Precessional effects on the LISA “constellation”

We investigate with a simple analytical approach some effects on the orbits of LISA due to the corrections of the gravitational potential of the Sun. The general relativistic correction in the weak field limit, responsible for the classical relativistic perihelion advance, can be obtained by adding to the potential a term scaling as r3 and parametrized by the Sun Schwarzschild radius. Another interesting correction term is provided by the intrinsic quadrupole moment of the Sun. With the current values of the parameters, the effects produced by both these terms are probably within the detection capabilities of LISA. With the same approach can also be evaluated the much smaller effect of a global stationary field, associated to sources like the interplanetary dust or a local dark matter component.