I enjoy a lively discussion. Perhaps that was my objective, rather than my original position regarding the direction and source of the force which causes the tides.
Each particle of each body "attracts" every other particle. The actual number of forces may be near infinity. If we assume both bodies to be emitting separate forces (which they do) not just one force between them (which the formula implies), then the total force between two bodies becomes the sum of the two (or vector sum) of the many individual forces.
Those two resultant forces are exactly equal in magnitude and exactly opposite in direction. Therefore they are calculated as if they were one force.
Because the two (or many) forces are calculated on different properties of the two bodies, and as there has always been discussion regarding the difference between the gravitational mass and the inertial mass, I'm wondering if we shouldn't assume a body to be both a gravitational and an inertial mass and be mindful of the separate forces.
Perhaps the formula for gravitational force could be rewritten to include those ideas.
Hopefully you can see how I've made the total force of gravity between two bodies proportionate to the sum of the two resultant forces, and then inverse to the single distance between them squared. What that does is change our presently accepted value of G = 6.6726e-11 using mks units to G = 3.3363e-11 using mks units.
The Physics book says 'that "attract" means that a body exerts a force on another body that is directed back to the first body along the line joining the two bodies'.
But, the law of gravity says that 'any two bodies "attract" each other'.
Therefore, there are separate forces exerted by each of the two bodies.
Gravity is not unlike russ_watters "skateboarders", IF BOTH PULL.
There is only one rope or line of force. The action and reaction to each force is equal and opposite.
When you talk about a tide on a celestial body, that body becomes the reference frame, and the force comes from within that body.
Yes it is true the other bodies are doing the same thing, it's just a matter of which one is the reference.
The Earth's oceans tides are caused when the Earth's oceans "attract" or gravitate towards the Moon and Sun. Those waters are the source of the gravitational force which moves them.
I have a copy of Newton's Principia (translation) here on the desk. Newton used the term "mutual attraction" more than once. He also stressed the fact that the force of gravity diminishes the farther away from the source you go.
And to perhaps clarify the direction he said this:
Please note where Newton said "each towards the other". This is my argument that the tides gravitate towards the Moon and Sun. Yes the Moon and Sun are cute and "attractive", but the tides gravitate or attract themselves to those other cute attractive bodies. Any body has the force of gravity and it uses that force to bootstrap or move itself unless it is restrained in some manner, such as the apple restrained by the tree.Originally Posted by Isaac Newton
Newton also said:
Can you see in that theorem that the moon "gravitates" or is the source of the gravitational force it bootstraps or causes itself to be moved or "drawn off"?Originally Posted by Isaac Newton