is there really a 26000 year period for the precession of the

My question may seem like a newbie's question, but I am now very confused.
I do not understand why the period of the precession is given to be around
26000 years. Consider this:

The annual precession was given by Bessel to be
50".2235 + t*0.0002443610 where t is the number of years since 1800
(Connaissance des temps for 1831)

I know that current formulas are a bit different, but this is just to set
the context, and the conclusion will be the same.

The previous formula gives a precession period of about 25800 years,
when only the constant term is taken into account. But take
the second term into account, and you find a precession period of about
24360 years.

Here, I have of course assumed that the formula stays valid for that
period, and I have also ignored quadratic terms.

Assuming the formula given above is still valid, after 24360 years
another shorter period will start, and so on.

But the problem is there.
Why does everybody keep writing of a 26000 years period, when there
doesn't seem to be such a thing?

Thanks.

Denis Roegel

Denis Roegel wrote:

My question may seem like a newbie's question, but I am now very confused.
I do not understand why the period of the precession is given to be around
26000 years. Consider this:

The annual precession was given by Bessel to be
50".2235 + t*0.0002443610 where t is the number of years since 1800
(Connaissance des temps for 1831)

I know that current formulas are a bit different, but this is just to set
the context, and the conclusion will be the same.

The previous formula gives a precession period of about 25800 years,
when only the constant term is taken into account. But take
the second term into account, and you find a precession period of about
24360 years.

Here, I have of course assumed that the formula stays valid for that
period, and I have also ignored quadratic terms.

Assuming the formula given above is still valid, after 24360 years
another shorter period will start, and so on.

But the problem is there.
Why does everybody keep writing of a 26000 years period, when there
doesn't seem to be such a thing?

There are more things at work here than may be immediately apparent.

1) The standard formulas for precession (Lieske et al. 1977, Astron
Astrophys 58, 1) are cubic polynomials in time. These are
approximations,
and strictly speaking they are valid only for the interval 1600-2100;
anything outside that interval is extrapolation.

2) The rate of lunisolar precession is directly proportional to the
sine of the obliquity. The orientation of the ecliptic changes due to
perturbations from the other planets, and one component of that change
will cause the obliquity to change. At present the obliquity is slowly
decreasing.

3) Because of 2), the period for a precessional cycle is not constant.
There is indeed no such thing as a unique period for precession. One
can, however, determine an average period over some time span. I did a
million-year numerical integration as part of my Ph.D. dissertation, and
I found an average period of 25,700 years.

So if the average period really is around 25,700 or 25,800 years, and
if this number can vary by a few hundred years, then I believe it's
reasonable for most textbook authors to give only two significant
digits.

-- Bill Owen,

Denis Roegel wrote:

My question may seem like a newbie's question, but I am now very confused.
I do not understand why the period of the precession is given to be around
26000 years. Consider this:

The annual precession was given by Bessel to be
50".2235 + t*0.0002443610 where t is the number of years since 1800
(Connaissance des temps for 1831)

I know that current formulas are a bit different, but this is just to set
the context, and the conclusion will be the same.

The previous formula gives a precession period of about 25800 years,
when only the constant term is taken into account. But take
the second term into account, and you find a precession period of about
24360 years.

Here, I have of course assumed that the formula stays valid for that
period, and I have also ignored quadratic terms.

Assuming the formula given above is still valid, after 24360 years
another shorter period will start, and so on.

But the problem is there.
Why does everybody keep writing of a 26000 years period, when there
doesn't seem to be such a thing?

There are more things at work here than may be immediately apparent.

1) The standard formulas for precession (Lieske et al. 1977, Astron
Astrophys 58, 1) are cubic polynomials in time. These are
approximations,
and strictly speaking they are valid only for the interval 1600-2100;
anything outside that interval is extrapolation.

2) The rate of lunisolar precession is directly proportional to the
sine of the obliquity. The orientation of the ecliptic changes due to
perturbations from the other planets, and one component of that change
will cause the obliquity to change. At present the obliquity is slowly
decreasing.

3) Because of 2), the period for a precessional cycle is not constant.
There is indeed no such thing as a unique period for precession. One
can, however, determine an average period over some time span. I did a
million-year numerical integration as part of my Ph.D. dissertation, and
I found an average period of 25,700 years.

So if the average period really is around 25,700 or 25,800 years, and
if this number can vary by a few hundred years, then I believe it's
reasonable for most textbook authors to give only two significant
digits.

-- Bill Owen,