Relativistic Reference System Service (R2S2)

The R2S2 Python package provides a systematic solution for relativistic spacetime coordinate transformations in the cislunar space.

Features

The core functions encapsulated in R2S2 package enable bidirectional and strictly IAU-resolution-compliant transformation calculations between any two of the six commonly used spacetime coordinates across three reference systems in the cislunar space:

• Barycentric Celestial Reference System (BCRS)
• Geocentric Celestial Reference System (GCRS)
• Lunar Celestial Reference System (LCRS)

Documentation

For detailed information, please refer to the package documentation:

• Chinese version: 中文版PDF.

Dependencies

R2S2 depends on the following Python library:

• numpy
• calcephpy

Data files for the following ephemerides are required:

• Planetary and lunar ephemeris with a built-in earth time ephemeris.

  We recommend DE440 (de440t.bsp variant, note the t for built-in time ephemeris), which is available at JPL website with this link.

• Lunar time ephemeris.

  The lunar time ephemeris, LTE440, is developed by our team and included in R2S2 package. No manually downloads are required.

Installation

The detailed installation steps are as follows:

1. Install calcephpy

   For 64-bit windows systems with Python 3.10 to 3.14, we provide the wheel packages of calcephpy v4.0.5 for easy installation

   pip install calcephpy-4.0.5-cp314-cp314-win_amd64.whl
   

   For other Python versions or OSes, the package can be installed from PyPi with pip install calcephpy. But it needs locally building as described in the official install instructions. We also provide a step-by-step guide here.

2. Install R2S2

   The R2S2 package can be installed with pip

   pip install r2s2
   

   This will install its dependencies, and install the R2S2 package.

Quick Start

Take transformation from lunar coordinates (TCL, Y) to barycentric (TCB, x) as an example

1. Import necessary Python packages

   import numpy as np
   import R2S2
   

2. Import the local planetary ephemeris file containing the time ephemeris (note: modify the actual file path accordingly).

   R2S2.init_E("/path/to/de440t.bsp")
   

3. Input the integer and fractional parts of the Julian Day in Lunar Coordinate Time (TCL), in days. The following corresponds to approximately 2026-01-04 11:23:39 TCL.

   jd1 = 2460094
   jd2 = 0.9747569458346726
   

4. Input the spatial coordinates in the selenocentric system compatible with TCL, in kilometers.

   Y = np.array([3000, 1813, 454])
   

5. Call the TCL2TCB function in R2S2 to compute the transformation from (TCL, Y) to (TCB, x), where Delta_t and Delta_x represent the iterative accuracy of time and space transformations, with units of seconds and kilometers respectively.

   TCB1, TCB2, x = R2S2.TCL2TCB(jd1, jd2, Y, Delta_t = 10**(-9), Delta_x = 10**(-6))
   

Output should be

TCB1 =  2460094
TCB2 =  0.9750082547331026
x =  [-5.72776989e+07 -1.29690213e+08 -5.61695394e+07]