How to convert coordinates from GSE to RTN

Question

I have tried to search all across the web for a solution, even asked ChatGPT-4, yet received no results.

The problem is stated like this. For each timestamp I have position of the spacecraft and x, y, z coordinates of the magnetic field vector (both in GSE coordinates). I need to convert the coordinates of the magnetic field vector from GSE to RTN based on the spacecraft positions in Python. Any solution is acceptable (using basic NumPy or any specific library for astronomy). Any other help is also appreciated.

P.S. If this is easily achieved in another programming language rather than Python, such solutions are also welcome.

Answer 1

We can achieve this using Python with the help of libraries like NumPy, which is excellent for handling arrays and mathematical operations.

1. The code should calculate the unit vectors for the RTN system based on the spacecraft's position in GSE coordinates.
2. Make sure to construct the transformation matrix from GSE to RTN using these unit vectors.
3. Then apply this matrix to the magnetic field vectors o convert their coordinates

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def gse_to_rtn(position, b_gse):

r_unit = position / np.linalg.norm(position)  
t_unit = np.array([-r_unit[1], r_unit[0], 0])  
t_unit = t_unit / np.linalg.norm(t_unit)
n_unit = np.cross(r_unit, t_unit)  

transform_matrix = np.array([r_unit, t_unit, n_unit]).T

b_rtn = np.dot(transform_matrix, b_gse)

return b_rtn

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This function converts the spacecraft's position and the magnetic field vector from GSE coordinates to RTN coordinates, taking into account that the spacecraft's movement is mainly in the GSE XY plane. Keep in mind, you may need to tweak this depending on your specific situation.