The centrifugal and Coriolis forces do not appear as a result of physically imposed forces, but are due to a special property of a rotation. Thus, these forces are called pseudo-forces or ‘fictitious forces’. They are merely an artifact of the rotation of the reference frame adopted. This paper studies the motion of a test particle in the neighbourhood of the triangular point L4 in the framework of the perturbed relativistic restricted three-body problem (R3BP) when small perturbations are conferred to the centrifugal and Coriolis forces. It is found that the position and stability of the triangular point are affected by both the relativistic factor and small perturbations in the Coriolis and centrifugal forces. As an application, the Sun–Earth system is considered.

Effect of Perturbations in the Coriolis and Centrifugal Forces on the Stability of L 4 in the Relativistic R3BP

Considering both the special and general relativistic approximations, we analyze the gravitational redshift in the Schwarzschild problem (i.e. the two body problem associated to a potential of the form A/r+C/r3, where r is the distance between photon and the center of a star, and A,C well-established positive constants). We present the difference between the redshift for Newton’s potential and the one for Schwarzschild’s potential in the third order terms. In both cases (special and general relativistic approximations) the difference value reaches the ratio γ/R3, where R is the geometrical radius of the star and γ =C/c2, c being speed of the light). In the general relativistic approximation, we show that a black hole effect appears at a ratio noted by us ρs which is larger than Rs Schwarzschild gravitational radius.

/pdf/gravitational-redshift-in-the-post-newtonian-potential-field-7vfb5i3se1.pdf

Gravitational Redshift in the post-Newtonian potential field: The Schwarzschild Problem

In this paper we find some families of central configurations for the Schwarzschild three body problem. Since in this case the potential is the sum of two homogeneous functions, the total number of the central configurations depend of the size of the system measured by the moment of inertia. Depending of the values of the masses and the sign of the constants which appear in the equations of motion, we find the bifurcation values for our families in terms of the moment of inertia.

Central Configurations in the Schwarzschild Three Body Problem

The restricted three-body problem in Schwarzschild’s gravitational field is analyzed. The existence of the equilibrium points in the orbital plane is discussed and the corresponding positions are established. There are three collinear libration points, and, if they exist, two triangular libration points (situated in the orbital plane of the primaries). If triangular points exist, they may not form equilateral triangles; the triangles are isosceles for equal masses of the primaries, and scalene else.

Libration Points in Schwarzschild's Circular Restricted Three-Body Problem

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Libration Points in Schwarzschild's Circular Restricted Three-Body Problem