i could understand that the moon could attain a perfect balance between gravity and centrigal force that permits the moon to rotate endlessly around ethe earth, but that both moon and earth are also rotating around the sun makes it completely invalid, i think
Okay, I think I understand your issue.
If I understand correctly, you are suggesting that Earth orbits the sun with a circular path.
The moon then orbits Earth with a "circular" path.
These 2 paths intersect. Thus the moon should crash into Earth.
(Also note: I am ignoring the ecentricity of these paths for now. In reality, all of these parts are elipses, but that is not significant).
The issue is that everything on and near Earth is also orbiting the sun. So they also have their own circular orbits around the sun.
This is affected by Earth (and Earth is effected by the moon to a lesser extent), which results in this circular orbit deforming into a circle with a sine curve overlapping them.
e.g. consider just a single satellite, (X), orbitting in this particular direction, (going the other way works as well, but is somewhat more complex):
Let start outside Earth, (i.e. so in a line, you have the sun, Earth and X). X experiences the gravity of the sun, as well as the Earth.
This makes it's orbit faster than Earth so it starts to race ahead of Earth.
This now makes Earth start to pull it back slightly, but not directly and its inertia want to keep it moving, so not only does it go ahead of Earth it also starts to curve and go in front of Earth (i.e. along Earth's orbital path).
At this point, if it stopped magically (or was just orbiting the sun and Earth magically appeared), it would fall to Earth, but its velocity keeps it moving out of Earth's path, and the same pull of Earth now causes it to bend around to the inside of Earth (between Earth and the sun).
Now when it is between Earth and the sun, it's orbital speed will be slower than Earth, due to the gravity from Earth cancelling out some of that from the sun (as they are now pulling in different directions), and thus it slows down and starts to fall behind Earth.
Then similar to above, its path curves and it falls in directly behind Earth and then starts to speed up.
So while their path's intersect, they are at those points at different times and thus don't crash.
Does that make sense?
Also note: This only holds when you are between Earth and it's Lagrangian points with the sun, and aren't within the moons influence.
If you are at L1 or L2, the Earth's gravity combines with the suns so it (the satellite) orbits at the same angular rate as Earth. (L3, L4 and L5 are the same, but in significantly different positions.)