Tidal Forces Misunderstanding
I'm sure there are several misconceptions here and I'd greatly appreciate it if someone could help me identify and correct them.
When calculating tidal forces across an object, the earth for example, why does one neglect the gravitational force due to the mass of that object (the earth) and instead only consider the force due to the moon's mass?
To clarify, I am wondering why one does not consider the differing force of attraction between different point on (and within) the earth when calculating the tidal effects due to a satellite.
Here is the situation in which I'm trying to understand tidal forces:
The earth and the moon, some distance apart (but "fixed" in space, i.e. not orbiting each other and not accellerating toward each other). From what I've read, this situation should produce tidal bulges in both the near and far oceans.
Here is what I'm thinking:
On the point of earth's surface closest to the moon, the net force on that point mass is the sum of the force of the earth's gravity on that point and the force of the moon's gravity on that point.
At the center of the earth there is no net force due to earth's gravity so the net force is toward the moon
On the point furthest from the moon, the forces of the earth and the moon on that point are in the same direction (toward the moon)
I fail to see how this produces tidal bulges on opposite sides of the earth.
It seems to work out correctly if one only considers the forces on the points due to the moon's gravity, but I don't understand why you're allowed to disregard the earth's gravity.
I feel that if I understood this quote from the link below, it may shed some light on the issue:
"Since we have taken the near-spherical earth as a baseline, and the tidal effects are superimposed on that, we can ignore the earth's own gravitational forces on itself, leaving only the forces due to the moon. They are the forces causing tidal effects."
https://www.lhup.edu/~dsimanek/scenario/tides.htm 319