I'm trying to analyze a situation wherein a ship is moving across the surface of the earth. I am trying to analyze this situation in a reference frame that is rotating with the earth (NED frame).

I am confused about the relationship between gravitational, centripetal, and centrifugal forces acting on the boat. Gravitation is simple enough and would exist even if the earth was not spinning.

My question is, the earth is spinning, and we learned in physics class that an object undergoing circular motion experiences a center seeking (centripetal) acceleration. Wouldn't this therefore increase the force experienced by the boat beyond just the mass attraction between the boat and planet (gravitation)?

When I search online though, I really only find mention of the centrifugal force reducing the effect of the gravitational force, most notably on the equator where the distance from the rotational axis is maximized. Why isn't centripetal force included in the calculations?