Constants Module

This is the module for all Constants defined in pryngles.

You will find two types of constants distinguished between physical and numerical

Physical

Values associated to physical and astronomical quantities, defined in SI units. Most of them are imported from rebound package.

Attribute	Value	Unit	Description
s	1.0	s	Second (SI base unit)
hr	3600.0	s	Hour
d	86400.0	s	Day
day	86400.0	s	Synonym for day
days	86400.0	s	Plural of day
yr	31557600.0	s	Julian year (exact)
year	31557600.0	s	Synonym for Julian year
years	31557600.0	s	Plural of Julian year
yrs	31557600.0	s	Abbreviation for years
jyr	31557600.0	s	Jovian year (alias)
sidereal_yr	31558149.7635	s	Sidereal year
kyr	3.15576e10	s	Thousand years
myr	3.15576e13	s	Million years
gyr	3.15576e16	s	Billion years
yr2pi	5022642.89091303	s	Alias for year/2π
m	1.0	m	Meter (SI base unit)
cm	0.01	m	Centimeter
km	1000.0	m	Kilometer
au	149597870700.0	m	Astronomical Unit
aus	149597870700.0	m	Plural of AU
pc	3.085677581e16	m	Parsec
parsec	3.085677581e16	m	Synonym for parsec
rearth	6.378137e6	m	Earth’s mean radius
rsun	6.957e8	m	Solar radius (nominal)
rjupiter	7.1492e7	m	Jupiter’s equatorial radius
rsaturn	6.0268e7	m	Saturn’s equatorial radius
kg	1.0	kg	Kilogram (SI base unit)
g	1e-3	kg	Gram
gram	1e-3	kg	Synonym for gram
msun	1.988409870698051e30	kg	Solar mass
msolar	1.988409870698051e30	kg	Synonym for solar mass
msaturn	5.683e26	kg	Saturn’s mass
mjupiter	1.898e27	kg	Jupiter’s mass
mearth	5.972e24	kg	Earth’s mass
mmars	6.417e23	kg	Mars’ mass
muranus	8.681e25	kg	Uranus’ mass
mneptune	1.024e26	kg	Neptune’s mass
mmercury	3.302e23	kg	Mercury’s mass
mvenus	4.867e24	kg	Venus’ mass
mpluto	1.309e22	kg	Pluto’s mass
sunmass	1.988409870698051e30	kg	Synonym for solar mass
solarmass	1.988409870698051e30	kg	Synonym for solar mass
massist	2.258e25	kg	Normalized Earth mass unit (G=1 system)
ppm	1e6	—	Parts per million
ppb	1e9	—	Parts per billion
rad	57.2957795	rad/deg	Radians per degree
deg	0.01745329	deg/rad	Degrees per radian

Numerical

Quantities used accross the package. Usually, numerical constants are grouped by modules

Orbital Constants

Sampler Constants

These are the numerical attributes to define the body shapes we consider in pryngles to Spangle and Sampling its surface. For Stars, Planets and Moons it defines a sphere-sampling. Ring is considered as a circle-sampling with a circle-sampling hole

Sample presets are the values of N-Spangles for which there are already stored samples

Spangler Constants

A spangle is the discrete unit with which we sample the surface of an astrophysical body. With the intention of modeling different surfaces in exoplanetary systems, we define the following numerical attributes to define them.

In order to characterize the radiation-matter interaction on each discrete unit of the body surface (Spangle), we can assign distinct states, coordinates and physical parameters wich will allow us to perform the computation of photometric signatures.

Note

1. All lenghts and areas attributes are scaled by the scale factor attribute.

2. To see a detailed description of the Canonical Units (\(u_l, u_m, u_t\)) implemented in the attributes definition, see our System Module Reference.

3. The attributes are assign by computing them in their respective class, e.g., all Spangles coordinates are computed by the surface sampling.

4. The underscore distinction obs/int/luz means the reference frame in wich the attribute is computed (Observer/Intersection/Light-Source)

Key	Data Type	Description	Units/Values
name	str	Identification of the body having the spangler.	Body name (name)
spangle_type	consts	Type of spangle. For a list of spangle types, see the constants module.	(e.g., consts.SPANGLE_SOLID_ROCK)
geometry	consts	Geometry of the spangle. (See Sampler module constants).	(e.g., consts.SAMPLER_GEOMETRY_CIRCLE)
scale	float	The length scale of the body, e.g., for a ring this is the outer radius.	Length unit (e.g., km, \(u_l\))
n_equ	list, array	Direction of the equator of the body with respect to the barycenter.	[x, y, z] (unit vector)
alpha_equ	float	Zero meridian of the equatorial system.	radians
w	float	Rotational angular velocity.	rad/\(u_t\)
q0	float	Initial longitude (azimuthal angle) at time :math: t_0. Longitude at time \(t\) is \(q = q_0 + w (t - t_0)\)	radians
center_equ	list, array	Center of the body with respect to the barycenter in the body-centric equatorial system.	[x, y, z] (length units)
x_equ, y_equ, z_equ	float	Cartesian coordinates of the spangle in the body-centric equatorial system.	Length units
r_equ	float	Radial coordinate of the spangle in the body-centric equatorial system.	Length units
q_equ	float	Longitude (azimuthal angle) of the spangle in the body-centric equatorial system.	radians
f_equ	float	Latitude of the spangle in the body-centric equatorial system.	radians
ns_equ	list, array	Unitary vector normal to the spangle in the body-centric equatorial system.	[x, y, z] (unit vector)
center_ecl	list, array	Center of the body with respect to the barycenter in the ecliptic system.	[x, y, z] (length units)
x_ecl, y_ecl, z_ecl	float	Cartesian coordinates of the spangle in the ecliptic system.	Length units
wx_ecl	list, array	y-axis on the surface of the tangent plane to the spangle in the ecliptic system: \(\mathbf{w_x = (w_y \times n_s)}\).	[x, y, z] (unit vector)
wy_ecl	list, array	y-axis on the surface of the tangent plane to the spangle in the ecliptic system: \(\mathbf{w_y = (n_s \times e_z)}\).	[x, y, z] (unit vector)
ns_ecl	list, array	Unitary vector normal to the spangle, calculated in the class, in the ecliptic system.	[x, y, z] (unit vector)
center_int	list, array	Center of the body in the intersection system.	[x, y, z] (length units)
x_int, y_int, z_int	float	Cartesian coordinates of the spangle in the intersection system.	Length units
ns_int	list, array	Unitary vector normal to the spangle, calculated in the class, in the intersection system.	[x, y, z] (unit vector)
rho_int	float	Pseudo cylindrical radial coordinate of the spangle in the intersection system.	Length units
az_int	float	Azimuthal angle of the spangle in the intersection system.	radians
cosf_int	float	\(cos(\theta)\) coordinate of the spangle in the intersection system.	dimensionless
cos_int	float	Angle between the normal to the spangle and the direction of intersection \(cos(\gamma)\).	dimensionless
azim_int	float	Azimuth of the direction of intersection.	radians
n_int	list, array	Vector from the intersection origin to each spangle.	[x, y, z] (length units)
n_int_ecl	list, array	Vector from the intersection origin to each spangle in the ecliptic system.	[x, y, z] (length units)
d_int	float	Distance of the Spangle to the intersection.	Length units
asp_int	float	Effective area of the spangle with respect to the intersection perspective.	Area units
z_cen_int	float	z-coordinate of the center of the body to which the spangle belongs in the intersection system.	Length units
hidden_by_int	str	Indicates which body intersects the observer or light coming to a Spangle (in the intersection system context).	Body name (pr.Body.name)
transit_over_int	str	Indicates which body is intersected by the Spangle (is transiting over) (in the intersection system context).	Body name (pr.Body.name)
string_int	str	Temporal string related to the intersection.	Arbitrary string
center_obs	list, array	Center of the body in the observer system.	[x, y, z] (length units)
x_obs, y_obs, z_obs	float	Cartesian coordinates of the spangle in the observer system.	Length units
ns_obs	list, array	Unitary vector normal to the spangle, calculated in the class, in the observer system.	[x, y, z] (unit vector)
rho_obs	float	Cylindrical radial coordinate of the spangle in the observer system.	Length units
az_obs	float	Azimuthal angle of the spangle in the observer system.	radians
cosf_obs	float	\(cos(\theta)\) coordinate of the spangle in the observer system.	dimensionless
cos_obs	float	Angle between the normal to the spangle and the direction of the observer \(cos(\epsilon)\).	dimensionless
azim_obs	float	Azimuth of the direction of the observer.	radians
n_obs	list, array	Vector from the observer origin to each spangle.	[x, y, z] (length units)
d_obs	float	Distance of the Spangle to the observer.	Length units
asp_obs	float	Effective area of the spangle with respect to the observer perspective.	Area units
z_cen_obs	float	z-coordinate of the center of the body to which the spangle belongs in the observer system.	Length units
hidden_by_obs	str	Indicates which body intersects the observer or light coming to a Spangle (in the observer system context).	Body name (pr.Body.name)
transit_over_obs	str	Indicates which body is intersected by the Spangle (is transiting over) (in the observer system context).	Body name (pr.Body.name)
beta_loc	float	Beta angle that rotates the local scattering plane to the planetary scattering plane.	radians
center_luz	list, array	Center of the body in the light-source system.	[x, y, z] (length units)
x_luz, y_luz, z_luz	float	Cartesian coordinates of the spangle in the light-source system (calculated in the class).	Length units
ns_luz	list, array	Unitary vector normal to the spangle, calculated in the class, in the light-source system.	[x, y, z] (unit vector)
rho_luz	float	Cylindrical radial coordinate of the spangle in the light-source system.	Length units
az_luz	float	Azimuthal angle of the spangle in the light-source system.	radians
cosf_luz	float	\(\mathbf{cos(\theta)}\) coordinate of the spangle in the light-source system.	dimensionless
cos_luz	float	Angle between the normal to the spangle and the direction of the light-source (\(\mathbf{cos(i)}\)).	dimensionless
azim_luz	float	Azimuth of the direction of the light-source.	radians
n_luz	list, array	Vector from the light-source origin to each spangle.	[x, y, z] (length units)
d_luz	float	Distance of the Spangle to the light-source.	Length units
asp_luz	float	Effective area of the spangle with respect to the light-source perspective.	Area units
z_cen_luz	float	z-coordinate of the center of the body to which the spangle belongs in the light-source system.	Length units
hidden_by_luz	str	Indicates which body intersects the observer or light coming to a Spangle (in the light-source system context).	Body name (string)
transit_over_luz	str	Indicates which body is intersected by the Spangle (is transiting over) (in the light-source system context).	Body name (string)
azim_obs_luz	float	Difference between the azimuth of the observer over the spangle and that of the light-source.	radians
asp	float	Effective area of the spangle in 3D.	Area units
dsp	float	Effective diameter of spangle, \(d_{sp} = 2 \sqrt{(a_{sp} / \pi)}\).	Length units
scatterer	str	Hash (identifier) of the scatterer used for this spangle.	Hash string (scatterer.SCATTERER)
albedo_gray_normal	float	Wavelength-independent normal albedo.	dimensionless (0 to 1)
albedo_gray_spherical	float	Wavelength-independent spherical albedo.	dimensionless (0 to 1)
tau_gray_optical	float	Wavelength-independent optical depth.	dimensionless (non-negative)
F, Q, U, V	float	Stokes vector components.	Flux units
P	float	Degree of linear polarization, \(\mathbf{P = \sqrt{Q^2 + U^2} / F}\).	dimensionless
emmitter	str	Hash (identifier) of the emitter used for this spangle.	Hash string
Teq	float	Equilibrium temperature.	K (Kelvin)
Tem	float	Emission temperature.	K (Kelvin)
emmisivity	float	Emissivity (1 for a perfect black body).	dimensionless (0 to 1)
unset	bool	Boolean indicating if the state has not been set.	True/False
hidden	bool	Boolean indicating if the spangle is not taken into account for photometry.	True/False
source	bool	Boolean indicating if the spangle belongs to a light-source (it does not reflect light).	True/False
visible	bool	The spangle is visible from observer	True/False
intersect	bool	Intermediate state to calculate intersections	True/False
shadow	bool	The spangle is in the shadow of other spangler	True/False
indirect	bool	The spangle is indirectly illuminated	True/False
emit	bool	The spangle is emmitting	True/False
above	bool	Intermediate state to calculate above or below state respect to ring	True/False
illuminated	bool	The spangle is illuminated by the light-source	True/False
transmit	bool	The spangle is illuminated but transmitting light	True/False
transit	bool	The spangle is transiting	True/False
occult	bool	The spangle is occulted by a light source	True/False
stellar_flux	float	Incident Stellar Flux at the location of the spangle	Normalized Flux units
reflected_flux	float	Reflected Flux from the spangle towards the observer	Normalized Flux units
transit_flux	float	Flux blocked from the star during transit	Normalized Flux units
thermal_flux	float	Thermal Emission Flux from the spangle towards the observer	Normalized Flux units

Body Constants

These are the numerical attributes and its defaults physical parameters to define and initialize the astrophysical body types we consider in pryngles to Spangle and create an exoplanetary system with orbital dynamic motion. Moons are considered as Planet-type body