Undergrad Help with formula to calculate the precession rate change

[phi]

First time caller, I'm a newb so go easy on me.

So I was trying to work through a calculation to figure out the precession rate variation in terms of the Precession of the Equinox.

I came across the following formula from (https://endgametime.wordpress.com/understanding-precession-of-the-equinox/)

I quote:

If we are moving away from apoapsis as proposed, our orbital velocity should be increasing – we are speeding up with respect to the binary center of mass – which means that the period of revolution perceived over astronomically short periods of time is decreasing; this in turn requires the constant of precession to increase as time goes by. Currently the yearly change is about 0.000349”/y, but that will continue to increase for a few more years, until the Sun reaches periapsis. In terms of the calculated period of revolution, that corresponds to a yearly decrease of .178 years, ignoring the short cyclic influences of nutation, etc. This roughly corresponds with the changes in precession calculations that have been reported in the literature.

Therefore, we make the following estimates for the years 2011:

Year Precession

Period of Revolution (years)

2010 50.24”/y

25,792.035

2100 50.325866”/y

25792.164

In 1900, Simon Newcomb offered a formula for precession: 50.2564” + 0.000222 * (year – 1900) (U.S. Naval Observatory 1900)

We offer the following alternative formula based on the proposed binary system model: 50.245223” – 0.000349 * (2012- year)

Observed precession has changed by 0.0337 from 1900 to 2000, for a yearly change of 0.000337” . This precession delta is approximately ten times closer to our proposed annual precession of 0.000349” than Newcomb’s annual precession adjustment of 0.000222”.

Minimum precession is about 1 degree every 84 years when the Sun is at apoapsis, and the maximum precession is about one degree every 71.665 years when the Sun is near periapsis. The Earth will average about one degree of precession per 77.83 years over the 24,000 year cycle.​

I tried using their formula to calculate the precession rate at year 2100
as above (50.245223” – 0.000349 * (2012- year))

So I used:

50.245223 - .000349 * (2012 - 2100)

50.245223 - .000349 * -88

50.245223 - -0.030712

I get = 50.275935

Their answer above though is: 50.325866”/y

I cannot for the life of me figure out what I am doing wrong. Any help would be greatly appreciated, starting to lose my mind :-)

Thanks!
Φ

 

[haruspex]

First time caller, I'm a newb so go easy on me.

So I was trying to work through a calculation to figure out the precession rate variation in terms of the Precession of the Equinox.

I came across the following formula from (https://endgametime.wordpress.com/understanding-precession-of-the-equinox/)

I quote:

If we are moving away from apoapsis as proposed, our orbital velocity should be increasing – we are speeding up with respect to the binary center of mass – which means that the period of revolution perceived over astronomically short periods of time is decreasing; this in turn requires the constant of precession to increase as time goes by. Currently the yearly change is about 0.000349”/y, but that will continue to increase for a few more years, until the Sun reaches periapsis. In terms of the calculated period of revolution, that corresponds to a yearly decrease of .178 years, ignoring the short cyclic influences of nutation, etc. This roughly corresponds with the changes in precession calculations that have been reported in the literature.

Therefore, we make the following estimates for the years 2011:

Year Precession

Period of Revolution (years)

2010 50.24”/y

25,792.035

2100 50.325866”/y

25792.164

In 1900, Simon Newcomb offered a formula for precession: 50.2564” + 0.000222 * (year – 1900) (U.S. Naval Observatory 1900)

We offer the following alternative formula based on the proposed binary system model: 50.245223” – 0.000349 * (2012- year)

Observed precession has changed by 0.0337 from 1900 to 2000, for a yearly change of 0.000337” . This precession delta is approximately ten times closer to our proposed annual precession of 0.000349” than Newcomb’s annual precession adjustment of 0.000222”.

Minimum precession is about 1 degree every 84 years when the Sun is at apoapsis, and the maximum precession is about one degree every 71.665 years when the Sun is near periapsis. The Earth will average about one degree of precession per 77.83 years over the 24,000 year cycle.​

I tried using their formula to calculate the precession rate at year 2100
as above (50.245223” – 0.000349 * (2012- year))

So I used:

50.245223 - .000349 * (2012 - 2100)

50.245223 - .000349 * -88

50.245223 - -0.030712

I get = 50.275935

Their answer above though is: 50.325866”/y

I cannot for the life of me figure out what I am doing wrong. Any help would be greatly appreciated, starting to lose my mind :-)

Thanks!
Φ

If you use their formula to calculate the value for 1900 it comes out too low. I suspect a typo: their formula should be 50.29522...

 

[phi]

Awesome that would explain it! Thanks so much for the reply!