Heliocentric coordinates

Having performed the reduction of the centre of mass and of the angular momentum, the Hamiltonian of the problem of three bodies can be written in heliocentric coordinates and using the Poincare variables as... 

Figure 2. A few revolutions of the satellites mi = 1 (diamonds, dashdotted) and m2 = 2 (circles, solid line) about the central body mo = 777, shown in heliocentric coordinates. Initial distances qi = 1.01, 2 = 1-00, opposite starting points, circular initial velocities.

The big problem in the expansion of Hi comes from the terms having A in the denominator. In heliocentric coordinates, we can write ... 

Here, r,R are (for example) mass scaled diatom and atom to center of mass of diatom distances (cf. Eqs. 1,8,9) and y the Tbend) angle between r and R. Actually r,R,y may represent a much wider definition of coordinates. For example, ,R may be the heliocentric coordinates of Smith. 

Figure 1. Main systems of coordinates heliocentric Jacobi s (right).

In Poincare heliocentric relative coordinates, the indirect part of Hi is (see equation 10) ... 

Centuries before the Christian era, several Greek philosophers had proposed heliocentric models to coordinate the observed motions of the sun, moon, and planets in relation to the fixed stars. However, the computational method of Alexandrian astronomer Claudius E tolemy which he... 

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