the Interceptor
Premium
- 4,191
- BEL / GER
- theInterceptor77
Dear GTP members,
I am facing an interesting problem which I was not able to solve yet. Since I know there are some very bright heads here, I am certain you can help me.
This is the problem: there is a contradiction in the following logical chain. I am trying to find that contradiction, and why it is there.
Okay, imagine the planet Earth. We know that the earth has the shape of a sphere. Yet, if you look into the physics behind our home planet some more, you will discover that it actually isn't a perfectly shaped sphere. In reality, Earth is a socalled oblate spheroid. The reason is the rotation, which leads to centrifugal forces pushing the area around the equator outwards.
Regarding the gravity on earth, its intensity is directly dependent on the distance to the center of the Earth. You know this from spaceflight: the further you get away from the Earth's center, the lighter your body becomes, because the Earth's mass loses hold of you. That said, it is a known and understandable fact that the gravity at the equator is slightly lower than at the poles, because due to the shape of the Earth, you are closer to the center and thus experiencing a more intense gravity at the poles. Others say you are lighter at the equator because of the centrifugal force. Whichever way it is, gravity is slightly lower here. Following me so far? Good! 👍
Now, let's talk about the sea. The water on Earth of course also follows gravity. Where there's more gravity, there will be more water. Only few people know (nevertheless it is a fact) that the mean sea level actually isn't perfectly level due to local gravity differences. The water doesn't level out, because it follows gravity. When there's more gravity at the poles compared to the equator, the water will naturally flow away from the equator.
Now, we take a different look at the water level. As long as you stay close to the Earth's surface, there is a simple equation for potential energy:
(potential) E(nergy) = m(ass) * g(ravity) * h(eight)
Put simply, this says that given a constant mass (note the difference between mass and weight. The mass of a body is constant, its weight depends on the gravity), the potential energy solely depends on the local gravity and the height the mass sits at. To visualize that, let's think of a bungee jumper that jumps from a platform that's 30 meters above ground. That jumper will have a different amount of potential energy at the north pole compared to the equator. To reach the same amount of potential energy, he would have to use a higher platform when at the equator, because the local gravity is lower. Still with me?
Now, back to the water. As we know, water tries to engange the lowest possible state of potential energy. That's why it always levels out. Water never has a gradient, because the water higher up would then have more potential energy. Thus, the water higher up will flow towards the water which is lower down until the surface is level. This, local influences aside, does also apply to the seas. Thus, one can say that all seas combined will engage the height of a specific equipotential surface, which is an imaginary level that states that the potential energy on this level is the same at every single place.
However ... coming back to the above equation, you end up with the antagonism I stumbled over. Gravity on Earth says that the water level should be higher at the poles compared to the equator regions. The equation however says that a lower gravity is followed by a larger height to ensure the same amount of potential energy. That means that water levels should be higher where gravity is lower. This contradicts the above statement, and only one of them can be correct. I'm sure there's a major fault in my thinking, but as you probably have noticed, this matter is quite complex.
Can you spot the error?
I am facing an interesting problem which I was not able to solve yet. Since I know there are some very bright heads here, I am certain you can help me.
This is the problem: there is a contradiction in the following logical chain. I am trying to find that contradiction, and why it is there.
Okay, imagine the planet Earth. We know that the earth has the shape of a sphere. Yet, if you look into the physics behind our home planet some more, you will discover that it actually isn't a perfectly shaped sphere. In reality, Earth is a socalled oblate spheroid. The reason is the rotation, which leads to centrifugal forces pushing the area around the equator outwards.
Regarding the gravity on earth, its intensity is directly dependent on the distance to the center of the Earth. You know this from spaceflight: the further you get away from the Earth's center, the lighter your body becomes, because the Earth's mass loses hold of you. That said, it is a known and understandable fact that the gravity at the equator is slightly lower than at the poles, because due to the shape of the Earth, you are closer to the center and thus experiencing a more intense gravity at the poles. Others say you are lighter at the equator because of the centrifugal force. Whichever way it is, gravity is slightly lower here. Following me so far? Good! 👍
Now, let's talk about the sea. The water on Earth of course also follows gravity. Where there's more gravity, there will be more water. Only few people know (nevertheless it is a fact) that the mean sea level actually isn't perfectly level due to local gravity differences. The water doesn't level out, because it follows gravity. When there's more gravity at the poles compared to the equator, the water will naturally flow away from the equator.
Now, we take a different look at the water level. As long as you stay close to the Earth's surface, there is a simple equation for potential energy:
(potential) E(nergy) = m(ass) * g(ravity) * h(eight)
Put simply, this says that given a constant mass (note the difference between mass and weight. The mass of a body is constant, its weight depends on the gravity), the potential energy solely depends on the local gravity and the height the mass sits at. To visualize that, let's think of a bungee jumper that jumps from a platform that's 30 meters above ground. That jumper will have a different amount of potential energy at the north pole compared to the equator. To reach the same amount of potential energy, he would have to use a higher platform when at the equator, because the local gravity is lower. Still with me?
Now, back to the water. As we know, water tries to engange the lowest possible state of potential energy. That's why it always levels out. Water never has a gradient, because the water higher up would then have more potential energy. Thus, the water higher up will flow towards the water which is lower down until the surface is level. This, local influences aside, does also apply to the seas. Thus, one can say that all seas combined will engage the height of a specific equipotential surface, which is an imaginary level that states that the potential energy on this level is the same at every single place.
However ... coming back to the above equation, you end up with the antagonism I stumbled over. Gravity on Earth says that the water level should be higher at the poles compared to the equator regions. The equation however says that a lower gravity is followed by a larger height to ensure the same amount of potential energy. That means that water levels should be higher where gravity is lower. This contradicts the above statement, and only one of them can be correct. I'm sure there's a major fault in my thinking, but as you probably have noticed, this matter is quite complex.
Can you spot the error?
Last edited: