plane:
With the third can anyone point to empirical evidence of a smaller mass 'pulling' a larger mass.
The moon pulling on the Earth is a good example. The Moon creates tides on Earth, and the Earth obviously pulls on the Moon because otherwise the Moon would not orbit the Earth.
This seems to be in conflict with the high tide under the moon being the result only of an interaction of earth and moon gravities.
In mathematics, the moon's gravity doesn't reach the earth. It lessens the earth's gravity to cause a high tide. Doesn't actually pull the ocean. To theorize from there that the moon's 'pull' accounts for the earth criss cross of it's solar orbit is interesting but not to the point.
Gravity is an inverse-square law. The gravity of a particular mass, like the moon, NEVER goes to zero, although it drops off with distance.
The moon doesn't "lessen" Earth's gravity. The Moon's own gravity
combines with (technically, adds vectorially to) the Earth's gravity to create a net force on the oceans.
We know that mathematical analysis of the high tide under the moon yields the high tide being a result of the earth and moon gravities interacting.
I.E. You subtract the moon's gravity at an ocean from the earth's gravity at an ocean and you are at the beginning of mathematical logic of why the ocean weighs less under the moon. The moon's gravity has lessened the earth's gravity under the moon.
That explanation is ok, but in making it you're already presupposing that the Moon exerts a force on the ocean, which proves the point that the Moon attracts the Earth.
Oooh... wait a minute. Are you saying that the moon (a large mass) only attracts the oceans (a smaller mass), but not the entire Earth (which is larger than the moon)?
Are you saying that masses somehow "know" which one is bigger, and the bigger one then dominates? If so, think about this:
Suppose I have two 1-kilogram masses in space, side by side. Then, I add 1 gram to mass number 1. Mass number 1 is then bigger than mass 2, so by your argument, mass 2 is attracted by mass 1's gravity, but mass 1 doesn't attract mass 2 at all. On the other hand, if I added the 1 gram to mass 2 instead, the opposite would happen. Is that what you're claiming? In other words, what determines the entire attraction is not the 1000 grams of mass in each object we started with, but really the 1 gram that is added at the end? Does that not seem a little strange to you?
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I should say that there are very good theoretical reasons why a small mass must attract a large mass.
First and foremost we have Newton's third law: for every action, there is an equal and opposite reaction. This says, in effect, that
all forces involve an
interaction between two objects. When object A exerts a force on object B, object B always exerts a force of equal magnitude but in the opposite direction on object A.
If this was not true, laws of physics such as the conservation of momentum in collisions simply would not hold, and yet thousands of experiments are taking place every day which verify the law of conservation of momentum.
Second, you can look at Newton's law of gravity itself.
$$F = \frac{GMm}{r^2}$$
This law does not make a distinction between M and m. Swap the positions of the two masses and the magnitude of the force is the same.
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There are many astronomical examples where a smaller mass clearly pulls on a larger one. These include binary stars orbiting each other, the "wobbles" of stars due to planets pulling on them (mentioned earlier), even the motion of galaxies in our local group.