The seasons and angular momentum

In the FAQ, the seasons on a flat earth are described as being caused by a variation in the radius of the sun's motion. This, however, would violate conservation of angular momentum. The angular momentum of the sun would be:

L = I w = mr^2 w, where m is the mass of the sun, r is the radius of rotation and w is the angular velocity.

The angular velocity remains the same, as the length of each day remains at 24 hours. Hence, as r decreases, the angular momentum would decrease.

So, my question is, how do you reconcile this model of the seasons with conservation of angular momentum?

While you are heading in the right direction, such an application of angular momentum doesn't necessarily disprove a flat Earth.

An FEer might make a similar argument about how the radius of the Earth's orbit increases and decreases without violating conservation laws. Bear in mind that angular momentum is the cross product of the radial vector (r) and the linear momentum (mv). From a RE perspective, the solution to such a problem is to have the velocity of the Earth increase as it gets closer to the sun and decrease as it gets further away. On a FE the the sun's velocity would change in a similar fashion.

You may very well say that the velocity of the Earth/sun is constant because the time is takes to move across the sky is constant. However, this is not true. If you were to record the length of time between sunrise and sunset, you would actually find that this value increases and decreases predictably throughout the year.

In short, in both a RE and FE world angular momentum is conserved.

An FEer might make a similar argument about how the radius of the Earth's orbit increases and decreases without violating conservation laws. Bear in mind that angular momentum is the cross product of the radial vector (r) and the linear momentum (mv). From a RE perspective, the solution to such a problem is to have the velocity of the Earth increase as it gets closer to the sun and decrease as it gets further away. On a FE the the sun's velocity would change in a similar fashion.

Except that, in the FE model proposed, the sun's linear velocity must decrease as the radius decreases (Because it is taking the same amount of time, a day, to travel a shorter distance - the circumference shrinks), rather than increasing. This would lead to a change in the angular momentum.

You may very well say that the velocity of the Earth/sun is constant because the time is takes to move across the sky is constant. However, this is not true. If you were to record the length of time between sunrise and sunset, you would actually find that this value increases and decreases predictably throughout the year.

This is true, and explained by both the RE and FE models. However, the change in time between sunrise and sunset is due to a change in the distance travelled by the sun (due to a change in the position of the sun in FE, and the tilt of the earth in RE), and not a change in its velocity, isn't it?

I agree that this doesn't disprove a flat earth, but it does show that this model of the seasons is flawed.

Quote from: jraffield1 on October 08, 2011, 07:23:57 PM

An FEer might make a similar argument about how the radius of the Earth's orbit increases and decreases without violating conservation laws. Bear in mind that angular momentum is the cross product of the radial vector (r) and the linear momentum (mv). From a RE perspective, the solution to such a problem is to have the velocity of the Earth increase as it gets closer to the sun and decrease as it gets further away. On a FE the the sun's velocity would change in a similar fashion.

Except that, in the FE model proposed, the sun's linear velocity must decrease as the radius decreases (Because it is taking the same amount of time, a day, to travel a shorter distance - the circumference shrinks), rather than increasing. This would lead to a change in the angular momentum.

Quote from: jraffield1 on October 08, 2011, 07:23:57 PM

You may very well say that the velocity of the Earth/sun is constant because the time is takes to move across the sky is constant. However, this is not true. If you were to record the length of time between sunrise and sunset, you would actually find that this value increases and decreases predictably throughout the year.

This is true, and explained by both the RE and FE models. However, the change in time between sunrise and sunset is due to a change in the distance travelled by the sun (due to a change in the position of the sun in FE, and the tilt of the earth in RE), and not a change in its velocity, isn't it?

I agree that this doesn't disprove a flat earth, but it does show that this model of the seasons is flawed.

True, angular momentum is conserved if the sun moves over and under the Earth and its orbit is distorted to create differences in its radius and velocity, but itis not conserved if the sun moves in a circle above the Earth. I see what you're saying now, for some reason I had it in my head that the first case was what was being argued. As FEers cannot use this explanation, then angular momentum must not be conserved.

If FEers say that angular momentum is not conserved, then a few very big questions are raised. For example, if one uses the Lagrangian formulation of angular momentum, then that means the rotational symmetry of space is broken and that an object rotated in space would behave differently.

As this has never been observed, we must conclude that rotational symmetry exists for space, conservation of angular momentum exists, and that on a flat Earth the sun cannot move in the same way it appears to on a round Earth.

While you are heading in the right direction, such an application of angular momentum doesn't necessarily disprove a flat Earth.

An FEer might make a similar argument about how the radius of the Earth's orbit increases and decreases without violating conservation laws. Bear in mind that angular momentum is the cross product of the radial vector (r) and the linear momentum (mv). From a RE perspective, the solution to such a problem is to have the velocity of the Earth increase as it gets closer to the sun and decrease as it gets further away. On a FE the the sun's velocity would change in a similar fashion.

You may very well say that the velocity of the Earth/sun is constant because the time is takes to move across the sky is constant. However, this is not true. If you were to record the length of time between sunrise and sunset, you would actually find that this value increases and decreases predictably throughout the year.

In short, in both a RE and FE world angular momentum is conserved.

The length of time between sunrise and sunset may change, but the length of time between one sunrise and another remains the same. You are ignoring the velocity of the sun while it cannot be seen. One pass of the sun always takes the same time, and if - as FET claims - it is sometimes following a path of larger radius, then it is violating the angular momentum laws.