Could it be that the axis deviated from its normal cycle, may be a few minutes or a degree off? May be as we are moving away from the center of the galaxy we experience lesser gravitational pull, and thus the change in motion? It would then be another factor in global warming, as well as the man made one.
One of the main thing astronomers do is measure angles with greater and greater precision. A degree of arch is 0.0027777 of a full circle. A minute of arc is one sixtieth of a degree, or 0.0000462 of a full circle. Astronomers routinely measure angle sin arc seconds, or 0.0000007 of a full circle, and tenths of arc seconds, 0.00000007 of a full circle, and hundredths of an arc second, etc. So if the axis of the Earth points a single degree of arc, or even a single arc minute, off its calculated position that would be discovered very quickly.
The strength of the gravitational force of the center of the galaxy would diminish with with the square of the distance. Since the combined masses of Earth and the center of the galaxy, and the gravitational constant all remain the same, the only thing that varies with the distance of Earth from the center of the galaxy is the square of the distance between Earth and the center of the galaxy. To get the present gravitational attraction equal to 1, set the masses to 1 and the distance to the center of the galaxy as 1. One divided by one squared is one divided by one, or one.
Suppose you increase the distance between Earth and the center of the galaxy by one percent. Then the distance is 1.01, and the distance squared is 1.0201. 1 divided by 1.0201 is 0.980296, so the force of the gravity of the center of the galaxy would diminish by only 0.019704 of its previous strength.
The center of the milky Way Galaxy is about 26,500 light years from Earth. Thus our solar system would have to travel about 265 light years farther out to get about 1 percent farther from the center of the galaxy. I wonder how many thousands of years it would take for our solar system to travel even a single light year (and not necessarily in the right direction for your question). Since the Sun takes about 225,000,000 to 250,000,000 years to travel a distance of about 166,504.27 light years around the galaxy, the solar system should take about 1,351.316 years to travel a single light year around the center of the galaxy - and many times that long to change its distance from the galactic center by 1 light year.
The Solar System is traveling at an average speed of 230 km/s (828,000 km/h) or 143 mi/s (514,000 mph) within its trajectory around the galactic center, a speed at which an object could circumnavigate the Earth's equator in 2 minutes and 54 seconds; that speed corresponds to approximately 1/1300 of the speed of light.
At a speed of 828,000 kilometers per hour, the Sun would orbit a distance of 19,872,000 kilometers per day, or 7,258,248,000 kilometers per year. A light year is defined as 9460730472580800 metres (exactly) , or 9,460,730,472,580.8 kilometers.
Light-year - Wikipedia
So it should take the Sun about 1,303.445 years to orbit 1 light year around the center of the galaxy - and many times that long to change its distance from the galactic center by 1 light year.
As the Earth and Jupiter orbit around the Sun in different orbits, the angles between the Sun, Earth, and Jupiter constantly change, as does the distance between Earth and Jupiter. An Astronomical Unit or AU is the average distance between Earth and the Sun, now defined as exactly 149,597,870.7 kilometers. Astronomical unit - Wikipedia
When Jupiter is closest to the Sun it is 4.9501 AU from the Sun, and when Jupiter is farthest from the Sun it is 5.4588 AU from the Sun. Jupiter - Wikipedia So the distance between Earth and Jupiter can vary between about 3.9501 AU to about 6.4588 AU, a significant difference. But assume that the distance between Earth and Jupiter is always 6.4588 AU, to make Jupiter's gravitational influence on Earth its minimum. So if the gravity of Jupiter and a distance of 6.4588 AU are both set at 1, the gravitational force o f Jupiter on Earth will be 1.
A light year is 9,460,730,472,580.8 kilometers, which is also 63241.077 astronomical units , so a light year is 9,791.4592 times a distance of 6.4588 AU. And the center of the Milky Way galaxy is about 26,490 light years from Earth, or about 259,375,754.2 times as distant as Jupiter. And 259,375,754.2 squared is 6.7275781 x 10 to the 16th power, or roughly 67,275,000,000,000,000. So at the distance of the galactic center it would have to have roughly 67,275,000,000,000,000 times the mass of Jupiter to have the same gravitational attraction on Earth as Jupiter.
Milky Way - Wikipedia
The mass of Jupiter is 1/1047 the mass of the Sun. Jupiter - Wikipedia
So the Milky way has approximately 1,047 times 1,500,000,000,000, or 1,570,500,000,000,000 times, the mass of Jupiter. So according to my rough calculations, Jupiter should have approximately 42,836,67 times the gravitational attraction on Earth as the Milky Way galaxy has. And that is when Jupiter is at its maximum possible distance and its gravitational force on Earth is at its weakest. furthermore, a lot of the mass of the galaxy is dark matter in the halo, beyond the orbit of Earth and he Solar System, so I am not certain that it is accurate to count all of that mass to be mathematically concentrated at the galactic center for the purpose of these calculations.
Thus the Sun, the Moon, and the planets in the solar system should all have much stronger gravitational forces on Earth than the galactic center has. Furthermore the directions and distances to those solar system objects are constantly changing as the planets orbit around the Sun, so the net gravitational force on the Earth from solar system objects is constantly changing significantly, while the gravitational force of the galactic center on Earth remains almost exactly the same in strength and direction for thousands and millions of years.
It would be interesting to find out which astronomical bodies astronomers use in calculating the future precession of the axis of the Earth.