Difference in the precession regarding the gravitational gradient Let say a less massive star acts on a planet causing it to precess.Does a more massive star cause less precession of this planet if in both cases the gravitational force applied to the planet center is of same magnitude? What I am really asking is: is precession in astrophysics caused only by the difference of the gravitational force caused by the star at closer and distant points of the inclined spinning planet?
 A: By the looks of it you are asking about precession of the equinoxes.
The Earth is not perfectly spherical, there is an equatorial bulge.
Recapitulating:
If a celestial body is perfectly spherical then the center of gravitational attraction (by another celestial body) coincides with that celestial body's center of mass.
When the celestial body is not quite spherically symmetric then the center of gravitational attraction is displaced towards the attracting body.
The displacement of the center of gravitational attraction  is mainly dependent on the following two factors.
(1) As you will expect: the larger the equatorial bulge, the larger the effect.
(2) The amount of displacement of the center of gravitational attraction is affected by the gradient of gravitational potential between the point of the Earth that is instantaneously closest to the Sun and the point of the Earth that is instantaneously furthest away from the Sun.
I'm describing it in terms of 'point of the Earth that is instantaneously closest to the Sun', because the Earth is rotating. The essence is: over the distance of the Earth's diameter there is a gradient in the Sun's gravitational potential.

Think of the gradient of the gravitational potential as the slope of a vulcano. The closer you are to the edge, the steeper the slope. The larger the vulcano, then for a given distance to the vulcano the slope is steeper.
For a less massive star: in order to be subject to the same gravitational acceleration as the Earth is the planet must orbit at a closer distance to its star. At closer range the gradient in gravitational potential is steeper.
The steeper the potential gradient, the larger the displacement of the center of gravitational attraction, hence the precession of the equinoxes of that planet will be faster.
The difference will be small; when you double the mass of the star (as compared to the Sun) then at Earth-Sun distance to that star you don't get double the gradient.
