On this page we'll very specifically focus on subject of earth rotation axis (in other words "axial tilt" or "obliquity of the ecliptic"). Because that's a very important indication the book puts forward. It is something which can be scientifically and precisely measured. So we have to search and verify validity of this claim. If we can't validate; it might refute the whole message as well.
Bottom line first : I don't have yet a concrete conclusion (either proving or refuting it). It's currently work in progress. Coming to a clear conclusion can take time.
For the record; I'm also not an astronomer. Just an engineer with curiosity.
Definition :
1) Axial tilt (ε) is the angle between : either Earth's rotational axis (polar axis) and its orbital axis,
Bottom line first : I don't have yet a concrete conclusion (either proving or refuting it). It's currently work in progress. Coming to a clear conclusion can take time.
For the record; I'm also not an astronomer. Just an engineer with curiosity.
Definition :
1) Axial tilt (ε) is the angle between : either Earth's rotational axis (polar axis) and its orbital axis,
The important differentiation is; our subject is the geographical pole (not the magnetic pole).
Earth's magnetic field is a dynamo action resulting from the movement of molten iron in our planet’s core.
This mechanism is a delicate two-way street. In that; physical fluctuations in Earth’s core directly changes both level of magnetic field and locations of the magnetic poles. But magnetic effects coming from outside of the Earth also effect the very same mechanism. So magnetic poles are constantly in motion.
But the book is claiming a shift in geographical poles (i.e. rotation axis). There is only one reason which can shift the rotation axis of a planet; another large enough object passing by. Should the passing by object be in close proximity; then gravitational force would first act on Earth's orbit (which the book doesn't refer at all). But if the object is further distant to solar system (without causing gravitational effect); it's magnetic effect would act on Earth's (and all other solar system members') axial tilt.
Physically getting our hands on to polar axis is not quite possible. If we travel to north or south pole; unfortunately we don't find a tangible pole sticking out of ice. Also the trajectory of polar axis doesn't really point to a meaningful reference point for our axial tilt measurement purposes.
2) or equivalently; _Axial tilt (ε) is the angle between between Earth's equatorial plane and orbital plane.
Same difficulty here; how do we tangibly put our hands of ecliptic plane or equatorial plane? Both Earth itself has an irregular shape and it's orbit around the sun is a crumpled plane.
Earth's magnetic field is a dynamo action resulting from the movement of molten iron in our planet’s core.
This mechanism is a delicate two-way street. In that; physical fluctuations in Earth’s core directly changes both level of magnetic field and locations of the magnetic poles. But magnetic effects coming from outside of the Earth also effect the very same mechanism. So magnetic poles are constantly in motion.
But the book is claiming a shift in geographical poles (i.e. rotation axis). There is only one reason which can shift the rotation axis of a planet; another large enough object passing by. Should the passing by object be in close proximity; then gravitational force would first act on Earth's orbit (which the book doesn't refer at all). But if the object is further distant to solar system (without causing gravitational effect); it's magnetic effect would act on Earth's (and all other solar system members') axial tilt.
Physically getting our hands on to polar axis is not quite possible. If we travel to north or south pole; unfortunately we don't find a tangible pole sticking out of ice. Also the trajectory of polar axis doesn't really point to a meaningful reference point for our axial tilt measurement purposes.
2) or equivalently; _Axial tilt (ε) is the angle between between Earth's equatorial plane and orbital plane.
Same difficulty here; how do we tangibly put our hands of ecliptic plane or equatorial plane? Both Earth itself has an irregular shape and it's orbit around the sun is a crumpled plane.
So we defined axial tilt being an angle. Now we should also define how do we quantify an angle?
1) We either measure it (geometrically) : if the angle is on piece of paper, we put a protractor on and simply
measure it. That seems like not an easy task when it comes to measuring Earth's axial tilt; as we have nothing tangible at hand.
2) We calculate it (trigonometricaly) : specially if we can fit a right triangle and measure distance between corners
of it; ratio of these lengths will give us the angle. That's also problematic for finding Earth's axial tilt; as we can't measure distances.
3) We solve it mathemathically : if two axis or two surfaces can be modelled by an equation; solving that equation would give us the angle between the two. As both Earth's shape and it's rotation / orbit is completely irregular; that method has no use for us.
When I first started searching methods of finding actual axial tilt, I came across equations as these :
1) We either measure it (geometrically) : if the angle is on piece of paper, we put a protractor on and simply
measure it. That seems like not an easy task when it comes to measuring Earth's axial tilt; as we have nothing tangible at hand.
2) We calculate it (trigonometricaly) : specially if we can fit a right triangle and measure distance between corners
of it; ratio of these lengths will give us the angle. That's also problematic for finding Earth's axial tilt; as we can't measure distances.
3) We solve it mathemathically : if two axis or two surfaces can be modelled by an equation; solving that equation would give us the angle between the two. As both Earth's shape and it's rotation / orbit is completely irregular; that method has no use for us.
When I first started searching methods of finding actual axial tilt, I came across equations as these :
It seemed that it was going to be so easy to tackle this. One simply enters date in Julian format and there you have the exact precise axial tilt for that date... But then such sheer sense of ease didn't feel right, as well as the input and output of that equation. How can time input give you an angle output?
This is called a fundamental ephemeris. Axial tilt is found by observation of the motions of the Earth and planets over last few centuries. First numerical value in the equation is basic axial tilt : ε = 23° 27′ 08.26″
Then astronomers try to model successive modules in the equation. Each celestial body (Sun, Moon etc.) in solar system has a rhythmic effect (repeating pattern) on Earth's axial tilt. Astronomers try to convert their observations in to further refining modules on that ephemerides.
J. Laskar computed an expression good to 0″.02 over 1000 years and several arcseconds over 10,000 years:
This is called a fundamental ephemeris. Axial tilt is found by observation of the motions of the Earth and planets over last few centuries. First numerical value in the equation is basic axial tilt : ε = 23° 27′ 08.26″
Then astronomers try to model successive modules in the equation. Each celestial body (Sun, Moon etc.) in solar system has a rhythmic effect (repeating pattern) on Earth's axial tilt. Astronomers try to convert their observations in to further refining modules on that ephemerides.
J. Laskar computed an expression good to 0″.02 over 1000 years and several arcseconds over 10,000 years:
Here is the issue with ephemerides ; they are not actual measurements.
They are mere modelling based on observation for a certain time period. They also presume that the solar neighborhood is a "closed circuit" (i.e. assuming that all celestial objects indefinitely repeat their motion without any change on their orbit). That's obviously fine and valid ... till it's not. If a sizable enough object (planet) changes it's course and approaches our solar system; then such fundamental ephemerides obviously becomes irrelevant.
Agreed; such event doesn't take place every other day (or millenia). That's the point; we are not investigating a regular / repeating pattern. As the book informs us; this is an irregular / controlled event. So we have to reach means of actual axial tilt measurements (and not presumed modelling of it).
ACTUAL MEASUREMENT OF AXIAL TILT :
A very simple (and actually the only possible geometrical) measurement of axial tilt. So simple that; all previous ancient civilizations were aware and be able to use the same method. It was so important; that they erected huge stone monuments for that measurement.
You need to take two measurements on two special days : summer solstice (where the daylight is longest - about June 21st) and winter solstice (where the daylight is shortest - about December 21st). The actual date of solstice is known/calculated precisely. You can do these measurements any where on Earth.
When we hear "longest / shortest daylight", we don't come to grasp of importance of these two magical days right away. We can also repeat the definition of solstice in other words :
On winter solstice; Earth's axial tilt is as far from the sun as possible.
On summer solstice; Earth's axial tilt is as close towards the sun as possible.
Finally and suddenly we have our elusive target at sight : The difference below two simple angle measurements (max and min) will directly reveal the axial tilt itself.
You need to place a stick perpendicular to a flat surface. Obviously precision is of importance. A water level can be used for ensuring both flatness (0 degree) and perpendicularity (90 degree). Length of the stick is "a". On summer and winter solstices as the Sun reaches its highest point in the sky (not necessarily at 12:00pm, mind you, but at its astronomical zenith); you measure length of the shadow "b". You calculate angle of the Sun from tan(θ) = a/b formula.
They are mere modelling based on observation for a certain time period. They also presume that the solar neighborhood is a "closed circuit" (i.e. assuming that all celestial objects indefinitely repeat their motion without any change on their orbit). That's obviously fine and valid ... till it's not. If a sizable enough object (planet) changes it's course and approaches our solar system; then such fundamental ephemerides obviously becomes irrelevant.
Agreed; such event doesn't take place every other day (or millenia). That's the point; we are not investigating a regular / repeating pattern. As the book informs us; this is an irregular / controlled event. So we have to reach means of actual axial tilt measurements (and not presumed modelling of it).
ACTUAL MEASUREMENT OF AXIAL TILT :
A very simple (and actually the only possible geometrical) measurement of axial tilt. So simple that; all previous ancient civilizations were aware and be able to use the same method. It was so important; that they erected huge stone monuments for that measurement.
You need to take two measurements on two special days : summer solstice (where the daylight is longest - about June 21st) and winter solstice (where the daylight is shortest - about December 21st). The actual date of solstice is known/calculated precisely. You can do these measurements any where on Earth.
When we hear "longest / shortest daylight", we don't come to grasp of importance of these two magical days right away. We can also repeat the definition of solstice in other words :
On winter solstice; Earth's axial tilt is as far from the sun as possible.
On summer solstice; Earth's axial tilt is as close towards the sun as possible.
Finally and suddenly we have our elusive target at sight : The difference below two simple angle measurements (max and min) will directly reveal the axial tilt itself.
You need to place a stick perpendicular to a flat surface. Obviously precision is of importance. A water level can be used for ensuring both flatness (0 degree) and perpendicularity (90 degree). Length of the stick is "a". On summer and winter solstices as the Sun reaches its highest point in the sky (not necessarily at 12:00pm, mind you, but at its astronomical zenith); you measure length of the shadow "b". You calculate angle of the Sun from tan(θ) = a/b formula.
You find angle of the Sun (θ) for both winter and summer solstices.
Half of the difference between two angles gives the exact axial tilt :
axial tilt ε = 1/2 (θwinter - θsummer)
Half of the difference between two angles gives the exact axial tilt :
axial tilt ε = 1/2 (θwinter - θsummer)