kwargs gets passed to the elements class specified by elements_type. The element names for the default elements_type are included below for convenience.

elements_typestr (optional)

Ignore if you pass in an instantiated OrbitalElements object. This argument controls the class that the kwargs are passed to. The default is 'kepler', meaning all keyword arguments get passed to the twobody.KeplerElements class.

barycentertwobody.Barycenter (optional)

Parameters that control specification of the barycenter of the orbit.

Examples

As described above, you can either create an Elements object and then pass this to KeplerOrbit, e.g.,

>>> import astropy.units as u
>>> from astropy.time import Time
>>> from twobody import KeplerElements
>>> t0 = Time(2459812.641, format='jd') # reference epoch
>>> elem = KeplerElements(a=1.5*u.au, e=0.5, P=1.*u.year,
...                       omega=67*u.deg, i=21.*u.deg,
...                       Omega=33*u.deg, M0=53*u.deg, t0=t0)
>>> orb = KeplerOrbit(elem)


Or, you can pass in the element names as arguments to the KeplerOrbit class:

>>> orb = KeplerOrbit(a=1.5*u.au, e=0.5, P=1.*u.year,
...                   omega=67*u.deg, i=21.*u.deg, Omega=33*u.deg,
...                   M0=53*u.deg, t0=t0)


Attributes Summary

Methods Summary

 icrs(self, time) Return the ICRS (i.e. orbital_plane(self, time) Compute the orbit at specified times in the two-body barycentric frame aligned with the orbital plane (xyz). plot_rv(self, time[, ax, rv_unit, t_kwargs, …]) Plot the line-of-sight or radial velocity at the specified times. radial_velocity(self, time[, anomaly_tol, …]) Compute the radial velocity of the body at the specified times relative to the barycenter or reference point, i.e. reference_plane(self, time) Compute the orbit at specified times in the two-body barycentric frame aligned with the reference plane coordinate system (XYZ). unscaled_radial_velocity(self, time[, …]) Compute the unscaled radial velocity of the body at the specified times relative to the barycenter or reference point, i.e.

Attributes Documentation

barycenter

Methods Documentation

icrs(self, time)[source]

Return the ICRS (i.e. reference plane) position and velocity of the orbit at the specified time(s).

Parameters
timearray_like, Time

Time array. Either in BMJD or as an Astropy time.

orbital_plane(self, time)[source]

Compute the orbit at specified times in the two-body barycentric frame aligned with the orbital plane (xyz).

Parameters
timearray_like, astropy.time.Time

Array of times as barycentric MJD values, or an Astropy Time object containing the times to evaluate at.

plot_rv(self, time, ax=None, rv_unit=None, t_kwargs=None, plot_kwargs=None)[source]

Plot the line-of-sight or radial velocity at the specified times.

Parameters
timearray_like, Time

Time array. Either in BMJD or as an Astropy time.

axAxes, optional

The axis to draw on (default is to grab the current axes using gca).

rv_unitUnitBase, optional

Units to plot the radial velocities in (default is km/s).

t_kwargsdict, optional

Keyword arguments passed to astropy.time.Time with the input time array. For example, dict(format='mjd', scale='tcb') for Barycentric MJD.

plot_kwargsdict, optional

Any additional arguments or style settings passed to matplotlib.pyplot.plot().

Returns
axAxes

The matplotlib axes object that the RV curve was drawn on.

radial_velocity(self, time, anomaly_tol=None, anomaly_maxiter=None)[source]

Compute the radial velocity of the body at the specified times relative to the barycenter or reference point, i.e. in the reference plane system not in a solar system barycentric frame.

This should always be close (in a machine precision sense) to the z velocity of orbit.reference_plane(time).

When the barycenter is assumed to be at rest with respect to tangential motion relative to the observer, this should be equivalent to orbit.icrs(time).radial_velocity

As mentioned above and in Compute and plot a radial velocity curve given orbital elements, the radial velocity computed this way assumes that the barycenter does not move tangentially between epochs and thus ignores spherical projection effects. For sources with large proper motions, the true observable line-of-sight velocity will change slightly over time. We can visualize the expected differences given a full specification of the position and motion of the barycenter:

>>> import astropy.units as u
>>> import astropy.coordinates as coord
>>> from astropy.time import Time
>>> from twobody import Barycenter, KeplerOrbit
>>> origin = coord.ICRS(ra=170.8743*u.deg, dec=-71.34*u.deg,
...                     distance=57.134*u.pc,
...                     pm_ra_cosdec=-206.718*u.mas/u.yr,
...                     pm_dec=301.82*u.mas/u.yr,
>>> baryc = Barycenter(origin=origin, t0=Time('J2000'))
>>> orb = KeplerOrbit(P=1.5*u.year, e=0.67, a=1.77*u.au,
...                   omega=17.14*u.deg, i=65*u.deg, Omega=0*u.deg,
...                   M0=35.824*u.deg, t0=Time('J2015.0'),
...                   barycenter=baryc)
>>> t = Time('J2000') + np.linspace(0, 15, 10000) * u.year
>>> (true_rv - approx_rv).to(u.m/u.s).max()
<Quantity 3.315196290913036 m / s>


In this case, the maximum difference is only ~3 m/s.

Parameters
timearray_like, astropy.time.Time

Array of times as barycentric MJD values, or an Astropy Time object containing the times to evaluate at.

anomaly_tolnumeric (optional)

Tolerance passed to eccentric_anomaly_from_mean_anomaly for solving for the eccentric anomaly. See default value in that function.

anomaly_maxiternumeric (optional)

Maximum number of iterations to use in eccentric_anomaly_from_mean_anomaly for solving for the eccentric anomaly. See default value in that function.

reference_plane(self, time)[source]

Compute the orbit at specified times in the two-body barycentric frame aligned with the reference plane coordinate system (XYZ).

Parameters
timearray_like, astropy.time.Time

Array of times as barycentric MJD values, or an Astropy Time object containing the times to evaluate at.

unscaled_radial_velocity(self, time, anomaly_tol=None, anomaly_maxiter=None)[source]

Compute the unscaled radial velocity of the body at the specified times relative to the barycenter or reference point, i.e. in the reference plane system not in a solar system barycentric frame.

See the docstring of radial_velocity for more information and caveats.

Parameters
timearray_like, astropy.time.Time

Array of times as barycentric MJD values, or an Astropy Time object containing the times to evaluate at.

anomaly_tolnumeric (optional)

Tolerance passed to eccentric_anomaly_from_mean_anomaly for solving for the eccentric anomaly. See default value in that function.

anomaly_maxiternumeric (optional)

Maximum number of iterations to use in eccentric_anomaly_from_mean_anomaly for solving for the eccentric anomaly. See default value in that function.

Returns
rvnumeric [m/s]

Relative radial velocity - does not include systemtic velocity!