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Over the weekend, I wrote a little program that simulates the solar system (or any set of bodies). I use off-the-shelf orbital elements to set the starting conditions and then do a simulation of gravity to move the bodies, rather than just incrementing the time dimension of the orbital elements formula.

To test it, I let it simulate an entire century of solar system dynamics at a one second temporal resolution (that took 21 hours). Then I measured the precession of Mercury's orbit. Obviously, fast computers that can do this job numerically did not exist in 1910. How was it possible to figure Mercury's orbit accurately enough to know it was "wrong" (and General Relativity correct) back then? I know they didn't do it the way I did.

Scott Hurst
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  • "Computers" are older than you think. – J.G. May 17 '22 at 20:05
  • I am familiar with the idea of the human computer. I'm sure they were involved. I'm also really confident that they didn't do it anything like the way I did. There must be an "easier" way. There must be a means more clever than what I did. – Scott Hurst May 17 '22 at 20:20
  • They may have imposed useful approximations, such as all planets being in one plane with their individual angular momenta conserved, or including fewer gravitational interactions than you did, or summarizing the potential Mercury sees as a polynomial in $1/r$ with time-averaged coefficients. But HSM would give you a more definitive answer than you'll likely get here. – J.G. May 18 '22 at 05:14

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