Case 0: "Dark Star" Steals Planet (перехват спутника)

[ValeryOchkov]

In this simulation of three gravitating Newtonian particles, a blue "planet" orbits a red "star" until they meet the "dark star." The physics is simple, yet the numerical behavior is extreme. Indeed, Mathcad's numerical integrators have difficulty modeling the motions correctly.

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[ValeryOchkov]

The view point is the black planet

Video Link : 5780

[ValeryOchkov]

Solution is sensitive to the choosing numerical methods for solving

Same initial condition but the method is not RADAU (see the first video) but Adams/BDF:

Video Link : 5781

[ValeryOchkov]

Radau and Adams/BDF Methods of the ODE solution on the one plot:

Video Link : 5991

[ValeryOchkov]

Radau and Adptive Methods of the ODE solution on the one plot:

Video Link : 5992

[ValeryOchkov]

Mathcad Prime - with units but without animation

I think it is the Adams/BDF method of ODE solution.

[ValeryOchkov]

Radau and Fixed Methods of the ODE solution on the one plot:

Video Link : 5993