The article was published in the journal "Astronomy" published by the Israeli Astronomical Society and is presented with the approval of the journal editors
Yehuda Sabdarmish
Thoughts on Newton's gravitation formula at cosmological distances
By Sabdarmish Yehuda
Unlike others who will start the history of gravitation with the story of Galileo Galilei, or Newton, I prefer to start with the story of Tycho Brahe.
Tycho Brahe (1546-1610), made very precise measurements on the planets known at the time (Mercury to Saturn). He made the measurements with the help of instruments he built himself and without the help of a telescope that had not yet been invented at the time. These data were transferred to his assistant Johannes Kepler (1630-1571) for a little over a year. Because of the great accuracy of the measurements, Kepler realized that the movement of the planets around the sun is not circular but elliptical, and hence the path to arrive at the three laws known by his name was short:
1. Ellipse - the planets move in an elliptical orbit with the sun at one of its foci.
2. Equal areas at equal times - the radius and vector connecting a planet to the sun passes over equal areas at equal times.
3. The distance of the planet from the sun in the third, divided by the square of its cycle time, is constant.
Isaac Newton (1643-1727), who discovered the three laws of motion known by his name, also had Tycho Brahe's data and Kepler's laws. He understood that the gravitation in the planets is proportional to the centrifugal force and from all this information he deduced the law of universal gravitation:
F=M*m*G(R/2)
M m the masses, R the distance between them, G the gravitational constant.
Newton's initial conclusion was that gravitation works from the edge of the universe to the edge of every two pieces of matter at any distance. Is this too overwhelming a decision? It is clear that he did not test this at every point in the universe, but what, we must not forget that the known universe in Newton's time was relatively small. The solar system known at the time was as far as the planet Saturn, about ten astronomical units, and apart from it, there was at most another count of Saturn stars. So Newton actually did not exaggerate too much when he said that his gravitation formula was proven for the entire universe known at the time. Also the movement of the planet Saturn, somewhere, close to the edge of the universe (known in his day) behaved according to its gravitation formula.
In the meantime, the discovery of the distant planets: Uranus - (1781), Neptune - (1846) and especially Pluto - (1930), which moves at a distance between 30-50 YA from the Sun, contributed to the proof of the gravitation formula up to a distance of 50 YA, while
Henry Cavendish in an experiment he conducted in 1798 with the help of scales invented by John Mitchell, proved the gravity formula for a distance of about one cm and determined the gravitational constant - G.
Conclusion: The gravitation formula is now proven to be correct from one cm to fifty eleven.
However, this is still the known size of the universe, so it was still not an exaggeration to state that Newton's gravitation formula is true for the entire universe.
However, from this moment on, the universe turns out to be a much larger body.
Measurements using the parallax method reveal that the distance to the stars closest to the sun is already measured in light years (a light year is a unit of length that is 63,240 astronomical units!)
Measurements using cupid variable stars show that the distance to the nearest galaxies is measured in millions of light years, and finally, measurements using the rate of expansion of the universe and the Hubble constant show that the size of the universe is actually billions of light years! To remind you, the proof of Newton's gravitation formula was done with certainty up to a distance of fifty astronomical units.
Examples of distances in the universe:
50 YA - Limit of proof of the gravitation formula in the solar system.
250,000 Ya - the distance to the nearest star (Proxima Centauri).
10,000,000,000 YA - diameter of an average spiral galaxy.
1,000,000,000,000 YA - the distance to the nearest galaxies.
1,000,000,000,000,000 YA - the radius of the visible universe.
There is no doubt now that the formula must be proven for greater distances as well. Attempting to ignore this contradicts the problem of induction already raised by the English philosopher David Yom, which simply says that one can draw conclusions from a certain statement only regarding the limits in which that statement was tested.
Attempts to prove Newton's gravitation formula were made using the rotational motion of the spiral galaxies when the rotational speed of different regions in the galaxy was measured using the Doppler effect.
Assuming that the rotation of the galaxy is due to the force of gravity, then the force of gravity resulting from the mass of the galaxy should be equal to the centrifugal force of different regions in the galaxy.
Those whose result did not match the theory. The speed of rotation did not correspond to that resulting from the size of the visible mass in the spiral galaxy!
This discrepancy could be due to an inaccuracy in one or both of the formulas we used to calculate: the gravity formula and/or Newton's acceleration formula. On the other hand, maybe our measurements are flawed?
We will then check all the possibilities for the discrepancy:
A. The possibility that Newton's gravitation formula is correct at large distances, therefore:
1. The mass of the galaxy is at least 10 times greater than the apparent mass.
2. Most of the mass is concentrated in the region of the gas clouds of the galaxy (stated without proof).
3. From measurements it becomes clear that in galaxy clusters the mass must be 100 times greater than the apparent mass in order to maintain the structure of the cluster.
4. At large distances there must also be a repulsive force of the vacuum to explain anti-gravitational phenomena such as the accelerated expansion of the universe.
The possibility expressed in section A is actually the accepted knowledge of most scientists today and hence the extensive search for the missing mass of galaxies.
B. The possibility that Newton's gravitation formula is not correct at large distances and therefore:
It must be replaced with another one.
Many scientists try their hand at changing Newton's gravitation formula.
third. The possibility that Newton's acceleration formula: F=m*a is not correct for small accelerations and therefore:
It must be replaced with another one. For example: Professor Milgrom from the Weizmann Institute developed a theory that explains the movement of galaxies by changing Newton's acceleration formula with small accelerations.
d. The possibility that gravitation does not explain the movement of galaxies but something else.
God. A combination of some of the above options explains the incompatibility.
A final conclusion
Newton's gravitation formula and all that derives from its expansion by the general theory of relativity is miraculously proven only for a tiny region of the cosmic distances and their use for distances greater than the proven one is done carelessly and the conclusions resulting from the "excessive" use of Newton's formula may be misleading.
And for all the skeptics, try to bring a proof of Newton's gravitation formula to a distance of only one light year.
The author of the article did not succeed!
The author of the article is looking forward to comments!, and will be happy to respond to any comments here on the site or privately!
Sevdermish Yehuda Phone: 052-570989 E-mail: sevdermish@surfree.net.il
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