Reading Ephemeris Data
This tutorials will walk you through the basic features and interfaces that allow you to compute translation and orientation data from binary ephemeris kernels.
Computing state vectors
Ephemerides.jl
allows the computation of a relative position between two points and its higher order derivatives up to order 3 (i.e., velocity, acceleration and jerk). All these computations are natively thread-safe and compatible with Automatic Differentiation (AD) with respect to time via ForwardDiff.jl.
In particular, the following methods are available to compute translation data:
ephem_vector3(eph, from, to, time)
ephem_vector6(eph, from, to, time)
ephem_vector9(eph, from, to, time)
ephem_vector12(eph, from, to, time)
They all share the same interface, requiring an EphemerisProvider
object as the first input. from
and to
are integer numbers representing the ID of the center and target points that we desired. The time
argument is expressed in TDB seconds since J2000.0.
Differently, from traditional ephemerides readers, Ephemerides.jl
is only meant to read the data stored in the binary kernels and it does not perform any concatenation of state vectors. This means that if data from point 399 is expressed with respect to point 3, we will only be able to compute the relative position of 339 with respect to 3 or viceversa, but not of 399 with respect to another point. The reason behind this is that Ephemerides.jl
is meant to be used in combination with FrameTransformations.jl, which already enables tranformations between different user-defined point and axes.
An example to compute the position of the Moon (399) with respect to the Earth-Moon Barycenter (3) at J2000 (time = 0), is the following:
using Ephemerides
# Load an ephemeris kernel containing the requested data
kernel = "path_to_de440"
eph = EphemerisProvider(kernel)
# Compute the position
pos = ephem_vector3(eph, 3, 399, 0)
Instead, if one desires the whole state vector, up to the jerk components, the functions become:
# Compute position and velocity
pv = ephem_vector6(eph, 3, 399, 0)
# Compute position, velocity and acceleration
pva = ephem_vector9(eph, 3, 399, 0)
# Compute position, velocity, acceleration and jerk
pvaj = ephem_vector12(eph, 3, 399, 0)
In all these examples, the returned data is always in the form of a StaticArray
in order to minimise memory allocations.
SPK segments of types 1 5, 15, 17 and 21 do not natively support acceleration and jerk computations. However, these values can be computed by Automatic Differentiation (AD) of the position and/or velocity components.
Computing orientation angles
Similarly to position components, Ephemerides.jl
also allows the computation of orientation angles and their derivatives up to order 3. All these computations are natively thread-safe and compatible with Automatic Differentiation (AD) with respect to time via ForwardDiff.jl.
In particular, the following methods are available to compute orientation data:
ephem_rotation3(eph, from, to, time)
ephem_rotation6(eph, from, to, time)
ephem_rotation9(eph, from, to, time)
ephem_rotation12(eph, from, to, time)
Again, they all share the same interface, requiring an EphemerisProvider
object as the first input. from
and to
are integer numbers representing the ID of the reference and target axes that we desired. The time
argument is expressed in TDB seconds since J2000.0.
An example to compute the Euler angles of the PA440 axes (31008) with respect to the ICRF (1) at J2000 (time = 0), is the following:
using Ephemerides
# Load an ephemeris kernel containing the requested data
kernel = "path_to_pa440"
eph = EphemerisProvider(kernel)
# Compute the position
ang = ephem_rotation3(eph, 1, 31008, 0)
Instead, if one desires the whole vector, up to the 3rd order derivative, the functions become:
# Compute angles and derivatives
pv = ephem_rotation6(eph, 1, 31008, 0)
pva = ephem_rotation9(eph, 1, 31008, 0)
pvaj = ephem_rotation12(eph, 1, 31008, 0)
The returned orientation data is always in the form of a StaticArray
in order to minimise memory allocations.
Differently from the translational data contained in SPK kernels, the orientation angles can only be computed in one direction, i.e., if the orientation of the Moon's Principal Axes (PA) is defined with respect to the ICRF, it is not possible to compute the rotation from the PA to the ICRF with this routine.