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## Main Question or Discussion Point

Over the last year or so I've been doing quite a bit of reading trying to find out what is actually causing lunar nodal precession. There seems to be a lot of handwaving but no definitive answer, which I find rather odd.

Maybe I've just not found the right source. Google seems obsessed with returning links to WonkyPedia these days and most articles there, rather than enlighten me, make we want to scream.

Firstly let me try to fend off some of the more erroneous likely answers.

The precession of a significantly sized satellite like the Earth's moon is NOT the same as a very small moon ( satellite in astronomy terms ) and man-made low earth orbit satellites. For the latter. the precession is apparently mainly caused by the Earth's oblateness. So please do not reply saying this is the cause of lunar nodal precession unless you have some solid maths and refs to back it up.

One of the more credible explanations seems to be the torque exerted on the Earth-Moon angular momentum by the sun. Now if that is the case, we have the numbers and should be able to get something very close to 18.61 tropical years. I have only found some rather handwaving and admittedly approximate maths. I suspect this is only part of the story but I'll rather surprised that with the precission of astronomic calculations made these days we don't have a better account of something we have been studying for several millennia !

The corollary question is what is the most accurate assessment we now have for this period? Of course none of this is constant with the number of bodies in the calculation.

The best I have managed to find was fourth order polynomial credited to Chapront and relative to Y2K reference period:

# Lunar nodal cycle comes from (derived by T. Peter from Chapront [2002],

T_1000 = time from J2000.0 [1000 Year]

(6793.476501 + T_1000 * ( 0.0124002 + T_1000 * ( 0.000022325 - T_1000 * 0.00000013985 ) ) ) / 365.25

# thus evaluating this for year 2000 it is a constant :

print pNodal= 6793.476501/365.25

18.5995249856263

This is in sidereal years.

I did at one stage find some maths that produced a sin().cos() type formula for the torque on the E-M couple, though sadly I've lost the source of that information.

AFAICR, this ( counter intuitively ) gives zero torque with the moon at 0 , 90,180, 270 degrees from the line from sun to EM barycentre and max amplitude at the four "45" degree points .

So, if I am recalling this correctly there will be a cyclic change in the torque exerted on the E-M couple with a period half that of the nodal precession period.

ie there will be cyclically varying acceleration / deceleration with a period of circa 9.3 years.

The time series (3rd order) for Lunar apse cycle comes from (Chapront [2002], page 704)

(3232.60542496 + T_1000 * ( 0.0168939 + T_1000 * ( 0.000029833 - T_1000 * 0.00000018809 ) )) / 365.25

## evaluate at y2k:

=3232.60542496/ 365.25

=8.85039130721424

Since this is from the same source, I assume that this is also sidereal years.

Can anyone see any faults in this or add to this level of understanding?

Thanks.

Maybe I've just not found the right source. Google seems obsessed with returning links to WonkyPedia these days and most articles there, rather than enlighten me, make we want to scream.

Firstly let me try to fend off some of the more erroneous likely answers.

The precession of a significantly sized satellite like the Earth's moon is NOT the same as a very small moon ( satellite in astronomy terms ) and man-made low earth orbit satellites. For the latter. the precession is apparently mainly caused by the Earth's oblateness. So please do not reply saying this is the cause of lunar nodal precession unless you have some solid maths and refs to back it up.

One of the more credible explanations seems to be the torque exerted on the Earth-Moon angular momentum by the sun. Now if that is the case, we have the numbers and should be able to get something very close to 18.61 tropical years. I have only found some rather handwaving and admittedly approximate maths. I suspect this is only part of the story but I'll rather surprised that with the precission of astronomic calculations made these days we don't have a better account of something we have been studying for several millennia !

The corollary question is what is the most accurate assessment we now have for this period? Of course none of this is constant with the number of bodies in the calculation.

The best I have managed to find was fourth order polynomial credited to Chapront and relative to Y2K reference period:

# Lunar nodal cycle comes from (derived by T. Peter from Chapront [2002],

T_1000 = time from J2000.0 [1000 Year]

(6793.476501 + T_1000 * ( 0.0124002 + T_1000 * ( 0.000022325 - T_1000 * 0.00000013985 ) ) ) / 365.25

# thus evaluating this for year 2000 it is a constant :

print pNodal= 6793.476501/365.25

18.5995249856263

This is in sidereal years.

I did at one stage find some maths that produced a sin().cos() type formula for the torque on the E-M couple, though sadly I've lost the source of that information.

AFAICR, this ( counter intuitively ) gives zero torque with the moon at 0 , 90,180, 270 degrees from the line from sun to EM barycentre and max amplitude at the four "45" degree points .

So, if I am recalling this correctly there will be a cyclic change in the torque exerted on the E-M couple with a period half that of the nodal precession period.

ie there will be cyclically varying acceleration / deceleration with a period of circa 9.3 years.

The time series (3rd order) for Lunar apse cycle comes from (Chapront [2002], page 704)

(3232.60542496 + T_1000 * ( 0.0168939 + T_1000 * ( 0.000029833 - T_1000 * 0.00000018809 ) )) / 365.25

## evaluate at y2k:

=3232.60542496/ 365.25

=8.85039130721424

Since this is from the same source, I assume that this is also sidereal years.

Can anyone see any faults in this or add to this level of understanding?

Thanks.