Posted: Mar 27, 2017 6:03 am
It's been a while since I posted here but I do recall some discussion that got into the modelling of the Earth-Moon/(Sun) system and the length of the Earth day. The short story was that, if the model was true, then the Earth could not be expanding. Perhaps someone with better search-fu that I could find the posts. I found some of the discussion here.
Eventually the "discussion" degenerated into the expansionist stance that since the three-body problem was not solvable then the entire line of reasoning was spurious because we could not predict (for past or future) the positions and velocities of the Earth and Moon. Unfortunately, at the time, I did not have the knowledge to refute that position.
Now I do.
It is true that the three-body problem does not have an analytical solution. That is, there is no equation or set of equations that can be produced to accurately pinpoint the location of any of the objects at some arbitrary time in the future.
That does not mean that there is no solution!
There is, in fact, a numerical solution to the three-body problem with general solution characteristics as below:
By using arbitrarily small time units, the forces are constant across the time unit and the above solution steps produce a time-step simulation of the three-body problem that can generate a solution.
Thus, we have the debunking:
Eventually the "discussion" degenerated into the expansionist stance that since the three-body problem was not solvable then the entire line of reasoning was spurious because we could not predict (for past or future) the positions and velocities of the Earth and Moon. Unfortunately, at the time, I did not have the knowledge to refute that position.
Now I do.
It is true that the three-body problem does not have an analytical solution. That is, there is no equation or set of equations that can be produced to accurately pinpoint the location of any of the objects at some arbitrary time in the future.
That does not mean that there is no solution!
There is, in fact, a numerical solution to the three-body problem with general solution characteristics as below:
- Use the position of the objects to calculate the forces on all three objects.
With the net forces, find the new momentum of each object at the end of the time interval.
Using the momentum, find the new position of the object at the end of the time interval.
Update the time and repeat the process until you have reached the desired time period.
By using arbitrarily small time units, the forces are constant across the time unit and the above solution steps produce a time-step simulation of the three-body problem that can generate a solution.
Thus, we have the debunking:
- The Earth was rotating faster at some point in the past ie. the day was shorter
The Moon was closer to Earth in the past but has receded and slowed the Earth's rotation
Expansion models assume Earth's rotation is a constant speed
The assumption is false, the expansion model is false