Can the Euler Method Accurately Solve Orbital Gravity Equations?

Thread starter Timothy S
Start date Jun 15, 2015
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Euler Euler method Method Orbits

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The discussion centers on the use of the Euler Method for solving gravitational differential equations related to orbital mechanics. While the Euler Method is a straightforward numerical approach, it is generally deemed inadequate for accurate orbital calculations due to rapid error propagation, necessitating smaller time steps that are impractical for computation. Participants recommend using higher-order methods like Runge-Kutta, which provide better stability and accuracy for simulating orbits. The conversation also touches on the importance of choosing appropriate time steps and the challenges of maintaining precision in simulations. Ultimately, for reliable orbital simulations, more sophisticated numerical methods are essential.

Oct 29, 2015

Kodogo

I've been tooling around with this, and found that the method known in some quarters as "Leapfrog" gives pretty good results even with modest computing power. The method is the same as described in Feynman Lectures volume 1 chapter 9. It seems to be the same as what some people call Verlet. There's an excellent discussion here:
http://young.physics.ucsc.edu/115/leapfrog.pdf

For a free iPad app to show the results of the method see here:
https://itunes.apple.com/nz/app/orbit-simulator/id1048345753?mt=8

The main problem I see is that highly elliptical orbits do start to precess, depending on the time step you use. Also when the speed gets very high the orbits develop sharp corners. To get round this you's need smaller steps or a method with adaptive step size, but Leapfrog is well good enough just to play around with.