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Module airball.stars

The following documentation was automatically generated from the docstrings.

airball.stars.Star

This is the AIRBALL Star class. It encapsulates the relevant parameters for a given star. Only the mass is a quantity intrinsic to the object. The impact parameter, velocity, inclination, argument of periastron, and longitude of the ascending node quantities are defined with respect to the host star and plane passing through the star.

Parameters:

Name Type Description Default
m float

The mass of the star. Default units are in solMass.

 required
b float

The impact parameter of the star. Default units are in AU.

 required
v float

The velocity at infinity of the star. Default units are in km/s.

 required
inc float

The inclination of the star. Default units are in radians.

 'isotropic'
omega float

The argument of the periastron of the star. Default units are in radians.

 'isotropic'
Omega float

The longitude of the ascending node of the star. Default units are in radians.

 'isotropic'
UNIT_SYSTEM list

The unit system to use for the parameters. Default is [u.solMass, u.AU, u.km/u.s, u.rad].

 []

Attributes:

Name Type Description
m Quantity

The mass of the star. Default units are in solMass.
b Quantity

The impact parameter of the star. Default units are in AU.
v Quantity

The velocity at infinity of the star. Default units are in km/s.
inc Quantity

The inclination of the star. Default units are in radians.
omega Quantity

The argument of the periastron of the star. Default units are in radians.
Omega Quantity

The longitude of the ascending node of the star. Default units are in radians.
units UnitSet

The unit system to use for the parameters. Default is [u.solMass, u.AU, u.km/u.s, u.rad].
impulse_gradient Quantity

The impulse gradient of the star. Default units are in km/s/AU.
params list

A list of the parameters of the star in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega.
param_values list

A list of the values of the parameters of the star in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega.

Examples:

import airball

star = airball.Star(m=1.0, b=1.0, v=1.0, inc=0.0, omega=0.0, Omega=0.0)

import airball

star = airball.Star(m=1.0, b=1.0, v=1.0, inc="isotropic", omega="isotropic", Omega="isotropic")

import airball

star = airball.Star(m=1.0, b=1.0, v=1.0)
Source code in src/airball/stars.py 
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class Star:
    """
    This is the AIRBALL Star class.
    It encapsulates the relevant parameters for a given star. Only the mass is a quantity intrinsic to the object. The impact parameter, velocity, inclination, argument of periastron, and longitude of the ascending node quantities are defined with respect to the host star and plane passing through the star.

    Args:
      m (float): The mass of the star. Default units are in solMass.
      b (float): The impact parameter of the star. Default units are in AU.
      v (float): The velocity at infinity of the star. Default units are in km/s.
      inc (float, optional): The inclination of the star. Default units are in radians.
      omega (float, optional): The argument of the periastron of the star. Default units are in radians.
      Omega (float, optional): The longitude of the ascending node of the star. Default units are in radians.
      UNIT_SYSTEM (list, optional): The unit system to use for the parameters. Default is [u.solMass, u.AU, u.km/u.s, u.rad].

    Attributes:
      m (astropy.units.Quantity): The mass of the star. Default units are in solMass.
      b (astropy.units.Quantity): The impact parameter of the star. Default units are in AU.
      v (astropy.units.Quantity): The velocity at infinity of the star. Default units are in km/s.
      inc (astropy.units.Quantity): The inclination of the star. Default units are in radians.
      omega (astropy.units.Quantity): The argument of the periastron of the star. Default units are in radians.
      Omega (astropy.units.Quantity): The longitude of the ascending node of the star. Default units are in radians.
      units (airball.tools.UnitSet): The unit system to use for the parameters. Default is [u.solMass, u.AU, u.km/u.s, u.rad].
      impulse_gradient (astropy.units.Quantity): The impulse gradient of the star. Default units are in km/s/AU.
      params (list): A list of the parameters of the star in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega.
      param_values (list): A list of the values of the parameters of the star in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega.

    Examples:
      ```python
      import airball

      star = airball.Star(m=1.0, b=1.0, v=1.0, inc=0.0, omega=0.0, Omega=0.0)
      ```

      ```python
      import airball

      star = airball.Star(m=1.0, b=1.0, v=1.0, inc="isotropic", omega="isotropic", Omega="isotropic")
      ```

      ```python
      import airball

      star = airball.Star(m=1.0, b=1.0, v=1.0)
      ```
    """

    def __init__(
        self,
        m: float | _u.Quantity,
        b: float | _u.Quantity,
        v: float | _u.Quantity,
        inc: float | _u.Quantity | str = "isotropic",
        omega: float | _u.Quantity | str = "isotropic",
        Omega: float | _u.Quantity | str = "isotropic",
        UNIT_SYSTEM=[],
        **kwargs,
    ) -> None:
        self.units = _u.UnitSet(UNIT_SYSTEM)

        seed = kwargs.get("seed", _np.random.randint(0, int(2**32 - 3)))
        if inc == "isotropic" or inc is None:
            inc = 2 * _np.arcsin(_np.sqrt(_uniform.rvs(size=1, random_state=seed + 1)))[0]
        if omega == "isotropic" or omega is None:
            omega = _uniform.rvs(loc=0, scale=(2.0 * _np.pi), size=1, random_state=seed + 2)[0]
        if Omega == "isotropic" or Omega is None:
            Omega = _uniform.rvs(loc=-_np.pi, scale=(2.0 * _np.pi), size=1, random_state=seed + 3)[0]
        if inc == "uniform" or inc is None:
            inc = _uniform.rvs(loc=-_np.pi, scale=(2.0 * _np.pi), size=1, random_state=seed + 1)[0]
        if omega == "uniform" or omega is None:
            omega = _uniform.rvs(loc=-_np.pi, scale=(2.0 * _np.pi), size=1, random_state=seed + 2)[0]
        if Omega == "uniform" or Omega is None:
            Omega = _uniform.rvs(loc=-_np.pi, scale=(2.0 * _np.pi), size=1, random_state=seed + 3)[0]

        self.mass = m
        self.impact_parameter = b
        self.velocity = v
        self.inc = inc
        self.argument_periastron = omega
        self.longitude_ascending_node = Omega

    @property
    def UNIT_SYSTEM(self):
        return self.units.UNIT_SYSTEM

    @UNIT_SYSTEM.setter
    def UNIT_SYSTEM(self, UNIT_SYSTEM):
        self.units.UNIT_SYSTEM = UNIT_SYSTEM

    @property
    def N(self):
        return 1

    @property
    def m(self):
        return self._mass.to(self.units["mass"])

    @m.setter
    def m(self, value):
        self._mass = _tools.verify_unit(value, self.units["mass"])

    @property
    def mass(self):
        return self.m

    @mass.setter
    def mass(self, value):
        self.m = value

    @property
    def b(self):
        return self._impact_parameter.to(self.units["length"])

    @b.setter
    def b(self, value):
        self._impact_parameter = _tools.verify_unit(value, self.units["length"])

    @property
    def impact_parameter(self):
        return self.b

    @impact_parameter.setter
    def impact_parameter(self, value):
        self.b = value

    @property
    def v(self):
        return self._velocity.to(self.units["velocity"])

    @v.setter
    def v(self, value):
        self._velocity = _tools.verify_unit(value, self.units["velocity"])

    @property
    def velocity(self):
        return self.v

    @velocity.setter
    def velocity(self, value):
        self.v = value

    @property
    def inc(self):
        return self._inclination.to(self.units["angle"])

    @inc.setter
    def inc(self, value):
        self._inclination = _tools.verify_unit(value, self.units["angle"])

    @property
    def inclination(self):
        return self.inc

    @inclination.setter
    def inclination(self, value):
        self.inc = value

    @property
    def omega(self):
        return self._argument_periastron.to(self.units["angle"])

    @omega.setter
    def omega(self, value):
        self._argument_periastron = _tools.verify_unit(value, self.units["angle"])

    @property
    def argument_periastron(self):
        return self.omega

    @argument_periastron.setter
    def argument_periastron(self, value):
        self.omega = value

    @property
    def Omega(self):
        return self._longitude_ascending_node.to(self.units["angle"])

    @Omega.setter
    def Omega(self, value):
        self._longitude_ascending_node = _tools.verify_unit(value, self.units["angle"])

    @property
    def longitude_ascending_node(self):
        return self.Omega

    @longitude_ascending_node.setter
    def longitude_ascending_node(self, value):
        self.Omega = value

    @property
    def impulse_gradient(self):
        # Calculate the impulse gradient for a flyby star.
        G = 1 * _u.au**3 / _u.solMass / _u.yr2pi**2
        return ((2.0 * G * self.m) / (self.v * self.b**2.0)).to(_u.km / _u.s / _u.au)

    @property
    def params(self):
        # Returns a list of the parameters of the Stars (with units) in order of:
        # Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega
        return [self.m, self.b, self.v, self.inc, self.omega, self.Omega]

    @property
    def param_values(self):
        # Returns a list of the parameters of the Stars in order of:
        # Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega
        return _np.array(
            [
                self.m.value,
                self.b.value,
                self.v.value,
                self.inc.value,
                self.omega.value,
                self.Omega.value,
            ]
        )

    def eccentricity(self, sim):
        return self.e(sim)

    def e(self, sim):
        sim_units = _tools.rebound_units(sim)
        G = sim.G * sim_units["length"] ** 3 / sim_units["mass"] / sim_units["time"] ** 2
        mu = G * (_tools.system_mass(sim) * sim_units["mass"] + self.m)

        numerator = self.b * self.v * self.v
        return _np.sqrt(1 + (numerator / mu) ** 2.0)

    def periastron(self, sim):
        return self.q(sim)

    def q(self, sim):
        sim_units = _tools.rebound_units(sim)
        G = sim.G * sim_units["length"] ** 3 / sim_units["mass"] / sim_units["time"] ** 2
        mu = G * (_tools.system_mass(sim) * sim_units["mass"] + self.m)

        numerator = self.b * self.v * self.v
        star_e = _np.sqrt(1 + (numerator / mu) ** 2.0)
        return self.b * _np.sqrt((star_e - 1.0) / (star_e + 1.0))

    def save(self, filename):
        """
        Save the current instance of the Star class to a file using pickle.

        Args:
          filename (str): The name of the file to save the instance to. The file will be saved in binary format.

        Example:
          ```python
          import airball

          star = airball.Star(m=1, b=250, v=1)
          star.save("my_special.star")
          ```
        """
        if not isinstance(filename, (str, Path)):
            raise ValueError("Filename must be a string or Path.")
        with open(filename, "wb") as pfile:
            _pickle.dump(self, pfile, protocol=_pickle.HIGHEST_PROTOCOL)

    def copy(self) -> "Star":
        """Returns a deep copy of the Star object."""
        return _deepcopy(self)

    @classmethod
    def from_file(cls, filename):
        """
        Load an instance of the Star class from a file using pickle.

        Args:
          filename (str): The name of the file to load the instance from. The file should be in binary format, pickled.

        Returns:
          loaded_star (Star): The loaded instance of the Star class.

        Example:
          ```python
          import airball

          stars = airball.Star.from_file("my_special.star")
          ```
        """
        try:
            if not isinstance(filename, (str, Path)):
                raise ValueError("Filename must be a string or Path.")
            with open(filename, "rb") as pfile:
                pickled = _pickle.load(pfile)
            dic = pickled.__dict__
            newStar = Star(
                m=dic["_mass"],
                b=dic["_impact_parameter"],
                v=dic["_velocity"],
                inc=dic["_inclination"],
                omega=dic["_argument_periastron"],
                Omega=dic["_longitude_ascending_node"],
                UNIT_SYSTEM=dic["units"],
            )
        except:  # noqa: E722
            raise Exception("Invalid filename.")
        return newStar

    def stats(self, returned=False):
        # Prints a summary of the current stats of the Star.
        s = f"<{self.__module__}.{type(self).__name__} object at {hex(id(self))}, "
        s += f"m= {self.mass:1.4g}, "
        s += f"b= {self.impact_parameter:1.4g}, "
        s += f"v= {self.velocity:1.4g}, "
        s += f"inc= {self.inc:1.4g}, "
        s += f"omega= {self.omega:1.4g}, "
        s += f"Omega= {self.Omega:1.4g}>"
        if returned:
            return s
        else:
            print(s)

    def __str__(self):
        return self.stats(returned=True)

    def __repr__(self):
        return self.stats(returned=True)

    def __len__(self):
        return NotImplemented

    def __eq__(self, other):
        # Overrides the default implementation
        if isinstance(other, Star):
            data = (
                (self.m == other.m)
                and (self.b == other.b)
                and (self.v == other.v)
                and (self.inc == other.inc)
                and (self.omega == other.omega)
                and (self.Omega == other.Omega)
            )
            properties = self.units == other.units
            return data and properties
        return NotImplemented

    def __hash__(self):
        # Overrides the default implementation.
        data = []
        for d in sorted(self.__dict__.items()):
            try:
                data.append((d[0], tuple(d[1])))
            except:  # noqa: E722
                data.append(d)
        data = tuple(data)
        return hash(data)
copy()

Returns a deep copy of the Star object.

Source code in src/airball/stars.py 
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def copy(self) -> "Star":
    """Returns a deep copy of the Star object."""
    return _deepcopy(self)
from_file(filename) classmethod

Load an instance of the Star class from a file using pickle.

Parameters:

Name Type Description Default
filename str

The name of the file to load the instance from. The file should be in binary format, pickled.

 required

Returns:

Name Type Description
loaded_star Star

The loaded instance of the Star class.
Example 
import airball

stars = airball.Star.from_file("my_special.star")
Source code in src/airball/stars.py 
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@classmethod
def from_file(cls, filename):
    """
    Load an instance of the Star class from a file using pickle.

    Args:
      filename (str): The name of the file to load the instance from. The file should be in binary format, pickled.

    Returns:
      loaded_star (Star): The loaded instance of the Star class.

    Example:
      ```python
      import airball

      stars = airball.Star.from_file("my_special.star")
      ```
    """
    try:
        if not isinstance(filename, (str, Path)):
            raise ValueError("Filename must be a string or Path.")
        with open(filename, "rb") as pfile:
            pickled = _pickle.load(pfile)
        dic = pickled.__dict__
        newStar = Star(
            m=dic["_mass"],
            b=dic["_impact_parameter"],
            v=dic["_velocity"],
            inc=dic["_inclination"],
            omega=dic["_argument_periastron"],
            Omega=dic["_longitude_ascending_node"],
            UNIT_SYSTEM=dic["units"],
        )
    except:  # noqa: E722
        raise Exception("Invalid filename.")
    return newStar
save(filename)

Save the current instance of the Star class to a file using pickle.

Parameters:

Name Type Description Default
filename str

The name of the file to save the instance to. The file will be saved in binary format.

 required
Example 
import airball

star = airball.Star(m=1, b=250, v=1)
star.save("my_special.star")
Source code in src/airball/stars.py 
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def save(self, filename):
    """
    Save the current instance of the Star class to a file using pickle.

    Args:
      filename (str): The name of the file to save the instance to. The file will be saved in binary format.

    Example:
      ```python
      import airball

      star = airball.Star(m=1, b=250, v=1)
      star.save("my_special.star")
      ```
    """
    if not isinstance(filename, (str, Path)):
        raise ValueError("Filename must be a string or Path.")
    with open(filename, "wb") as pfile:
        _pickle.dump(self, pfile, protocol=_pickle.HIGHEST_PROTOCOL)

airball.stars.Stars

Bases: MutableMapping

This class allows the user to access stars like an array using the star's index. Allows for negative indices and slicing. The implementation uses astropy.Quantity and numpy ndarrays underneath and only generates a airball.Star object when a single Star is requested.

Parameters:

Name Type Description Default
m list, ndarray, or Quantity

The masses of the stars. Default units are in solMass.

 required
b list, ndarray, or Quantity

The impact parameters of the stars. Default units are in AU.

 required
v list, ndarray, or Quantity

The velocities at infinity of the stars. Default units are in km/s.

 required
inc list, ndarray, or Quantity

The inclinations of the stars. Default units are in radians.

 required
omega list, ndarray, or Quantity

The arguments of the periastron of the stars. Default units are in radians.

 required
Omega list, ndarray, or Quantity

The longitudes of the ascending node of the stars. Default units are in radians.

 required
UNIT_SYSTEM list

The unit system to use for the parameters. Default is [u.solMass, u.AU, u.km/u.s, u.rad].

 required
size int

The number of stars to generate. Default is None.

 required
environment Environment

The environment to generate the stars in (if size > 1). env is an alias. Default is None.

 required
filename str

The name of the file to load the instance from. The file should be in binary format. Default is None.

 None

Attributes:

Name Type Description
m Quantity

The masses of the stars. Default units are in solMass.
b Quantity

The impact parameters of the stars. Default units are in AU.
v Quantity

The velocities at infinity of the stars. Default units are in km/s.
inc Quantity

The inclinations of the stars. Default units are in radians.
omega Quantity

The arguments of the periastron of the stars. Default units are in radians.
Omega Quantity

The longitudes of the ascending node of the stars. Default units are in radians.
units UnitSet

The unit system to use for the parameters. Default is [u.solMass, u.AU, u.km/u.s, u.rad].
median_mass Quantity

The median mass of the stars. Default units are in solMass.
mean_mass Quantity

The mean mass of the stars. Default units are in solMass.
N int

The number of stars.
shape tuple

The shape of the stars array.
params list

A list of the parameters of the stars in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega.
param_values list

A list of the values of the parameters of the stars in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega.

Examples:

# Explicitly specify the stellar parameters.
import airball

stars_from_params1 = airball.Stars(
    m=[1.0, 1.0, 1.0],
    b=[1.0, 1.0, 1.0],
    v=[1.0, 1.0, 1.0],
    inc=[0.0, 0.0, 0.0],
    omega=[0.0, 0.0, 0.0],
    Omega=[0.0, 0.0, 0.0],
)
stars_from_params2 = airball.Stars(m=[1.0, 1.0, 1.0], b=[1.0, 1.0, 1.0], v=[1.0, 1.0, 1.0])  # random orientation angles
stars_from_params3 = airball.Stars(
    m=1, b=200, v=5, omega=0, Omega=0, size=100
)  # 100 identical stars with isotropically random inclinations
stars_from_params4 = airball.Stars(
    m=[1.0, 1.0, 1.0], b=[1.0, 1.0, 1.0], v=[1.0, 1.0, 1.0], inc="uniform", omega="uniform", Omega="uniform"
)  # uniformly random orientation angles

# Randomly generate the stellar parameters from a given environment.
import airball

stars_from_env1 = airball.Stars(environment=airball.OpenCluster(), size=3)
stars_from_env2 = airball.Stars(env=airball.LocalNeighborhood(), size=5)
stars_from_env3 = airball.Stars(airball.GlobularCluster(), size=9)

# Load the stellar parameters from a file.
import airball

stars_from_file1 = airball.Stars(filename="open_cluster.stars")
stars_from_file2 = airball.Stars("open_cluster.stars")
Source code in src/airball/stars.py 
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class Stars(MutableMapping):
    """
    This class allows the user to access stars like an array using the star's index.
    Allows for negative indices and slicing.
    The implementation uses astropy.Quantity and numpy ndarrays underneath and only generates a airball.Star object when a single Star is requested.

    Args:
      m (list, ndarray, or Quantity): The masses of the stars. Default units are in solMass.
      b (list, ndarray, or Quantity): The impact parameters of the stars. Default units are in AU.
      v (list, ndarray, or Quantity): The velocities at infinity of the stars. Default units are in km/s.
      inc (list, ndarray, or Quantity, optional): The inclinations of the stars. Default units are in radians.
      omega (list, ndarray, or Quantity, optional): The arguments of the periastron of the stars. Default units are in radians.
      Omega (list, ndarray, or Quantity, optional): The longitudes of the ascending node of the stars. Default units are in radians.
      UNIT_SYSTEM (list, optional): The unit system to use for the parameters. Default is [u.solMass, u.AU, u.km/u.s, u.rad].
      size (int, optional): The number of stars to generate. Default is None.
      environment (airball.Environment, optional): The environment to generate the stars in (if `size` > 1). `env` is an alias. Default is None.
      filename (str, optional): The name of the file to load the instance from. The file should be in binary format. Default is None.

    Attributes:
      m (astropy.units.Quantity): The masses of the stars. Default units are in solMass.
      b (astropy.units.Quantity): The impact parameters of the stars. Default units are in AU.
      v (astropy.units.Quantity): The velocities at infinity of the stars. Default units are in km/s.
      inc (astropy.units.Quantity): The inclinations of the stars. Default units are in radians.
      omega (astropy.units.Quantity): The arguments of the periastron of the stars. Default units are in radians.
      Omega (astropy.units.Quantity): The longitudes of the ascending node of the stars. Default units are in radians.
      units (airball.tools.UnitSet): The unit system to use for the parameters. Default is [u.solMass, u.AU, u.km/u.s, u.rad].
      median_mass (astropy.units.Quantity): The median mass of the stars. Default units are in solMass.
      mean_mass (astropy.units.Quantity): The mean mass of the stars. Default units are in solMass.
      N (int): The number of stars.
      shape (tuple): The shape of the stars array.
      params (list): A list of the parameters of the stars in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega.
      param_values (list): A list of the values of the parameters of the stars in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega.

    Examples:
      ```python
      # Explicitly specify the stellar parameters.
      import airball

      stars_from_params1 = airball.Stars(
          m=[1.0, 1.0, 1.0],
          b=[1.0, 1.0, 1.0],
          v=[1.0, 1.0, 1.0],
          inc=[0.0, 0.0, 0.0],
          omega=[0.0, 0.0, 0.0],
          Omega=[0.0, 0.0, 0.0],
      )
      stars_from_params2 = airball.Stars(m=[1.0, 1.0, 1.0], b=[1.0, 1.0, 1.0], v=[1.0, 1.0, 1.0])  # random orientation angles
      stars_from_params3 = airball.Stars(
          m=1, b=200, v=5, omega=0, Omega=0, size=100
      )  # 100 identical stars with isotropically random inclinations
      stars_from_params4 = airball.Stars(
          m=[1.0, 1.0, 1.0], b=[1.0, 1.0, 1.0], v=[1.0, 1.0, 1.0], inc="uniform", omega="uniform", Omega="uniform"
      )  # uniformly random orientation angles
      ```

      ```python
      # Randomly generate the stellar parameters from a given environment.
      import airball

      stars_from_env1 = airball.Stars(environment=airball.OpenCluster(), size=3)
      stars_from_env2 = airball.Stars(env=airball.LocalNeighborhood(), size=5)
      stars_from_env3 = airball.Stars(airball.GlobularCluster(), size=9)
      ```

      ```python
      # Load the stellar parameters from a file.
      import airball

      stars_from_file1 = airball.Stars(filename="open_cluster.stars")
      stars_from_file2 = airball.Stars("open_cluster.stars")
      ```
    """

    def __init__(self, filename=None, **kwargs) -> None:
        try:
            self.units = _u.UnitSet(kwargs["UNIT_SYSTEM"])
            del kwargs["UNIT_SYSTEM"]
        except KeyError:
            try:
                self.units = kwargs["units"]
            except KeyError:
                self.units = _u.UnitSet()

        if filename is not None:
            # Initialize Stars from file.
            if isinstance(filename, (str, Path)):
                try:
                    loaded = Stars._load(filename)
                    self.__dict__ = loaded.__dict__
                except:  # noqa: E722
                    raise Exception("Invalid filename.")
                return
            # If filename is a Star object, then initialize Stars with the same parameters.
            elif isinstance(filename, Star):
                self._shape = (kwargs.get("size", 1),)
                self._m = (_np.ones(self.shape) * filename.m) << self.units["mass"]
                self._b = (_np.ones(self.shape) * filename.b) << self.units["length"]
                self._v = (_np.ones(self.shape) * filename.v) << self.units["velocity"]
                self._inc = (_np.ones(self.shape) * filename.inc) << self.units["angle"]
                self._omega = (_np.ones(self.shape) * filename.omega) << self.units["angle"]
                self._Omega = (_np.ones(self.shape) * filename.Omega) << self.units["angle"]
                self.environment = None
                return

        # If nothing is specified, return an empty Stars object.
        if not kwargs:
            self._m = _np.array([]) << self.units["mass"]
            self._b = _np.array([]) << self.units["length"]
            self._v = _np.array([]) << self.units["velocity"]
            self._inc = _np.array([]) << self.units["angle"]
            self._omega = _np.array([]) << self.units["angle"]
            self._Omega = _np.array([]) << self.units["angle"]
            self._shape = (0,)
            self.environment = None
            return

        # Determine the number of stars to generate.
        self._shape = (0,)
        for key in kwargs:
            try:
                if isinstance(kwargs[key], _u.Quantity):
                    shape = kwargs[key].shape
                    N = 0
                    if len(shape) >= 1:
                        N = _np.prod(shape)
                    else:
                        shape = (0,)
                    if N > self.N:
                        self._shape = shape
                elif _tools.isList(kwargs[key]):
                    if _np.prod(_np.shape(kwargs[key])) > self.N:
                        self._shape = _np.shape(kwargs[key])
                else:
                    pass
            except TypeError as err:
                print(err)
                self._shape = (len(kwargs[key]),)
            except Exception as err:
                raise err

        # if 'size' in kwargs and self.N != 0:
        #   raise OverspecifiedParametersException('If lists are given then size cannot be specified.')
        if "size" in kwargs:
            if isinstance(kwargs["size"], tuple):
                self._shape = tuple([int(i) for i in kwargs["size"]])
            else:
                self._shape = (int(kwargs["size"]),)
        elif self.N == 0:
            self._shape = ()  # raise UnspecifiedParameterException('If no lists of parameters are given then size must be specified.')
        else:
            pass  # No errors or issues, continue.

        # Initialize Stars from environment.
        self.environment = kwargs.get("environment", None)
        if (("environment" in kwargs or "env" in kwargs) or isinstance(filename, _env.StellarEnvironment)) and "size" in kwargs:
            if self.N <= 1:
                raise InvalidValueForKeyException("If a generating environment is given then size must be greater than 1.")
            if "environment" in kwargs:
                se = kwargs["environment"]
                del kwargs["environment"]
            elif "env" in kwargs:
                se = kwargs["env"]
                del kwargs["env"]
            else:
                se = filename
                del filename
            stars = se.random_stars(**kwargs)
            self.__dict__ = stars.__dict__
            return

        # Initialize Stars from kwargs.
        keys = ["m", "b", "v"]
        units = ["mass", "length", "velocity"]
        unspecifiedParameterExceptions = [
            "Mass, m, must be specified.",
            "Impact Parameter, b, must be specified.",
            "Velocity, v, must be specified.",
        ]

        for k, u, upe in zip(keys, units, unspecifiedParameterExceptions):
            try:
                # Check to see if was key is given.
                value = kwargs[k]
                # Check if shape matches other key values.
                if len(value) != len(self):
                    raise ListLengthException(f"Difference of {len(value)} and {len(self)} for {k}.")
                # Length of value matches other key values, check if value is a list.
                elif isinstance(value, list):
                    # Value is a list, try to turn list of Quantities into a ndarray Quantity.
                    try:
                        quantityValue = _np.array([v.to(self.units[u]).value for v in value]) << self.units[u]
                    # Value was not a list of Quantities, turn list into ndarray and make a Quantity.
                    except:  # noqa: E722
                        quantityValue = _np.array(value) << self.units[u]
                # Value was not a list, check to see if value is an ndarray.
                elif isinstance(value, _np.ndarray):
                    # Assume ndarray is a Quantity and try to convert ndarray into given units.
                    try:
                        quantityValue = value.to(self.units[u])
                    # ndarray is not a Quantity so turn ndarray into a Quantity.
                    except:  # noqa: E722
                        quantityValue = value << self.units[u]
                # Value implements __len__, but is not a list or ndarray.
                else:
                    raise IncompatibleListException()
            # This key is necessary and must be specified, raise and Exception.
            except KeyError:
                raise UnspecifiedParameterException(upe)
            # Value is not a list, so assume it is an int or float and generate an ndarray of the given value.
            except TypeError:
                value = value.to(self.units[u]) if _tools.isQuantity(value) else value * self.units[u]
                quantityValue = _np.ones(self.shape) * value
            # Catch any additional Exceptions.
            except Exception as err:
                raise err
            # Store Quantity Value as class property.
            if k == "m":
                self._m = quantityValue
            elif k == "b":
                self._b = quantityValue
            elif k == "v":
                self._v = quantityValue
            else:
                raise _tools.InvalidKeyException()
            # Double check for consistent shapes.
            if self._shape is not None:
                if quantityValue.shape != self._shape:
                    raise ListLengthException(f"Difference of {quantityValue.shape} and {self._shape} for {k}.")
            else:
                self._shape = quantityValue.shape

        seed = kwargs.get("seed", _np.random.randint(0, int(2**32 - 3)))
        for seedOffset, k in enumerate(["inc", "omega", "Omega"]):
            try:
                # Check to see if was key is given.
                value = kwargs[k]
                # Check to see if value for key is string.
                if isinstance(value, str):
                    # Value is a string, check to see if value for key is valid.
                    # Values 'isotropic' or 'uniform' for key are valid, now generate an array of values for key.
                    if value == "isotropic":
                        # Set the distributions for the orientation angles.
                        if k == "inc":
                            quantityValue = (
                                2.0
                                * _np.arcsin(
                                    _np.sqrt(
                                        _uniform.rvs(
                                            size=self.shape,
                                            random_state=(seed + seedOffset),
                                        )
                                    )
                                )
                                << self.units["angle"]
                            )
                        elif k == "omega":
                            quantityValue = (
                                _uniform.rvs(
                                    loc=0,
                                    scale=(2.0 * _np.pi),
                                    size=self.shape,
                                    random_state=(seed + seedOffset),
                                )
                                << self.units["angle"]
                            )
                        elif k == "Omega":
                            quantityValue = (
                                _uniform.rvs(
                                    loc=-_np.pi,
                                    scale=(2.0 * _np.pi),
                                    size=self.shape,
                                    random_state=(seed + seedOffset),
                                )
                                << self.units["angle"]
                            )
                    elif value == "uniform":
                        quantityValue = (
                            _uniform.rvs(
                                loc=-_np.pi,
                                scale=(2.0 * _np.pi),
                                size=self.shape,
                                random_state=(seed + seedOffset),
                            )
                            << self.units["angle"]
                        )
                    else:
                        raise InvalidValueForKeyException()
                # Value is not a string, check if length matches other key values.
                elif len(value) != len(self):
                    raise ListLengthException(f"Difference of {len(value)} and {len(self)} for {k}.")
                # Length of value matches other key values, check if value is a list.
                elif isinstance(value, list):
                    # Value is a list, try to turn list of Quantities into a ndarray Quantity.
                    try:
                        quantityValue = _np.array([v.to(self.units["angle"]).value for v in value]) * self.units["angle"]
                    # Value was not a list of Quantities, turn list into ndarray and make a Quantity.
                    except:  # noqa: E722
                        quantityValue = _np.array(value) * self.units["angle"]
                # Value was not a list, check to see if value is an ndarray.
                elif isinstance(value, _np.ndarray):
                    # Assume ndarray is a Quantity and try to convert ndarray into given units.
                    try:
                        quantityValue = value.to(self.units["angle"])
                    # ndarray is not a Quantity so turn ndarray into a Quantity.
                    except:  # noqa: E722
                        quantityValue = value * self.units["angle"]
                # Value implements __len__, but is not a list or ndarray.
                else:
                    raise IncompatibleListException()
            # Key does not exist, assume the user wants an array of values to automatically be generated isotropically.
            except KeyError:
                if k == "inc":
                    quantityValue = (
                        2.0 * _np.arcsin(_np.sqrt(_uniform.rvs(size=self.shape, random_state=(seed + seedOffset))))
                        << self.units["angle"]
                    )
                elif k == "omega":
                    quantityValue = (
                        _uniform.rvs(
                            loc=0,
                            scale=(2.0 * _np.pi),
                            size=self.shape,
                            random_state=(seed + seedOffset),
                        )
                        << self.units["angle"]
                    )
                elif k == "Omega":
                    quantityValue = (
                        _uniform.rvs(
                            loc=-_np.pi,
                            scale=(2.0 * _np.pi),
                            size=self.shape,
                            random_state=(seed + seedOffset),
                        )
                        << self.units["angle"]
                    )
            # Value is not a list, so assume it is an int or float and generate an ndarray of the given value.
            except TypeError:
                value = value.to(self.units["angle"]) if _tools.isQuantity(value) else value * self.units["angle"]
                quantityValue = _np.ones(self.shape) * value
            # Catch any additional Exceptions.
            except Exception as err:
                raise err
            # Store Quantity Value as class property.
            if k == "inc":
                self._inc = quantityValue
            elif k == "omega":
                self._omega = quantityValue
            elif k == "Omega":
                self._Omega = quantityValue
            else:
                raise _tools.InvalidKeyException()
            # Double check for consistent shapes.
            if self.shape is not None:
                if quantityValue.shape != self.shape:
                    raise ListLengthException(f"Difference of {quantityValue.shape} and {self.shape} for {k}.")
            else:
                self._shape = quantityValue.shape

    @property
    def N(self):
        """The total number of Stars."""
        return _np.prod(self.shape)

    @property
    def shape(self):
        """The shape of the Stars arrays."""
        return self._shape

    @property
    def median_mass(self):
        """The median mass of the Stars."""
        return _np.median([mass.value for mass in self.m]) << self.units["mass"]

    @property
    def mean_mass(self):
        """The mean mass of the Stars."""
        return _np.mean([mass.value for mass in self.m]) << self.units["mass"]

    @property
    def m(self):
        return self._m << self.units["mass"]

    @m.setter
    def m(self, value):
        try:
            if _np.shape(value) != self.shape:
                raise ListLengthException(f"Difference of {_np.shape(value)} and {self.shape}.")
        except (TypeError, AttributeError):
            raise IncompatibleListException()
        self._m = _tools.verify_unit(value, self.units["mass"])

    @property
    def mass(self):
        """
        Set the masses of the Stars, alias of `m` (default units: Msun).

        Args:
          value (list, ndarray, or Quantity): The new mass values. Can be set with a list such that len(value) == len(Stars).

        Raises:
          ListLengthException: If the length of the provided list does not match the number of Stars.
          IncompatibleListException: If the provided list is not compatible.
        """
        return self.m

    @mass.setter
    def mass(self, value):
        try:
            self.m = value
        except Exception as err:
            raise err

    @property
    def b(self):
        return self._b << self.units["length"]

    @b.setter
    def b(self, value):
        try:
            if _np.shape(value) != self.shape:
                raise ListLengthException(f"Difference of {_np.shape(value)} and {self.shape}.")
        except (TypeError, AttributeError):
            raise IncompatibleListException()
        self._b = _tools.verify_unit(value, self.units["length"])

    @property
    def impact_parameter(self):
        """
        Set the impact parameters of the Stars, alias of `b` (default units: AU).

        Args:
          value (list, ndarray, or Quantity): The new impact parameter values. Can be set with a list such that len(value) == len(Stars).

        Raises:
          ListLengthException: If the length of the provided list does not match the number of Stars.
          IncompatibleListException: If the provided list is not compatible.
        """
        return self.b

    @impact_parameter.setter
    def impact_parameter(self, value):
        try:
            self.b = value
        except Exception as err:
            raise err

    @property
    def v(self):
        return self._v << self.units["velocity"]

    @v.setter
    def v(self, value):
        try:
            if _np.shape(value) != self.shape:
                raise ListLengthException(f"Difference of {_np.shape(value)} and {self.shape}.")
        except (TypeError, AttributeError):
            raise IncompatibleListException()
        self._v = _tools.verify_unit(value, self.units["velocity"])

    @property
    def velocity(self):
        """
        Set the velocities at infinity of the Stars, alias of `v` (default units: km/s).

        Args:
          value (list, ndarray, or Quantity): The new velocity values. Can be set with a list such that len(value) == len(Stars).

        Raises:
          ListLengthException: If the length of the provided list does not match the number of Stars.
          IncompatibleListException: If the provided list is not compatible.
        """
        return self.v

    @velocity.setter
    def velocity(self, value):
        try:
            self.v = value
        except Exception as err:
            raise err

    @property
    def inc(self):
        return self._inc << self.units["angle"]

    @inc.setter
    def inc(self, value):
        try:
            if _np.shape(value) != self.shape:
                raise ListLengthException(f"Difference of {_np.shape(value)} and {self.shape}.")
        except (TypeError, AttributeError):
            raise IncompatibleListException()
        self._inc = _tools.verify_unit(value, self.units["angle"])

    @property
    def inclination(self):
        """
        The inclinations of the Stars, alias of `inc` (default units: radians).

        Args:
          value (list, ndarray, or Quantity): The new inclination values. Can be set with a list such that len(value) == len(Stars).

        Raises:
          ListLengthException: If the length of the provided list does not match the number of Stars.
          IncompatibleListException: If the provided list is not compatible.
        """
        return self.inc

    @inclination.setter
    def inclination(self, value):
        try:
            self.inc = value
        except Exception as err:
            raise err

    @property
    def omega(self):
        return self._omega << self.units["angle"]

    @omega.setter
    def omega(self, value):
        try:
            if _np.shape(value) != self.shape:
                raise ListLengthException(f"Difference of {_np.shape(value)} and {self.shape}.")
        except (TypeError, AttributeError):
            raise IncompatibleListException()
        self._omega = _tools.verify_unit(value, self.units["angle"])

    @property
    def argument_periastron(self):
        """
        The argument of periastron of the Stars, alias of `omega` (default units: radians).

        Args:
          value (list, ndarray, or Quantity): The new values for the argument of periastron. Can be set with a list such that len(value) == len(Stars).

        Raises:
          ListLengthException: If the length of the provided list does not match the number of Stars.
          IncompatibleListException: If the provided list is not compatible.
        """
        return self.omega

    @argument_periastron.setter
    def argument_periastron(self, value):
        try:
            self.omega = value
        except Exception as err:
            raise err

    @property
    def Omega(self):
        return self._Omega << self.units["angle"]

    @Omega.setter
    def Omega(self, value):
        try:
            if _np.shape(value) != self.shape:
                raise ListLengthException(f"Difference of {_np.shape(value)} and {self.shape}.")
        except (TypeError, AttributeError):
            raise IncompatibleListException()
        self._Omega = _tools.verify_unit(value, self.units["angle"])

    @property
    def longitude_ascending_node(self):
        """
        The longitude of the ascending node of the Stars, alias of `Omega` (default units: radians).

        Args:
          value (list, ndarray, or Quantity): The new longitude of the ascending node values. Can be set with a list such that len(value) == len(Stars).

        Raises:
          ListLengthException: If the length of the provided list does not match the number of Stars.
          IncompatibleListException: If the provided list is not compatible.
        """
        return self.Omega

    @longitude_ascending_node.setter
    def longitude_ascending_node(self, value):
        try:
            self.Omega = value
        except Exception as err:
            raise err

    @property
    def impulse_gradient(self):
        """
        Calculate the impulse gradient for a flyby star.

        $$\\frac{2GM_\\star}{V_\\star b_\\star^2}$$
        """
        G = 1 * _u.au**3 / _u.solMass / _u.yr2pi**2
        return ((2.0 * G * self.m) / (self.v * self.b**2.0)).to(_u.km / _u.s / _u.au)

    @property
    def params(self):
        """
        A list of the parameters of the Stars (with units) in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega

        `[m, b, v, inc, omega, Omega]`
        """
        return [self.m, self.b, self.v, self.inc, self.omega, self.Omega]

    @property
    def param_values(self):
        """
        A list of the values of the parameters of the Stars in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega

        `[m.value, b.value, v.value, inc.value, omega.value, Omega.value]`
        """
        return _np.array(
            [
                self.m.value,
                self.b.value,
                self.v.value,
                self.inc.value,
                self.omega.value,
                self.Omega.value,
            ]
        )

    @property
    def param_dict(self):
        """
        A dictionary of the values of the parameters of the Stars including: Mass, "m"; Impact Parameter, "b"; Velocity, "v"; Inclination, "inc"; Argument of the Periastron, "omega"; and Longitude of the Ascending Node, "Omega".

        `{"m": stars.m, "b": stars.b, "v": stars.v, "inc": stars.inc, "omega": stars.omega, "Omega": stars.Omega}`
        """
        return {
            "m": self.m,
            "b": self.b,
            "v": self.v,
            "inc": self.inc,
            "omega": self.omega,
            "Omega": self.Omega,
        }

    @property
    def labels(self):
        """
        A list of labels for the parameters of the Stars in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega

        `["Mass", "Impact Parameter", "Velocity", "Inclination", "Argument of the Periastron", "Longitude of the Ascending Node"]`
        """
        return [
            "Mass",
            "Impact Parameter",
            "Velocity",
            "Inclination",
            "Argument of the Periastron",
            "Longitude of the Ascending Node",
        ]

    def eccentricity(self, sim):
        """
        The eccentricity of the Stars, alias for `e(sim)`.

        Args:
          sim (Simulation): The REBOUND Simulation to use for calculating the eccentricity.

        Returns:
          eccentricity (ndarray): The eccentricity of the Stars.
        """
        return self.e(sim)

    def e(self, sim):
        units = _tools.rebound_units(sim)
        G = sim.G * units.length**3 / units.mass / units.time**2
        mu = G * (_tools.system_mass(sim) * units.mass + self.m)

        numerator = self.b * self.v * self.v
        return _np.sqrt(1 + (numerator / mu) ** 2.0)

    def periastron(self, sim):
        """
        The periastron of the Stars, alias for `q(sim)`.

        Args:
          sim (Simulation): The REBOUND Simulation to use for calculating the periastron.

        Returns:
          periastron (ndarray): The periastron of the Stars.
        """
        return self.q(sim)

    def q(self, sim):
        sim_units = _tools.rebound_units(sim)
        G = sim.G * sim_units["length"] ** 3 / sim_units["mass"] / sim_units["time"] ** 2
        mu = G * (_tools.system_mass(sim) * sim_units["mass"] + self.m)

        numerator = self.b * self.v * self.v
        star_e = _np.sqrt(1 + (numerator / mu) ** 2.0)
        return self.b * _np.sqrt((star_e - 1.0) / (star_e + 1.0))

    def copy(self):
        """Returns a deep copy of the Stars."""
        return _deepcopy(self)

    def sort(self, key, sim=None, argsort=False):
        # Alias for `sortby`.
        return self.sortby(key, sim, argsort)

    def argsort(self, key, sim=None):
        # Alias for `sortby(argsort=True)`.
        return self.sortby(key, sim, argsort=True)

    def argsortby(self, key, sim=None):
        # Alias for `sortby(argsort=True)`.
        return self.sortby(key, sim, argsort=True)

    def sortby(self, key, sim=None, argsort=False):
        """
        Sort the Stars in ascending order by a defining parameter.

        Args:
          key (str): The parameter to sort by. Options include: 'm' (mass), 'b' (impact parameter), 'v' (relative velocity at infinity), 'inc' (inclination), 'omega' (argument of the periastron), 'Omega' (longitude of the ascending node), 'q' (periapsis), 'e' (eccentricity). For 'q' and 'e', a REBOUND Simulation is required.
          sim (Simulation, optional): The REBOUND Simulation to use for sorting by 'q' and 'e'. Default is None.
          argsort (bool, optional): If True, return the indices used to sort the Stars. Default is False.

        Returns:
          indices (list or None): The indices used to sort the Stars, if argsort is True. Otherwise, None and sorting is done in place.

        !!! Info
            The Stars can also be sorted arbitrarily by providing a list of indices of length len(stars) as the key.

        Examples:
          ```python
          import airball

          stars = airball.Stars(m=[1, 2, 3], b=[3, 2, 1], v=[6, 5, 7])
          stars.sortby("b")
          inds = stars.sortby("v", argsort=True)
          ```

          ```python
          import airball
          import rebound

          sim = rebound.Simulation()
          sim.add(m=1)
          sim.add(m=5e-5, a=30, e=0.01)
          stars = airball.Stars(airball.OpenCluster(), size=100)
          stars.sortby("q", sim=sim)
          ```

          ```python
          import airball

          stars = airball.Stars(airball.LocalNeighborhood(), size=5)
          inds = [0, 4, 1, 3, 2]
          stars.sortby(inds)
          ```
        """

        inds = _np.arange(len(self))
        if key == "m" or key == "mass":
            inds = _np.argsort(self.m)
        elif key == "b" or key == "impact" or key == "impact param" or key == "impact parameter":
            inds = _np.argsort(self.b)
        elif key == "v" or key == "vinf" or key == "v_inf" or key == "velocity":
            inds = _np.argsort(self.v)
        elif key == "inc" or key == "inclination" or key == "i" or key == "I":
            inds = _np.argsort(self.inc)
        elif key == "omega" or key == "ω" or key == "argument_periastron":
            inds = _np.argsort(self.omega)
        elif key == "Omega" or key == "Ω" or key == "longitude_ascending_node":
            inds = _np.argsort(self.Omega)
        elif key == "q" or key == "peri" or key == "perihelion" or key == "periastron" or key == "periapsis":
            if isinstance(sim, _rebound.Simulation):
                inds = _np.argsort(self.q(sim))
            else:
                raise InvalidParameterTypeException()
        elif key == "e" or key == "eccentricity":
            if isinstance(sim, _rebound.Simulation):
                inds = _np.argsort(self.e(sim))
            else:
                raise InvalidParameterTypeException()
        elif _tools.isList(key):
            print(key)
            if len(key) != len(self):
                raise ListLengthException(f"Difference of key: {len(key)} and stars: {len(self)}.")
            inds = _np.array(key)
        else:
            raise InvalidValueForKeyException()

        if argsort:
            return inds
        else:
            self.m[:] = self.m[inds]
            self.b[:] = self.b[inds]
            self.v[:] = self.v[inds]
            self.inc[:] = self.inc[inds]
            self.omega[:] = self.omega[inds]
            self.Omega[:] = self.Omega[inds]

    def save(self, filename):
        """
        Save the current instance of the Stars class to a file using pickle.

        Args:
          filename (str): The name of the file to save the instance to. The file will be saved in binary format.

        Example:
          ```python
          import airball

          se = airball.OpenCluster()
          stars = se.random_stars(100)
          stars.save("open_cluster.stars")
          ```
        """
        if not isinstance(filename, (str, Path)):
            raise ValueError("Filename must be a string or Path.")
        with open(filename, "wb") as pfile:
            _pickle.dump(self, pfile, protocol=_pickle.HIGHEST_PROTOCOL)

    @classmethod
    def _load(cls, filename):
        """
        Load an instance of the Stars class from a file using pickle.

        Args:
          filename (str): The name of the file to load the instance from. The file should be in binary format, pickled.

        Returns:
          loaded_stars (Stars): The loaded instance of the Stars class.

        Example:
          ```python
          import airball

          stars = airball.Stars("open_cluster.stars")
          ```
        """
        if not isinstance(filename, (str, Path)):
            raise ValueError("Filename must be a string or Path.")
        with open(filename, "rb") as pfile:
            return _pickle.load(pfile)

    def stats(self, returned=False):
        """
        Prints a summary of the current stats of the Stars object.
        The stats are returned as a string if `returned=True`.
        """
        s = f"<{self.__module__}.{type(self).__name__} object at {hex(id(self))}, "
        s += f"N={f'{self.N:,.0f}' if len(self.shape) == 1 else self.shape}"
        if self.N > 0:
            s += f", m= {_np.min(self.m.value):,.3f}-{_np.max(self.m.value):,.3f} {self.units['mass']}"
        if self.N > 0:
            s += f", b= {_np.min(self.b.value):,.0f}-{_np.max(self.b.value):,.0f} {self.units['length']}"
        if self.N > 0:
            s += f", v= {_np.min(self.v.value):,.0f}-{_np.max(self.v.value):,.0f} {self.units['velocity']}"
        s += f"{f', Environment={self.environment.name}' if self.environment is not None else ''}"
        s += ">"
        if returned:
            return s
        else:
            print(s)

    def __str__(self):
        return self.stats(returned=True)

    def __repr__(self):
        return self.stats(returned=True)

    def __getitem__(self, key):
        int_types = int, _np.integer

        # Basic indexing.
        if isinstance(key, int_types):
            # If the set of Stars is multi-dimensional, return the requested subset of stars as a set of Stars.
            if len(self.m.shape) > 1:
                return Stars(
                    m=self.m[key],
                    b=self.b[key],
                    v=self.v[key],
                    inc=self.inc[key],
                    omega=self.omega[key],
                    Omega=self.Omega[key],
                    UNIT_SYSTEM=self.units.UNIT_SYSTEM,
                )
            # Otherwise return the requested Star.
            else:
                return Star(
                    m=self.m[key],
                    b=self.b[key],
                    v=self.v[key],
                    inc=self.inc[key],
                    omega=self.omega[key],
                    Omega=self.Omega[key],
                    UNIT_SYSTEM=self.units.UNIT_SYSTEM,
                )

        # Allows for boolean array masking and indexing using a subset of indices.
        if isinstance(key, _np.ndarray):
            return Stars(
                m=self.m[key],
                b=self.b[key],
                v=self.v[key],
                inc=self.inc[key],
                omega=self.omega[key],
                Omega=self.Omega[key],
                UNIT_SYSTEM=self.units.UNIT_SYSTEM,
            )

        # Allow for speed efficient slicing by returning a new set of Stars which are a subset of the original object.
        if isinstance(key, slice):
            # Check for number of elements returned by the slice.
            numEl = _tools.numberOfElementsReturnedBySlice(*key.indices(self.N))
            # If the slice requests the entire set, then simply return the set.
            # if key == slice(None, None, None): return self #  !!! **Note: this is a reference to the same object.** !!!
            # If there are no elements requested, return the empty set.
            if numEl == 0:
                return Stars(m=[], b=[], v=[], size=0)
            # If only one element is requested, return a set of Stars with only one Star.
            elif numEl == 1:
                return Stars(
                    m=self.m[key],
                    b=self.b[key],
                    v=self.v[key],
                    inc=self.inc[key],
                    omega=self.omega[key],
                    Omega=self.Omega[key],
                    UNIT_SYSTEM=self.units.UNIT_SYSTEM,
                    size=1,
                )
            # Otherwise return a subset of the Stars defined by the slice.
            else:
                return Stars(
                    m=self.m[key],
                    b=self.b[key],
                    v=self.v[key],
                    inc=self.inc[key],
                    omega=self.omega[key],
                    Omega=self.Omega[key],
                    UNIT_SYSTEM=self.units.UNIT_SYSTEM,
                )

        # Allow for Numpy style array indexing.
        if isinstance(key, tuple):
            # Check if Stars data is multi-dimensional.
            if len(self.m.shape) == 1:
                raise IndexError(f"Too many indices: Stars are 1-dimensional, but {len(key)} were indexed.")
            # Check to see if the tuple has a slice.
            hasSlice = _tools.hasTrue([isinstance(k, slice) for k in key])
            if hasSlice:
                # Check the number of elements requested by the slice.
                numEl = [
                    _tools.numberOfElementsReturnedBySlice(*k.indices(self.m.shape[i])) if isinstance(k, slice) else 1
                    for i, k in enumerate(key)
                ]
                # If there are no elements requested, return the empty set.
                if numEl.count(0) > 0:
                    return Stars(m=[], b=[], v=[], size=0)
                # If multiple elements are requested, return a set of Stars.
                elif _np.any(_np.array(numEl) > 1):
                    return Stars(
                        m=self.m[key],
                        b=self.b[key],
                        v=self.v[key],
                        inc=self.inc[key],
                        omega=self.omega[key],
                        Omega=self.Omega[key],
                        UNIT_SYSTEM=self.units.UNIT_SYSTEM,
                    )
                # If only one element is requested, return a set of Stars with only one Star.
                else:
                    # Check to see if the single element is an scalar or an array with only one element.
                    if self.m[key].isscalar:
                        return Stars(
                            m=self.m[key],
                            b=self.b[key],
                            v=self.v[key],
                            inc=self.inc[key],
                            omega=self.omega[key],
                            Omega=self.Omega[key],
                            size=1,
                            UNIT_SYSTEM=self.units.UNIT_SYSTEM,
                        )
                    else:
                        return Stars(
                            m=self.m[key],
                            b=self.b[key],
                            v=self.v[key],
                            inc=self.inc[key],
                            omega=self.omega[key],
                            Omega=self.Omega[key],
                            UNIT_SYSTEM=self.units.UNIT_SYSTEM,
                        )
            # If there is no slice, the return the requested Star.
            else:
                return Star(
                    m=self.m[key],
                    b=self.b[key],
                    v=self.v[key],
                    inc=self.inc[key],
                    omega=self.omega[key],
                    Omega=self.Omega[key],
                    UNIT_SYSTEM=self.units.UNIT_SYSTEM,
                )

        raise _tools.InvalidKeyException()

    def __setitem__(self, key, value):
        star_type = Star, Stars
        if isinstance(value, star_type):
            (
                self.m[key],
                self.b[key],
                self.v[key],
                self.inc[key],
                self.omega[key],
                self.Omega[key],
            ) = value.params
        else:
            raise InvalidStarException()

    def __delitem__(self, key):
        raise ValueError("Cannot delete Star elements from Stars array.")

    def __iter__(self):
        for i in list(_np.ndindex(self.m.shape)):
            yield Star(
                m=self.m[i],
                b=self.b[i],
                v=self.v[i],
                inc=self.inc[i],
                omega=self.omega[i],
                Omega=self.Omega[i],
                UNIT_SYSTEM=self.units.UNIT_SYSTEM,
            )

    def __len__(self):
        return self.shape[0]

    def __eq__(self, other):
        # Overrides the default implementation
        if isinstance(other, Stars):
            attrs = [
                "m",
                "b",
                "v",
                "inc",
                "omega",
                "Omega",
                "N",
                "shape",
                "units",
                "environment",
            ]
            equal = True
            for attr in attrs:
                equal_attribute = _np.all(getattr(self, attr) == getattr(other, attr))
                if not equal_attribute:
                    if _tools.isQuantity(getattr(self, attr)):
                        equal_attribute = _np.all(getattr(self, attr).value == getattr(other, attr).value)
                        equal_attribute = equal_attribute and _np.all(
                            getattr(self, attr).unit.is_equivalent(getattr(other, attr).unit)
                        )
                if not equal_attribute:
                    return False
                equal = equal and equal_attribute
            return equal
        return NotImplemented

    def __hash__(self):
        # Overrides the default implementation
        data = []
        for d in sorted(self.__dict__.items()):
            try:
                data.append((d[0], tuple(d[1])))
            except:  # noqa: E722
                data.append(d)
        data = tuple(data)
        return hash(data)

    def __add__(self, other):
        # Overrides the default implementation
        if isinstance(other, Stars):
            if self.N == 0 and other.N == 0:
                return Stars()
            else:
                return Stars(
                    m=_np.concatenate((self.m, other.m)),
                    b=_np.concatenate((self.b, other.b)),
                    v=_np.concatenate((self.v, other.v)),
                    inc=_np.concatenate((self.inc, other.inc)),
                    omega=_np.concatenate((self.omega, other.omega)),
                    Omega=_np.concatenate((self.Omega, other.Omega)),
                )
        elif isinstance(other, Star):
            if self.N == 0 and other.N == 0:
                return Stars()
            else:
                return Stars(
                    m=_np.concatenate((self.m, [other.m])),
                    b=_np.concatenate((self.b, [other.b])),
                    v=_np.concatenate((self.v, [other.v])),
                    inc=_np.concatenate((self.inc, [other.inc])),
                    omega=_np.concatenate((self.omega, [other.omega])),
                    Omega=_np.concatenate((self.Omega, [other.Omega])),
                )
        return NotImplemented
N property

The total number of Stars.

argument_periastron property writable

The argument of periastron of the Stars, alias of omega (default units: radians).

Parameters:

Name Type Description Default
value list, ndarray, or Quantity

The new values for the argument of periastron. Can be set with a list such that len(value) == len(Stars).

 required

Raises:

Type Description
ListLengthException

If the length of the provided list does not match the number of Stars.
IncompatibleListException

If the provided list is not compatible.
impact_parameter property writable

Set the impact parameters of the Stars, alias of b (default units: AU).

Parameters:

Name Type Description Default
value list, ndarray, or Quantity

The new impact parameter values. Can be set with a list such that len(value) == len(Stars).

 required

Raises:

Type Description
ListLengthException

If the length of the provided list does not match the number of Stars.
IncompatibleListException

If the provided list is not compatible.
impulse_gradient property

Calculate the impulse gradient for a flyby star.

\[\frac{2GM_\star}{V_\star b_\star^2}\]
inclination property writable

The inclinations of the Stars, alias of inc (default units: radians).

Parameters:

Name Type Description Default
value list, ndarray, or Quantity

The new inclination values. Can be set with a list such that len(value) == len(Stars).

 required

Raises:

Type Description
ListLengthException

If the length of the provided list does not match the number of Stars.
IncompatibleListException

If the provided list is not compatible.
labels property

A list of labels for the parameters of the Stars in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega

["Mass", "Impact Parameter", "Velocity", "Inclination", "Argument of the Periastron", "Longitude of the Ascending Node"]

longitude_ascending_node property writable

The longitude of the ascending node of the Stars, alias of Omega (default units: radians).

Parameters:

Name Type Description Default
value list, ndarray, or Quantity

The new longitude of the ascending node values. Can be set with a list such that len(value) == len(Stars).

 required

Raises:

Type Description
ListLengthException

If the length of the provided list does not match the number of Stars.
IncompatibleListException

If the provided list is not compatible.
mass property writable

Set the masses of the Stars, alias of m (default units: Msun).

Parameters:

Name Type Description Default
value list, ndarray, or Quantity

The new mass values. Can be set with a list such that len(value) == len(Stars).

 required

Raises:

Type Description
ListLengthException

If the length of the provided list does not match the number of Stars.
IncompatibleListException

If the provided list is not compatible.
mean_mass property

The mean mass of the Stars.

median_mass property

The median mass of the Stars.

param_dict property

A dictionary of the values of the parameters of the Stars including: Mass, "m"; Impact Parameter, "b"; Velocity, "v"; Inclination, "inc"; Argument of the Periastron, "omega"; and Longitude of the Ascending Node, "Omega".

{"m": stars.m, "b": stars.b, "v": stars.v, "inc": stars.inc, "omega": stars.omega, "Omega": stars.Omega}

param_values property

A list of the values of the parameters of the Stars in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega

[m.value, b.value, v.value, inc.value, omega.value, Omega.value]

params property

A list of the parameters of the Stars (with units) in order of: Mass, m; Impact Parameter, b; Velocity, v; Inclination, inc; Argument of the Periastron, omega; and Longitude of the Ascending Node, Omega

[m, b, v, inc, omega, Omega]

shape property

The shape of the Stars arrays.

velocity property writable

Set the velocities at infinity of the Stars, alias of v (default units: km/s).

Parameters:

Name Type Description Default
value list, ndarray, or Quantity

The new velocity values. Can be set with a list such that len(value) == len(Stars).

 required

Raises:

Type Description
ListLengthException

If the length of the provided list does not match the number of Stars.
IncompatibleListException

If the provided list is not compatible.
copy()

Returns a deep copy of the Stars.

Source code in src/airball/stars.py 
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def copy(self):
    """Returns a deep copy of the Stars."""
    return _deepcopy(self)
eccentricity(sim)

The eccentricity of the Stars, alias for e(sim).

Parameters:

Name Type Description Default
sim Simulation

The REBOUND Simulation to use for calculating the eccentricity.

 required

Returns:

Name Type Description
eccentricity ndarray

The eccentricity of the Stars.
Source code in src/airball/stars.py 
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def eccentricity(self, sim):
    """
    The eccentricity of the Stars, alias for `e(sim)`.

    Args:
      sim (Simulation): The REBOUND Simulation to use for calculating the eccentricity.

    Returns:
      eccentricity (ndarray): The eccentricity of the Stars.
    """
    return self.e(sim)
periastron(sim)

The periastron of the Stars, alias for q(sim).

Parameters:

Name Type Description Default
sim Simulation

The REBOUND Simulation to use for calculating the periastron.

 required

Returns:

Name Type Description
periastron ndarray

The periastron of the Stars.
Source code in src/airball/stars.py 
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def periastron(self, sim):
    """
    The periastron of the Stars, alias for `q(sim)`.

    Args:
      sim (Simulation): The REBOUND Simulation to use for calculating the periastron.

    Returns:
      periastron (ndarray): The periastron of the Stars.
    """
    return self.q(sim)
save(filename)

Save the current instance of the Stars class to a file using pickle.

Parameters:

Name Type Description Default
filename str

The name of the file to save the instance to. The file will be saved in binary format.

 required
Example 
import airball

se = airball.OpenCluster()
stars = se.random_stars(100)
stars.save("open_cluster.stars")
Source code in src/airball/stars.py 
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def save(self, filename):
    """
    Save the current instance of the Stars class to a file using pickle.

    Args:
      filename (str): The name of the file to save the instance to. The file will be saved in binary format.

    Example:
      ```python
      import airball

      se = airball.OpenCluster()
      stars = se.random_stars(100)
      stars.save("open_cluster.stars")
      ```
    """
    if not isinstance(filename, (str, Path)):
        raise ValueError("Filename must be a string or Path.")
    with open(filename, "wb") as pfile:
        _pickle.dump(self, pfile, protocol=_pickle.HIGHEST_PROTOCOL)
sortby(key, sim=None, argsort=False)

Sort the Stars in ascending order by a defining parameter.

Parameters:

Name Type Description Default
key str

The parameter to sort by. Options include: 'm' (mass), 'b' (impact parameter), 'v' (relative velocity at infinity), 'inc' (inclination), 'omega' (argument of the periastron), 'Omega' (longitude of the ascending node), 'q' (periapsis), 'e' (eccentricity). For 'q' and 'e', a REBOUND Simulation is required.

 required
sim Simulation

The REBOUND Simulation to use for sorting by 'q' and 'e'. Default is None.

 None
argsort bool

If True, return the indices used to sort the Stars. Default is False.

 False

Returns:

Name Type Description
indices list or None

The indices used to sort the Stars, if argsort is True. Otherwise, None and sorting is done in place.

Info

The Stars can also be sorted arbitrarily by providing a list of indices of length len(stars) as the key.

Examples:

import airball

stars = airball.Stars(m=[1, 2, 3], b=[3, 2, 1], v=[6, 5, 7])
stars.sortby("b")
inds = stars.sortby("v", argsort=True)

import airball
import rebound

sim = rebound.Simulation()
sim.add(m=1)
sim.add(m=5e-5, a=30, e=0.01)
stars = airball.Stars(airball.OpenCluster(), size=100)
stars.sortby("q", sim=sim)

import airball

stars = airball.Stars(airball.LocalNeighborhood(), size=5)
inds = [0, 4, 1, 3, 2]
stars.sortby(inds)
Source code in src/airball/stars.py 
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def sortby(self, key, sim=None, argsort=False):
    """
    Sort the Stars in ascending order by a defining parameter.

    Args:
      key (str): The parameter to sort by. Options include: 'm' (mass), 'b' (impact parameter), 'v' (relative velocity at infinity), 'inc' (inclination), 'omega' (argument of the periastron), 'Omega' (longitude of the ascending node), 'q' (periapsis), 'e' (eccentricity). For 'q' and 'e', a REBOUND Simulation is required.
      sim (Simulation, optional): The REBOUND Simulation to use for sorting by 'q' and 'e'. Default is None.
      argsort (bool, optional): If True, return the indices used to sort the Stars. Default is False.

    Returns:
      indices (list or None): The indices used to sort the Stars, if argsort is True. Otherwise, None and sorting is done in place.

    !!! Info
        The Stars can also be sorted arbitrarily by providing a list of indices of length len(stars) as the key.

    Examples:
      ```python
      import airball

      stars = airball.Stars(m=[1, 2, 3], b=[3, 2, 1], v=[6, 5, 7])
      stars.sortby("b")
      inds = stars.sortby("v", argsort=True)
      ```

      ```python
      import airball
      import rebound

      sim = rebound.Simulation()
      sim.add(m=1)
      sim.add(m=5e-5, a=30, e=0.01)
      stars = airball.Stars(airball.OpenCluster(), size=100)
      stars.sortby("q", sim=sim)
      ```

      ```python
      import airball

      stars = airball.Stars(airball.LocalNeighborhood(), size=5)
      inds = [0, 4, 1, 3, 2]
      stars.sortby(inds)
      ```
    """

    inds = _np.arange(len(self))
    if key == "m" or key == "mass":
        inds = _np.argsort(self.m)
    elif key == "b" or key == "impact" or key == "impact param" or key == "impact parameter":
        inds = _np.argsort(self.b)
    elif key == "v" or key == "vinf" or key == "v_inf" or key == "velocity":
        inds = _np.argsort(self.v)
    elif key == "inc" or key == "inclination" or key == "i" or key == "I":
        inds = _np.argsort(self.inc)
    elif key == "omega" or key == "ω" or key == "argument_periastron":
        inds = _np.argsort(self.omega)
    elif key == "Omega" or key == "Ω" or key == "longitude_ascending_node":
        inds = _np.argsort(self.Omega)
    elif key == "q" or key == "peri" or key == "perihelion" or key == "periastron" or key == "periapsis":
        if isinstance(sim, _rebound.Simulation):
            inds = _np.argsort(self.q(sim))
        else:
            raise InvalidParameterTypeException()
    elif key == "e" or key == "eccentricity":
        if isinstance(sim, _rebound.Simulation):
            inds = _np.argsort(self.e(sim))
        else:
            raise InvalidParameterTypeException()
    elif _tools.isList(key):
        print(key)
        if len(key) != len(self):
            raise ListLengthException(f"Difference of key: {len(key)} and stars: {len(self)}.")
        inds = _np.array(key)
    else:
        raise InvalidValueForKeyException()

    if argsort:
        return inds
    else:
        self.m[:] = self.m[inds]
        self.b[:] = self.b[inds]
        self.v[:] = self.v[inds]
        self.inc[:] = self.inc[inds]
        self.omega[:] = self.omega[inds]
        self.Omega[:] = self.Omega[inds]
stats(returned=False)

Prints a summary of the current stats of the Stars object. The stats are returned as a string if returned=True.

Source code in src/airball/stars.py 
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def stats(self, returned=False):
    """
    Prints a summary of the current stats of the Stars object.
    The stats are returned as a string if `returned=True`.
    """
    s = f"<{self.__module__}.{type(self).__name__} object at {hex(id(self))}, "
    s += f"N={f'{self.N:,.0f}' if len(self.shape) == 1 else self.shape}"
    if self.N > 0:
        s += f", m= {_np.min(self.m.value):,.3f}-{_np.max(self.m.value):,.3f} {self.units['mass']}"
    if self.N > 0:
        s += f", b= {_np.min(self.b.value):,.0f}-{_np.max(self.b.value):,.0f} {self.units['length']}"
    if self.N > 0:
        s += f", v= {_np.min(self.v.value):,.0f}-{_np.max(self.v.value):,.0f} {self.units['velocity']}"
    s += f"{f', Environment={self.environment.name}' if self.environment is not None else ''}"
    s += ">"
    if returned:
        return s
    else:
        print(s)