lunar_lagrange_points_circular

ssapy.compute.lunar_lagrange_points_circular(t)[source][source]

Calculate the positions of the lunar Lagrange points in the GCRF frame for a given time.

This function calculates the positions of the five Lagrange points (L1, L2, L3, L4, and L5) in the Earth-Moon system at a specific time t. It accounts for the rotation of the Moon’s orbit around the Earth, providing the positions in a circular approximation of the Earth-Moon system.

Parameters:

tTime

The time at which to calculate the Lagrange points. The position of the Moon at this time is used to compute the Lagrange points.

Returns:

dict

A dictionary containing the coordinates of the five Lagrange points: - “L1”: Position of the first Lagrange point between the Earth and the Moon. - “L2”: Position of the second Lagrange point beyond the Moon. - “L3”: Position of the third Lagrange point directly opposite the Moon, relative to the Earth. - “L4”: Position of the fourth Lagrange point, forming an equilateral triangle with the Earth and Moon. - “L5”: Position of the fifth Lagrange point, forming an equilateral triangle with the Earth and Moon, but on the opposite side.

Notes:

  • The function assumes a circular orbit for the Moon and uses a rotation matrix to align the z-axis with the Moon’s normal vector.

  • The positions of L4 and L5 are calculated using a rotation matrix to align with the Moon’s orientation.

  • The gravitational parameters of the Earth and Moon are denoted as EARTH_MU and MOON_MU, respectively.

Example usage:

>>> t = Time("2024-01-01")
>>> lagrange_points = lunar_lagrange_points_circular(t)
>>> lagrange_points["L1"]
array([1.02e6, 0.0, 0.0])
>>> lagrange_points["L4"]
array([1.5e6, 1.5e6, 0.0])