`ThermalRadiation`#

class ThermalRadiation(origin: CelestialBody, spacecraft: Spacecraft, base_frame: Frame, thermal_model, t0: float = None, tf: float = None)#

Bases: DynamicModel

Recoil acceleration from the thermal radiation the spacecraft emits.

Each surface \(i\) of area \(A_i\), emissivity \(\varepsilon_i\) and outward normal \(\hat{\mathbf{n}}_i\) radiates as a Lambertian emitter at temperature \(T_i\). The recoil of that emission is

\[\mathbf{a}_i = -\frac{2}{3}\, \frac{\sigma A_i \varepsilon_i}{m\,c}\,T_i^4\,\hat{\mathbf{n}}_i\]

where \(\sigma\) is the Stefan-Boltzmann constant, \(m\) the spacecraft mass and \(c\) the speed of light. The factor 2/3 is the momentum a Lambertian surface carries away along its normal. The total acceleration is

\[\mathbf{a}_\text{therm} = \eta_\text{therm} \sum_i \mathbf{a}_i\]

with \(\eta_\text{therm}\) an estimable scale factor (default 1), read from the state under ("eta_thermal", spice_id).

Temperatures. A surface temperature is read from a table of temperature against off-Sun angle \(\theta\), given at a few Sun-spacecraft distances \(d\):

\[T_i = T_{\text{table}(i)}\!\left(\theta_i,\, d\right),\qquad \cos\theta_i = \hat{\boldsymbol{\rho}}_i\cdot\hat{\mathbf{u}}_\odot\]

where \(\hat{\mathbf{u}}_\odot\) is the spacecraft-to-Sun unit vector and \(\hat{\boldsymbol{\rho}}_i\) the table’s reference direction: the table’s angle_reference when it has one (for example the spacecraft axis the thermal analysis measured the off-Sun angle from), otherwise the surface’s own normal. Each distance row is a cubic spline in \(\theta\), with zero slope imposed at 0 and 180 degrees when the table reaches them, since a temperature is symmetric about those angles. Rows are joined by linear interpolation in \(d\). Outside the tabulated angles and distances the temperature is held at the nearest edge.

A surface can carry a second, shadow_temperature table, used when \(\hat{\mathbf{n}}_i\cdot\hat{\mathbf{u}}_\odot \le 0\). This is how a high-gain antenna built from many plates picks an illuminated or a shadowed temperature for each plate.

Attitude. Normals and angle references are fixed in the spacecraft frame and reach the inertial frame through the spacecraft-fixed to inertial rotation \(C\) of DynamicalUtils, for the "CK", "inertialFixedAttitude" and "nadirPointingSun" values of Spacecraft.attitudeMode. In the last one the spacecraft \(-X\) axis points at the Sun and the Y axis follows the heliocentric velocity, so \(C\) depends on the state, the partials carry the rotation terms and the model reports depends_on_velocity.

Thermal model. thermal_model is a dict, or the path of a JSON file holding one, with two entries:

"temperature_tables"

{name: table}, each table holding

"angles": ArrayWUnits of off-Sun angles, strictly increasing within [0, 180] degrees, at least two;
"distances": ArrayWUnits of Sun distances, strictly increasing, at least one;
"temperatures": array of shape (n_distances, n_angles) (a single distance may be given as a 1-D array);
"temperature_units": "K" or "degC";
"angle_reference" (optional): spacecraft-fixed direction the off-Sun angle is measured from.

"surfaces"

list of dicts, each holding

"name": label;
"area": ArrayWUnits area;
"emissivity": value in [0, 1];
"normal": outward normal in the spacecraft frame;
"temperature": name of its temperature table;
"shadow_temperature" (optional): name of the table used when the surface faces away from the Sun.

Quantities with units may also be given in their serialized form ({"values", "units"}, see awu_to_dict()), which is what model_to_dict() writes.

Parameters:

originCelestialBody: Propagation origin. Used for the Sun-relative geometry.
spacecraftSpacecraft: The emitting spacecraft. Its mass and attitude are read at evaluation time.
base_frameFrame: Inertial frame of the propagated state.
thermal_modeldict or str or pathlib.Path: Surfaces and temperature tables, as described above.
t0, tffloat, optional: Propagation span in TDB seconds past J2000. When both are given and the frame is J2000, the Sun position is read from a Chebyshev ephemeris cache instead of SPICE.

Attributes:

depends_on_velocity: Whether the acceleration depends on the spacecraft velocity.
frame: The inertial frame of the propagated state.
origin: The propagation origin.
origin_name: The name of the propagation origin.
param_name: State key of the estimable scale factor.
spacecraft: The emitting spacecraft.
surface_names: Surface names, in the order of surface_temperatures().
thermal_model: The validated thermal model (surfaces and temperature tables).

Methods

`compute_acceleration`(position, ...)	Thermal re-radiation acceleration.
`model_from_dict`(thermal_model)	Validate a thermal model and return it with live quantities.
`model_to_dict`(thermal_model)	Serialize a thermal model to plain JSON types.
`surface_temperatures`(position, ...)	Temperature of every surface, in the order of `surface_names`.
`to_dict`()	Serialize this model's thermal model; see `model_to_dict()`.

Raises:

InvalidThermalModelError: If thermal_model is not a dict or a JSON file of one, or lacks its two entries.
InvalidTemperatureTableError: If a temperature table is malformed.
InvalidSurfaceError: If a surface is malformed.
UnknownTemperatureTableError: If a surface names a table that is not defined.
DynamicalUtils.InvalidAttitudeModeError: If the spacecraft attitude mode is not one of the three above.
DynamicalUtils.InvalidFixedAttitudeError: If an inertialFixedAttitude spacecraft has no 3x3 attitude.
DynamicalUtils.MissingVelocityError: If a nadirPointingSun spacecraft has no velocity in the state.

ThermalRadiation#

`ThermalRadiation`#