Rafi Laupert, Israel Astronomical Society
The Earth's equatorial plane maintains an almost completely constant orientation in space throughout the year thanks to the stabilizing gyroscopic effect of the Earth's rotation on its axis. The plane of rotation of the earth around the sun is also kept constant. As you know, there is an angle of 23.50 between the two planes. Therefore, the intersection line of the two planes also remains fixed in space, when these planes maintain a fixed spatial orientation. At the equinoxes in spring and autumn, the sun is on this line at two opposite points relative to the earth. Because of the spatial stability of this line, it was used as a reference line for astronomical measurements already in the distant past (hereafter we will call this line "the line of equinoxes"). Nowadays, with the improvement of observation capabilities and measurement accuracy, the spatial orientation of a line is not accurate enough, and the movement of the sun around the center of gravity of the solar system must be taken into account, and hence the previous calculations must be corrected. Namely: the center of gravity of the entire solar system is currently the corrected astronomical reference point.
The old "habit" established a norm of concepts that is still in use today. From the same leg, the "longitude" angle of the position of the planets and other objects is measured from the vernal equinox point on the "equinox line" in the direction of orbital motion, where the intersection point of the orbit with the ecliptic plane (the plane of the sun's orbit) is known as the (AN) Ascending Node, and the measured angle to which is the angle of longitude of the AN. And the angle between the orbital plane and the ecliptic plane is the inclination angle. In AN, the movement path goes from the southern domain to the ecliptic plane to the northern domain ("from below" "up").
Parchus, around 150 BC, comparing measurements of contents that preceded him (including Babylonian contents), with measurements he made himself, found slight but systematic statics in the data of the longitude angle of various objects in relation to the above-mentioned line of equinoxes. His conclusion was that the position of the line in space is not exactly fixed but moves in a precession movement (changing its spatial orientation at a rate of 0.0127 degrees per year. The currently accepted figure for the rate of this precession is 0.01396 degrees per year, so his measurements of the convulsion and his calculations, considering the means at his disposal, were excellent! From the figure The current result is that the equator rotates in a precessional motion at the rate of a complete revolution (3600) every 26,000 years, and hence the earth's axis perpendicular to it also rotates at the same rate. Copernicus called this motion "the third motion of the earth", with the remaining two being the rotation around the sun (one revolution in about 365 days) and the autorotation around its own axis (one revolution in about 24 hours). The awareness of this movement of the earth, which has a very long time constant, is definitely an intellectual achievement of human culture, because its discovery was only possible thanks to the work of generations Many astronomers. Only repeated measurement of the deviations over time made it possible to stand for the fact that this is a permanent and stable phenomenon over time.
The reason for bringing this introduction is that when we observe the major axis of an elliptical orbit of a body in the solar system such as "Mercury" for an extended period, and compare its orientation in space to our equator, we should also find a precession of 0.01396 degrees per year, which corresponds to about 5025 seconds Keshet for 100 years, if we assume that the orbital axis of "Mercury" is stationary in space. However, astronomers have observed a precession of 5600 arcseconds in 100 years, so the axis is not truly stationary in space. This result, on the face of it, points to a problem in the ability of the Newtonian gravitation theory to match the results of the measurements. On the other hand, it must be remembered that the Newtonian theory of gravitation determines a stationary elliptical orbit only in the ideal case of two bodies acting on each other, in the absence of additional external influences. When accurately calculating Mercury's orbit, the influence of the other planets in the solar system, the size of the sun and the distribution of all the mass in the solar system must be taken into account, even though the sun itself constitutes about 99% of the mass of the system. Special importance is attached to "Venus" and "Earth" because of their relative proximity to "Mercury" and "Zedek" because of its size. It is not easy to calculate these effects and unfortunately, as we know, there is also no analytical solution to the problem of "n bodies" (generalized motion with mutual influence of three or more bodies) in Newtonian mechanics. By using calculation/approximation techniques developed by Lagrange Laplace, Hamilton and others, it is possible to come to the conclusion that the influence of all other bodies contributes to the precession of "Mercury" for another 532 seconds of arc in 100 years.
This result, combined with the precession of the Earth's equator, adds up to 5557 arc seconds per 100 years, which is much closer to the observed result of 5600 arc seconds per 100 years, but still 43 arc seconds per 100 years lower than it . Today's astronomers are convinced that their measurements are so precise that the deviation in them can explain a measurement error that does not exceed one arc second per 100 years. Thus, the remaining deviation, about 42 arcseconds per 100 years, seems to clearly represent a physical problem. The discovery of Neptune (1840) and the way in which this discovery was achieved, returned the astronomers to the examination of the anomaly of the "Mercury" axis. At a certain stage of the test, a theory was even examined that posited the existence of clumps of material in the vicinity of "Mercury", which affect its orbit.
These hypotheses have not been verified by observations. The conclusion drawn from these and other findings was that Newton's theory is probably inaccurate and that the force of attraction acting between two masses is not exactly inversely proportional to the square of the distance between their centers, but inversely proportional to r to the power of n when: 2 ≠n. Calculations showed that for n=2.00000016, the calculation result for "Mercury" agrees with the measurement results. Most of the experts in the field do not accept this assumption, because it creates a contradiction with Gauss's conservation laws, unless one assumes a change in dimensions at a similar rate in the spatial data as well...
Other explanations tried to attribute the difference to the sun's opacity, but this assumption was not proven or required large differences in the level of opacity between the outer mantle of the sun and its inner parts. Such a difference requires a rotation speed of the internal parts that is approximately 25 times higher than that of the external parts.
Furthermore, "abnormal" precession phenomena are now also observed in other bodies in the solar system. In bodies with elongated elliptical orbits like the asteroid "Icarus", the phenomenon is stronger than in bodies with the "Earth" or "Venus" bumps whose orbits are almost circular, therefore measuring the precession of the longitudinal axis of their orbit is much more difficult.
The best answer is currently given by the theory of general relativity. And it is particularly impressive because this theory is much "harder" than Newton's theory and does not allow "free explanations" for the effects of gravity of the type described above.
A schematic description of the orbital precession of bodies in the solar system is given on the upper right side of the image.
Sources:
1. http://www.mathpages.com/rr/s6-02/6-02.htm
Introduction to Orbital Mechanics; FT Geyling & HR Westerman, 1971, Addison Wesely, pp 32-42
3. Engineering Mechanics; S. Timoshenko & DH Young, 1956, McGraw Hill Book Comp., pp 417-423
4. Planets, Stars & Galaxies; SJ Inglis, 1966, Addison Wesley, pp 95-113.
Appendix: Explanation of the precession phenomenon
Precession is one of the least intuitive phenomena known to us in classical mechanics and is related to the properties of the angular momentum of a body in space. In classical Newtonian mechanics, a body will move with constant acceleration along a straight line, when a constant external force acts on it. The force is a vector and the direction of the movement will coincide with the direction of the force. The rate of acceleration that the body will receive as long as the force acts on it, will be directly proportional to the force and inversely proportional to the mass of the body. When no external force acts on the body, its acceleration will be zero and the body will move (in a vacuum) at a constant speed and in a straight line. Momentum in linear motion (linear momentum) is, as you remember, a vector, its direction is the direction of the velocity and its magnitude is equal to the velocity value multiplied by the mass of the body.
In classical mechanics, a body moving in circular motion (or moving along a curved line) is under the influence of a force directed to the center of the radius of curvature of the trajectory; In a circle - the center of the circle. In circular motion, the torque replaces the force as the cause of the motion, the angular acceleration and the angular velocity the linear acceleration and velocity, and the moment of inertia the mass. However, while in the linear motion the velocity and acceleration vectors merge with the force vector, in the circular motion the angular acceleration and angular velocity vectors are perpendicular to the plane of action of the torque (diagram).
Note: We assume that the axes of movement of the described device are practically frictionless, therefore the movement depends only on the properties of the device and the external forces acting on it.
A simple case of precession exists when a disk-like body rotates rapidly around an axis passing through the center of the disk area, (diagram). Assuming that the disk is homogeneous, it is customary to call such a device an axisymmetric body (a body with axial symmetry). The meaning of this definition is that the moment of inertia of the disk is symmetric with respect to the axis of rotation. The more homogeneous the mass of the disc and concentrated closer to the outer circumference, the greater will be its moment of inertia. Angular momentum is also a vector, but its direction, similar to the angular velocity, is perpendicular to the plane of rotation and its magnitude is given by multiplying the magnitude of the angular velocity by the moment of inertia around the axis of rotation. The size of the angular momentum is very important in creating the precession phenomenon, because the precession is proportional to the angular momentum. In the case described below, if we ignore the effect of gravity (or balance it with respect to the disk described), as long as no external torque acts on the rotating disk or axis, the disk and its axis of rotation passing through its center will continue to maintain a fixed direction (orientation) in space. This is an expression of the persistence of the rotational movement when its measure (the proportionality factor) is used as the moment of inertia.
If we apply a constant positive torque M (counter-clockwise) on the axis of rotation of the disk (which rotates as you can see from the diagram counterclockwise in the XY plane) so that it tries to rotate it in the YZ plane, then as long as this torque operates, the axis will move with the disk (to which a connection is connected) rigid) in a circle with a constant rotation speed Ω, in the XZ plane. It is worth noting that the XZ plane is perpendicular to both the plane of rotation of the disk and the plane of action of the torque. This rotation movement is the precession, and in the simple case described in the diagram its rate will be:
when are:
Ω, the speed of precession (in degrees or radians per second).
ω, the angular velocity of the disc, (constant).
I, the moment of inertia of the disc about the Z axis, (constant).
Comments:
The speed Ω gives the value of the constant torque M required to maintain a constant precession at this rate. The torque is as you remember: power double arm.
The phenomenon of precession is used, among other things, in a series of measuring devices called gyroscopes as well as in stabilization devices, such as in ships. The gyroscopic measurement devices are particularly suitable for use in space flights due to the property of persistence in space of the angular momentum vector, as described above. Until the introduction of GPS equipment into widespread and reliable use, gyro compasses were used as complementary navigational aids to the magnetic compasses, for navigation around the earth's poles, due to their ability to maintain a constant direction independent of the magnetic effects of the poles.
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