  We focus on the secular changes of the orbital elements of a planet in the
solar system, determined by the magnetic-like part of a gravitational wave
field. Using Fermi coordinates we show that the total force acting on a test
particle is made of two contributions: a gravito-electric one and a
gravito-magnetic one. While the electric-like force has been thoroughly
discussed in the past, the effect of the gravito-magnetic force, which depends
on the velocity of the test particle, has not been considered yet. We obtain
approximated results to some orders in the orbital eccentricity and show that
these effects are much smaller than the corresponding gravito-electric ones.
