# The Curvature of Motion in a Gravitational Field

Version 1.0.3.1 (76.1 KB) by
Calculate Orbital motion; Precession; Natural Frequency Shift; Light and Cosmic Ray Deflection; Shapiro Time Delay; Black Hole diameter
Updated 20 Jun 2022

Example Script files are provided to calculate the following solutions.
Example 1: Simple trajectory motion.
Example 2: Earth satellite motion and clock rate frequency shift.
Example 3: Orbital motion and precession of planets in our solar system.
Example 4: Orbital motion, precession, and redshift of Star S2 in the galactic center.
Example 5: Strong gravitational field orbital precession.
Example 6: The curved path and Shapiro time delay of light passing near the Sun.
Example 7: The gravitational bending of light and cosmic rays passing near a neutron star.
Example 8: The emissivity, shadow diameter, and curved path of light escaping from or passing near an apparent black hole or quasar. This is done for Sgr A* at the galactic center and the central gravitational body M87*.
For more detailed information, downloade the paper, "The Curvature of Motion in a Gravitational Field," at: https://vixra.org/abs/2106.0147
The method used to calculate these solutions is documented in the book, "Time Matter And Gravity." It can be downloaded from:
The associated math is easy to understand and is limited to basic geometry, vector algebra, and simple calculus. This enables advanced high school and undergraduate college students to understand and solve these examples on a mobil phone or tablet with an app capable of running MatLab script files. These solutions compared with data illustrate excellent agreement for both weak and strong gravitational fields.

### Cite As

Morris G. Anderson (2024). The Curvature of Motion in a Gravitational Field (https://www.mathworks.com/matlabcentral/fileexchange/94835-the-curvature-of-motion-in-a-gravitational-field), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2021a
Compatible with any release
##### Platform Compatibility
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Version Published Release Notes
1.0.3.1

Updated solver to reduce solution time.

1.0.3

Update the solver approach to reduce solution time.

1.0.2

Updated the description

1.0.1

Updated the Description

1.0.0