N-body Gravity Simulation by Curvature of Wave Propagation

Simulate the solar system, orbital precession, time delay, light deflection, black hole shadow, star clusters, and spacecraft trajectories.

For the Curvature of Wave Propogation Method (CWPM)

The Example script files included:

Example 1: The solar system and Mercury’s orbital precession.

Example_1_the_solar_system.m is the original file - fastest solution

Example_1_the_solar_system_dvdt.m is the Runge-Kutta option - traditional solver option. This calculates the solution with an acceleration vector that is derived from the curvature of motion.

The radial acceleration vector is derived from Equation TMG Eq 7-9 contained in the N-body paper listed below.

The tangential acceleration vector is derived from Equation 5

This paper will be revised to include the derivation, with a tentative

revision date of Fall 2025.

Sample results Movie_Ex_1_our_solar_system_Group_V_0.mp4 Movie_Ex_1_our_solar_system_Group_V_230.mp4

Example 2: Shapiro time delay and the bending of light. Sample results Movie_Ex_2_Shapiro_Time_delay_1967.mp4 Movie_Ex_2_Shapiro_Time_delay_1970.mp4

Example 3: Apparent black hole shadow diameter for M87. Sample results Movie_Ex_3_Apparent_black_hole_shadow_1.mp4

Example 4: Simple trajectory motion

Example 5: Star cluster, symmetric and random. Sample results Movie_Ex_5_Star_cluster_random_3nb_1.mp4 Movie_Ex_5_Star_cluster_random_3nb_2.mp4 Movie_Ex_5_Star_cluster_random_50nb_1.mp4 Movie_Ex_5_Star_cluster_random_50nb_2.mp4 Movie_Ex_5_Star_cluster_symmetric_3nb.mp4 Movie_Ex_5_Star_cluster_symmetric_8nb.mp4

Example 6: Pioneer 10, 11, Voyager 1, and 2 trajectories. Sample results Movie_Ex_6_Pioneer_and_voyager_probes_1.mp4

A pre-print of the paper

N-body Gravity Simulation by Curvature of Wave Propagation

documenting these script files is available at:

Initial paper:

N-body Gravity Simulation by Curvature of Wave Propagation

Updated paper with acceleration vector and full documentation of the CWPM method:

N-Body Dynamics via Curvature of Wave Propagation: A Flat-Space Framework Matching GR Solar-System and EHT Constraints

Please let me know if you find any errors or have suggested changes.