For my computational physics project I would like to investigate the relationship between the precession and the eccentricity of a planet’s orbit due to general relativity as detailed in chapter 4, section 3 of Computational Physics, by Nicholas J. Giordano and Hisao Nakanishi. Precession is the phenomenon of the rotation of the orientation of axes of a planet’s (elliptical) orbit with respect to time caused by the gravitational forces exerted by other planets. However, general relativity predicts deviations from the inverse-square law, which (for example) allows the Sun to contribute an additional 43 arcseconds per century to the precession of Mercury (as the distance between the two is small enough for the deviations to have an effect). The rate of precession examined in this project will only be that which is caused by the model planet’s host star. This will entail the construction of a planetary motion program using Newton’s law of gravitation and the Euler-Chromer method; which will later be adjusted to allow for the addition of a variable precession rate. The value of the planet’s perihelion will be held constant at the value for Mercury’s perihelion, but the eccentricity and size of the orbits will be allowed to vary. Mass of the planet will be held constant, at the same value as for Mercury.
If I have additional time left over I could also add another planet (such as Jupiter) to my code to make a three-body simulation of the “Mercury-like” planet.