This question relates to building a computer model of gravity under relativity in a frame by frame type animation where the force on an orbiting object is calculated between each frame and applied to the animation.(adsbygoogle = window.adsbygoogle || []).push({});

Its pretty easy to model normal planet orbits using Newtons inverse square lawf = g1 * (m2)/r²where m2 is the mass of the other object, r is the distance and g1 is the gravitational constant. The more accurate the numbers, the better an orbit you get and they all form nice ellipses that follow Kepler's laws.

Due to relativity, the orbit of Mercury precesses 43 arc seconds per century. In order to model precession, its a common programming trick to introduce ar³term, ie. calculate the forcef = g1 * (m2)/r² + g2 * (m2)/r. This works great and you can adjust the value of g2 to get any amount of precession you want, specifically you can make the orbit precess at 43 arc seconds per century and model Mercury's orbit with a great deal of accuracy.³

The question is why is this method so accurate in modelling the force of gravity under relativity? I have assumed that whatever the correct equation to use to calculate the force of gravity on a planet from the sun that includes relativity can be expressed as some kind of an infinite Taylor series along the lines off = g1 * (m2)/r²hence the+ g2 * (m2)/r³+ g3 * (m2)/r⁴+ g4 * (m2)/r⁵ ...r³term is simply reflecting the better accuracy.

Is there an expert here that know this for sure? Ie. What is the correct equation that should be used to calculate the force between a planet and the sun under relativity in a frame by frame type calculation? Can it be expressed in this form?

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# Modeling the orbit of Mercury under relativity

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