Anne-ke wrote on 02-25-2004 08:47 AM:
I can accept that such a force exists and that it has an effect. But in which direction?
An internal force is the 2d equivalent of pressure: pressure at a point exists in all directions at the same value. An internal force in a beam (or an object with two forces along the same axis) exists in both directions and is simply either a tension or compression.
Trick question (demonstration) from a physics lab I had: Two kids are standing on skateboards, holding a rope between them. One is the biggest guy in the class, the other is the smallest girl. They are told to pull toward each other as hard as they can. Who is pulling harder? Answer: tension is tension and they are both pulling with the same force.
Why is direct gravity from the moon not important? I could imagine that when there would be no difference in force between the 2 sides, the moon still exerts a force on the water. Apparently this force is not important (otherwise the sun would have more tidal influence...), but I don't understand why?
The force is important - its what keeps the moon and Earth in orbit around each other. You're seeing that the moon exerts a force on the water, but missing that the moon is also exerting a force on the
earth and those forces are doing exactly the same thing: accelerating the Earth toward the moon.
Perhaps another analogy: freefall. An astronaut doesn't fall toward the side of the space shuttle because the astronaut and the space shuttle are both in freefall and accelerating toward the Earth at the same rate. That's exactly the situation with the water on earth.
Another example: flying in formation in orbit. The water bulges on the near and far sides of the Earth are essentially flying in formation with each other but as a result, the water on one side is
below orbital velocity and the other is
above it.
Picture 3 space ships in orbit around the earth, all right next to each other. Two of them separate from the middle and fly exactly parallel to the center one, but several miles apart, one closer and one further from the earth. What happens? Tracing out a bigger circle, the further one out is now flying
faster to keep up with the leader and flying in a smaller circle, the lower one is flying
slower than the leader to keep in formation. But that's a problem: they are no longer flying at the right orbital speed. The outer one is flying too fast and unless it fires its engines constantly it'll spiral away from the earth. The inner one is flying below orbital speed for its altitude and will spiral into the Earth unless it fires its engines constantly. The force the engines must apply to keep the spaceships in orbit is the tidal force.
Another thing that I do not understand is why poeple use the Law of Newton for gravity with R square, and for tides with R to the power 3? Where does that 3 come from?
Its a mathematical relation resulting from the fact that it isn't just the distance that matters but the
difference in distance. Basically, its two equations combined. The % difference in distance decreases linearly with average distance while the total force decreases as a square function of average distance. Combine a linear and a square function and you get a cubic one.
About the centrifugal force: I thought it is not equal at all point on earth, because Earth is not spinning around its axis, but around the common center of gravity of Earth and moon. Because this point is located in the Earth on the side of the moon, the centrifugal force is bigger on the far side of the earth, then on the near side. Adding the gravitational and the centrifugal forces on both far and near sides, gives en equal force on both sides and thus equilibrium. Is this correct??
The Earth
rotates around its axis and
revolves around the center of gravity (COG) of the earth-moon system. You don't want to mix those up because you can use the rotation of Earth separately to calculate the equatorial bulge of the earth. The tidal bulge is
in addition to the bulge created by rotation.
