I am trying to understand how the Sun affects tides on the Earth's oceans and seas.
It is quite clear that when the Moon is in the first and in the third quarter, the Sun's and the Moon's gravitational forces are exerted in different directions (90° apart) and consequently the tidal range is at its minimum, and it is called neap tide.
It is also intuitive that when the Moon and the Sun are aligned on the same side of Earth (new moon), their gravitational forces sum up and cause the tidal range to reach its maximum (spring tide).
What I don't understand is the reason why spring tides are also caused by a full moon configuration, when the Moon and the Sun are still aligned but on Earth's opposite sides. Intuitively speaking, I would expect the resulting tidal range to be smaller than that occurring during a new moon (but still greater than a neap tide), because the Sun's gravitational force (though lower that the Moon's) actually opposes that of the Moon.
Having said that, am I missing some physical phenomena in the description above for the two spring tides to be equal (where I neglected the rotating Earth's centrifugal force for simplicity, though I'm aware of its role in tides) or am I just misunderstanding the fact that the two kind of spring tides actually have different ranges, although both greater than neap tides?