Exploring the Saros Cycle: Predicting Eclipses Through Time

[lewis198]

Hey guys.
I was wondering, does the period of the Saros cycle stay the same across all time? for example, using the saros cycle could you accurately predict eclipse times thousands of years into the past or future?

 

[mgb_phys]

Depends how accurately you mean "stay the same". The rotation rate of the Earth (ie length of a day) is the most variable since every volcanc erruption, tidal wave or earthquake has an effect. It is also slowing at a predicatable rate due to tidal braking from the moon. The Earth's orbit is also changing reasonably predictably.

When looking at ancient eclipses we can predict when and where they occurred but the "where" often differs from historical records. This is the best way of studying historical changes in the Earht's rotation rate.

 

[lewis198]

OK, so the decreasing mass of the Earth affects the location of the eclipse.
So the when would essentially be the same? If the error is residual, what kind of order are we looking at? the Saros Cycle period is approximately 6585⅓ days. If there is any error, is it <<6585.5 days? And would it be unsolvable because of the n-body problem? Is it negligible?

 

[mgb_phys]

When the eclipse happens depends on the position of the Earth and moon in orbit. Although technically chaotic because they depend on every othe piece of mass in the solar system these are relatively stable over long periods. Over very long periods the length of the cycle will increase because the moon is dirifting away from earth, this will also eventually stop total eclipses since the moon will be too small to cover the sun.

The 'where' depends on the length of the day which changes much more quickly, both in a predictable manner due to tidal friction from the moon lengthening the day and from random events.
The day is predicted to increase by about 2.5 ms/century from the effect of the moon but historical eclipses allow us to calculate it at about 1.7 ms/centrury. The missing 0.8 ms/century comes from changes in the earth.

The mass of the Earth doesn't matter (and is in fact actually increasing as comets land on us) it is the distribution of mass. Like a spinning ice skater if mass moves out toward the surface the rotation slows down - this provides the main random unknown. The biggest cause is probably the crust rebounding after the weight of ice removed at the end of the last ice age!

 

[Chronos]

An admittedly technical point, but the Earth's mass does not decrease over time - as noted by mgb. I also doubt the mass of ice on the surface of earth, melting or otherwise, is sufficient to influence plate tectonics.

 

[mgb_phys]

I also doubt the mass of ice on the surface of earth, melting or otherwise, is sufficient to influence plate tectonics.

"Post-glacial rebound" as it's called does have quite a large effect for northern europe. In the UK, Scotland has been rising since the weight of the ice was removed and London is sinking. This movement is at around the rate the sea level is rising - but unfortunately in the opposite direction.

This effect is large enough to have to be corrected for in Long Baseline interferometry between radio telescopes in Cambridge and other countries.
In addition the change in the length of the day and the barycentre of the Earth is continually monitored and corrections published. Although because these numbers are needed to accurately throw ICBMs around, the results are only published later when no-longer current.
After major seismic events a correction has to be hurridly calculated and published.