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Two planets are trading their satellites

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Case 6: Earth and Moon

In Mathcad Prime 3 - without animation but with units Read more...

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Case 5: Two planets are changing satellites (две планеты меняются спутниками)

Я знаю две супружеские пары. Они развелись и потом поженились, сменив своих партнеров.I know two couples. They divorced and then married, changing their partners.It is one math model of this life Read more...

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Case 4: Four planets - start from corners of square

See please at the end of the video the break of the numerical solution by Adams/BDF method

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

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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Case 2Reference [math/0011268] A remarkable periodic solution of the three-body problem in the case of equal masses Read more...

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Case 1: Two planets and one star

Two planets (A red and B blue) have the same mass (mass = 1), and the initial time are located at equal distances from the black star S (mass = 200) on a straight line with a star on the opposite side of it. If the speed of the planets are equal and in opposite directions, then it is easy to see symmetrical relative positioning of all three bodies of such a hypothetical planetary system will be maintained and the subsequent movement.

Пусть две планеты красная A и голубая B  имеют одинаковые массы (mass=1), и в начальный момент расположены на одинаковых расстояниях от черной звезды S (масса = 200) на одной прямой со звездой с противоположных сторон от нее. Если при этом скорости планет равны и направлены в противоположные стороны, то, как легко видеть, симметричное взаимное расположение всех трех тел такой гипотетической планетной системы будет сохраняться и при последующем движении.

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