Otherwise said, the axis of rotation of earth is at 66.5° to the 2-dimensional orbital plane (or the plane that the earth’s orbit forms as shown in Figure 01). This tilt, as is in common knowledge, varies oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle; the earth's mean obliquity is currently 23°26′13.2″ (or 23.437°). But for our purpose – which is to study the tilt itself we can maintain average tilt to be constant at 23.5degrees throughout the orbit of earth around sun. The same is exhibited lucidly in Figure 2.
3. Why does the inclination of earth’s axis maintain orientation vis-à-vis the orbital plane throughout the revolution of earth?
3.1. Nothing much has been mentioned in existing science literature on which the axis if earth maintains the axis of earth at a constant tilt of 66.5° to orbital plane throughout a year (one complete revolution of earth around sun). Since aforementioned tilt maintenance throughout the revolution of earth around sun is a well-established fact, it was considered as a primordial condition and hence granted the status of an axiom.
3.2. By Newtonian laws, the position of any point on an object held towards the centre of revolution with a centripetal force in circular motion will, with no other force acting upon it, experience no change in its position relative to the centre of revolution (distance of any point on a revolving object remains constant relative to the centre of revolution). The same is also pertinent from law of conservation of angular momentum which mandates that the product of vector ‘r’ (of radius) and vector ‘mv’ (of momentum) remains constant if not acted upon by external forces.
3.3. To showcase an analogy to ideal earth-sun movement, take two same size balls one heavier & other lighter & bond them together with an adhesive after which put the bonded balls into an inflated large transparent balloon. Inflate the balloon to considerable size so that the two balls can freely move inside the inflated balloon (see Figure 3).
Tie a knot on the balloon’s neck of the opening & a meter long thread to the neck of the inflated balloon. Now rotate balloon with hand, fingers being the centre of revolution. Watch the balls through the transparent wall of the balloon. The heavier ball will remain at the farthest point from the centre, the lighter ball being next to the heavier but towards the centre of revolution. The heavier ball has more angular momentum vis-à-vis lighter one & hence if there is no change in the state of this revolving balloon system, there will be no change in the distance at which any point on the two balls is located from the centre of revolution. The heavier ball will remain farthest throughout the trajectory of the balloon.
Hence, though the balls are free to move inside the balloon relative to the centre of the revolution, while being subject to centripetal force, no point on or inside the ball changes its position relative to the centre of the revolution if there is no change in the angular momentum. Similarly, suppose the earth is a ball that is revolving around sun, gravitation being the thread, the ball tilted away from the sun forming a 66.5° angle with the orbital plane. In such case, the position of any point of the axis of rotation should be at the same distance from the centre of revolution (sun). So the earth should have been revolving in the way depicted in Figure 3B.
As is evident, from fig 3B and fig 3C (green point, red point and blue point are projections of north pole, earth’s centre and south pole on the orbital plane), angular momentum is conserved as the radius vector of north or south pole are maintaining their constancy.
3.4. Let’s suppose that there exists a celestial motor which we use to switch the rotation of earth ‘on’. The moment the rotation is switched on, earth will start precessing. Now, let us assume that it is precessing only by a cycle length of 1/25771.50 cycles/year, then in such case there will be little (negligible) impact on the orientation of the earth’s axis vis-à-vis the orbital plane. It will only change by 1/25771 proportion (approx. 0.62km/year calculating the circumference of precessing poles at 23.55degrees to be 15,926.30km). This is negligible vis-à-vis the revolution cycle (940*10^6 km/year). Therefore, even after the earth started spinning with full speed, if one would assume that precession cycle is (as specified currently) 25771 years, the orientation of the axis would have digressed only by 600th trillionth proportion of path of revolution of earth, hence completely ignorable.
3.5. Thereby, the author crystallizes his pretention that earth is factually not revolving the way it should have been ideally – as in Figure 3A, until and unless there is an additional component of motion of earth that is yet unidentified or unaccounted by purpose or by neglect. Empirically, we know that the axis of earth maintains a constant angle to the orbital plane as in Figure 2. Therefore, it becomes important to discover this component of motion that leads to maintenance of orientation of earths’ axis, instead of behaving in way depicted in Figure 3.
3.6 To better understand this motion component we draw a graph depicting the distance of earth’s north pole from the centre of sun as a function of time (an year), for ease of understanding, let us also presume that the orbit of earth is not elliptical but circular (as we are considered about analysing the tilt not the distance of earth’s centre to that of sun’s). Figure 4B vividly depicts the graph of distance of North Pole from sun through a year.
3.7 As evident from Figure 04B, earth’s north pole undergoes a cyclic motion vis-à-vis sun’s centre. This means, that if for a moment, we presume that earth is not revolving around sun, then it would be undergoing a pendulum-like motion vis-à-vis sun centre.
3.8 If the north, south and centre of earth are projected on a plane that is parallel to the orbital plane and lies just below the south pole of sun. North Pole, South Pole & the Centre of earth would then get projected as three dots Grey (South), Blue (North), Red (Centre) (see figure 5B). They will lie on a line (centre of earth being sand-witched between the North & South Pole owing to the tilt of earth’s axis to the orbital plane.
3.9 As is evident from the Figure 5B, the North Pole (blue dot) would do an eclipse, if the axis of earth is holding the angle to the orbital plane constant as seen on the projected plane from a star north of Sun’s north pole, as is depicted in Figure 5A.
3.10 Hence, I point out a component of earth’s motion that results into a cyclic change in distance of any point on earth (say North Pole) from Sun.
3.11 The observed pendulum-like motion as shown in Figure 04B has to have a pattern that observes laws of physics. Furthermore, it is also apparent that the said pendulum-like motion has to be more complex that just - to & fro pendulum in a plane that is drawn by wiping the radius of earth’s revolution perpendicular to the orbital plane. By Newton’s first law, would earth simply change its tilt vis-à-vis the radius of revolution, there is no force known to stop it from taking to rotation around an axis that is tangential to the path of revolution of earth’s centre. Therefore, the motion is a more complex one; of which this pendulum-like motion is a component.
4. Precession-the cause of earth’s pendulum-like motion component
4.1. Through this section the author describes about his discovery that the pendulum-like motion is caused by Precession of earth, which is one year minus 20.41minutes, rather than 25,771.58years as currently stated in literature.
4.2. Precession: It is movement of earth in a manner that its axis sweeps the surface of a cone as depicted in Figure 06. The centre of earth could lie One such cycle happens in ~25,771.58 years. While in precession the fulcrum of precession (point ‘0’) may lie on the axis within or outside the body, in case of earth the fulcrum lies in the centre of earth.
4.4. First one is a carousel. Observe the carousel revolve. The figure 07 depicts it vividly. In the given example, kindly ignore gravity, which keeps the cabin’s orientation towards earth, as the purpose of this example is to showcase an analogous motion, not the cause of it.
4.5. In a carousel the viewer’s cabin (depicted as blue ball) constantly points towards the ground owing to gravity, while the giant wheel rotates around its centre. In a Carousel, as depicted in Figure 07 and 07A, the most important observation of the author was the interaction of the viewers’ cabin with the giant wheel. The wheel is represented by the grey arrows radiating out of the giant wheel, and fixed in their position relative to the wheel at each point from ‘A’ to ‘H’. On observing the cabin and the grey arrow interaction starting from position ‘A’ to position ‘H’ it is apparent that along with the rtation of the giant wheel from position A to H, the cabin revolves around the arrow that represents the wheel. Figure 07A depicts this vivdly.
4.6. In an analogy to earth’s movement around sun, had the viewer’s cabin (blue) in a carousel, been earth, and the rod connecting the cabin to the giant wheel been the north-pole, it would constantly point towards one single direction throughout the revolution of the giant wheel – that is away from ground. The cabin is revolving around a centre which lies on the giant wheel (where the cabin is connected with the wheel) & is analogous to earth’s precession. Replace, the giant wheel with earth’s path around sun and the cabin with earth, as shown in Figure 07 and in 07A, one will find earth precessing around its path of revolution around sun (giant wheel).
4.7. From a motion point-of-view, the cabin constantly points towards earth because, while the wheel is rotating anticlockwise the cabin rotates in opposite direction (clockwise) vis-à-vis the wheel with similar rate of angular displacement. Interaction of the two vectors leads to maintenance of a constant orientation of the cabin to the ground.
4.8. Similarly: Imagine a smaller wheel mounted on a bigger one as shown in figure 8, both capable of rotating independently. Now imagine that the observer is located on top and viewing the rotating wheels from top (as in figure 8). The rotation of the larger wheel will be akin to revolution of earth while that of the smaller wheel will be akin to precession of earth.
4.9. Let us first consider that the bigger wheel is rotating anticlockwise, while the smaller wheel is stationery relative to the bigger wheel as has been depicted in Figure 9. The purple triangle represents the earth, while the vertice of this triangle pointing away from centre of big wheel, denotes the north-pole. Had there been no motion of smaller wheel relative to the larger wheel, the triangle would have revolved in a circular orbit as is depicted in Figure 9. The triangle keeps changing its orientation vis-à-vis any observer standing above the Sun’s north pole. But its position is unchanged vis-à-vis the centre of large wheel.
Now, let us observe the phenomena that happens when the small wheel also starts rotating in a direction opposite to that of the large wheel (clockwise) and at the same angular velocity as the large wheel. In such case, as in Figure 10, the triangle (earth – the vertice being the North Pole) constantly points in one direction – that is – its direction is unchanged vis-à-vis an observer (located above the sun’s north-pole), while its direction is constantly varying relative to sun. Pointing towards the sun at ‘B’ & away from Sun at ‘A’.
4.10. Therefore, the constant orientation of the earth’s inclined axis, towards a distant star throughout the 365.25 day revolution of earth owes its existence to precession of earth that happens with almost the same rate of angular displacement as the revolution of earth around sun but in opposite direction. This precession is represented in Figure 10B by the movement the orientation of projections of north pole, centre and south pole (green, red and blue dots joined by the blue dotted line) vis-à-vis the Newtonian position (represented by the black arrow) that north pole should have had, had we wanted to conserve the radius vector r, thereby conserving angular momentum).
4.11. Therefore, it implies from 0 and those before it, that Precession of earth is not 25,771.58years but approx. 1 year and in direction opposite to that of earth’s revolution. Since there is a distinction, that needs to be drawn amongst that what is currently referred to as Precession, and what I prove in the present paper, I have for avoidance of doubt, termed this ~1year precession cycle that I discovered as D-Precession.
5. Exact Precession Cycle of Earth
5.1. The exact D-precession cycle of earth is 1 year less 20.41minutes. This gap of 20.41minutes every year results into what science today refers to as precession. In case the angular velocity of the small wheel of figure 10 (clockwise) is more than the angular velocity of Large Wheel (anticlockwise), the direction of the triangle will keep on shifting clockwise on completion of the cycle of large wheel. Hence, it will point differently at the same position after one year than it would have, had the angular velocity of both the wheels been exactly same. As demonstrated in figure 11, the north-pole (vertice of the purple triangle) in such case would have completed not one, but 1+d cycles in one year. Analogously, if the cycle of D-Precession is faster than the revolution of earth by 20.41 minutes per annum (this is known from existing science as the length of precession); then on the same day & time, after one year, the earth’s axis will not point in the exact same direction as an year ago but would have drifted slightly ahead by a small angle of 1/25,771.58th part of the year (20.41min). The cumulative drift in any year shall be = ‘n’ x 1/25,771.58th of an year (where ‘n’ is the number of years for which the cumulative drift is sought to be calculated). Therefore, after 25,771.58 years the earth’s axis’ orientation would have drifted for 360degrees cumulatively, and would therefore lie exactly at the same orientation as it was 25,771.58 years ago, after having drifted by 20.41 minutes annually to complete the entire cycle.
5.2. This difference of 20.41 minutes between D-Precession and Precession (what seems precession as described in science currently) is defined as A-Precession.
5.3. As is seen in Figure 11 a demonstrative drift of orientation of earth is shown, owing to the difference of the D-Precession and revolution cycles. And this is the cause of science ignoring true precession (D-Precession) in favour of what seemed to be precession, which is actually A-Precession.
5.4. As is apparent from Figure 13 versus Fig 12, the earth’s north pole owing to faster precession cycle vis-à-vis revolution of earth around sun, actually surpasses the point of reference ‘A’ from where it started exactly one year ago. Figure 12 shows the positions had the precession cycle been equal to the revolution of earth, while figure 13 showcases the actual position – that is precession cycle being faster than revolution of earth (one year).
5.5. It is pertinent to mention, that would the constantly-oriented axis of earth be taken as a primordial given, the slight change (1/25,771.58th of an year) in the orientation of axis per annum would naturally be treated as precession. While in reality Precession (D-Precession) cycle length is (365.25days x 24hrs x 60) x (25,770/25,771.58) minutes [=5’25’939.59 minutes]. While A-Precession is the difference between D-Precession and an year [=20.41minutes].
6. Conclusion
6.1. While axis of earth and the north-pole on it should have pointed away from sun throughout earth’s revolution around it; it does not. It maintains its axis in constant orientation to a distant star. This happens because while the
6.1.1. earth is revolving anticlockwise (keeping the north-pole pointed away from sun), simultaneously;
6.1.2. earth precesses in opposite direction (clockwise) that happens almost with rates of angular displacement, similar to those of revolution of earth.
6.1.3. the resultant of the aforementioned two motions results into maintenance of the orientation of axis - constant, vis-à-vis distant star.
6.2. D-Precession is
6.2.1. the true precession discovered by the author that occurs in direction, opposite to revolution (clockwise, when seen from north pole of sun);
6.2.2. leads to cancellation of impact of revolution of earth (which otherwise could have kept the north-pole pointed away from sun throughout the revolution of earth around sun)
6.2.3. and is equal to 365.25days x 24hrs x 60 x (25770.58-1) / 25,771.58 minutes [=5’25’939.59 minutes].
6.3. A-Precession is
6.3.2. what, to current science, seems as precession (which it is not as is stated in 6.3.1);
6.3.3. equal to 1/25770.58 of an year [=20.41 minutes].
6.4. Earth-Sun System Energy Impact: My discovery has a major impact on the calculation of the Energy of the Earth-Sun system. Calculations of catastrophic celestial collisions with earth of artificial or natural objects will undergo a major change. This quantum of change will vary with latitude.
6.4.1 With vectors of rotation and revolution (both pointing counterclockwise) cumulatively remaining unchanged, the only change now is the annual precession cycle related vector, which is pointed in the clockwise direction (opposite to rotation & revolution). The precession caused velocity vector keeps on reducing as one travels from poles towards equator. Closer to the poles the precession vector’s size is enhanced by 25771.50 times (it is now 1cycle/year instead of 1/25771.50 cycle/year). Discovery of this changed vector of precession leads to an enhanced disparity in calculation of the impact that a celestial collision of a body with earth will undergo if it falls on around the poles vis-à-vis the equator. The impact at equator is minimal whereas towards the poles it is maximum. The velocity at the poles owing to precession is increased by 0.5m/s vis-à-vis earlier data. This disparity has been calculated to be around 0.50m/s. These changes in the vector quantities lead to change in the Earth-Sun System Energy.
1. References
[[1]] the discovery of precession usually is attributed to Hipparchus (190–120 BC) of Rhodes or Nicaea, a Greek astronomer though the Indians are reported to have discussed it in 750 BC.
[[1]]N. Capitaine et al. 2003, p. 581 expression 39
[[1]] The Columbia Electronic Encyclopedia, 6th ed., 2007
[[1]]Astronomical Almanac 2010, p. B52
[[1]] oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle; the earth's mean obliquity is currently 23°26′13.2″ (or 23.437°)
[[i]]Astronomical Almanac 2010, p. B52
[[ii]] oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle; the earth's mean obliquity is currently 23°26′13.2″ (or 23.437°)
[[ii]]N. Capitaine et al. 2003, p. 581 expression 39
[[iii]] The Columbia Electronic Encyclopedia, 6th ed., 2007
