Mathematics

Common Math Misconceptions



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Which way is up?

We are now living in a world where most everything has been discovered for us. We are told that there are just so many planets and how far apart they are, how big they are, why they revolve around he Sun as they do, etc., etc. That is just the tip of the mountain of information that has been gathered for us. I suppose we must be thankful and seek not to dispute any of this collected knowledge and wisdom. Not many of us get to use billion dollar telescopes and other expensive equipment to scan the heavens so it is not well received by the privileged when the bottom feeders venture an idea intruding on their exclusive domain.

This discussion could have started with excerpts from astronomy textbooks written 30 years ago and then updated the data every 5 years from textbooks written in those years
by which to compare the progression of documented facts and theories as time passed. This would not be a popular effort and, in fairness, I must admit that more discoveries will always produce better data for the authors and the publishers of textbooks. My attention is drawn to the vigor that was exerted by the authors of the textbooks in support of their original conclusions until proven discoveries showed they were only partially correct or not at all correct in their original assessment of the facts. Well, you probably feel that "no harm done" so what is the problem. I ask, "Will we ever know how much harm was done, not by an erroneous contention, but by the wrath by which that viewpoint was enforced?" The answer is no. We cannot anticipate how many budding concepts get squashed in their infancy when confronted with "established views".

We can thank Johannes Kepler and Isaac Newton for the breakthrough in astronomical physics. Newton's formulas give us the means to calculate the Mass of an object, such as the Sun or a Star, that has objects in orbit around it. In our case within the limits of the two-body system and the use of Newton's "constant" the Sun's Mass can be calculated. I recall reading that Newton's "constant" was 6.67e-7 many years ago. Possibly 100 years after Newton Henry Cavendish revised the "constant" by experiment to G = 6.67e-11. This looks like .0000000000667 or four more zeros than the original constant.

Newton's Universal Law of Gravitation tells us that all objects of Mass in space atract all other objects of Mass. This means that the Sun attracts the Earth that in turn attracts the Moon. A common offer of proof of the Earth Moon attraction is the reference of the tide sequence the oceans of the Earth show by their movement of the water. The Sun also affects the tides of Earth but not as much. Newton's formulas provide us with the means of calculating the Mass of the Sun by reference to the Earths orbital data. The Moon gives us the means to calculate the Mass of the Earth based on the moon's orbital data.
This due to the fact that the Earth's orbit around the Sun results from the gravitation of the Sun pulling on the Earth holding Earth in its orbit- hence the data relates to the Sun's Mass. In the same way the Moons orbit tells us about the Earth's Mass.

Just to exercise our brains a little we should, for fun, decide why the tide movements on the Earth prove they are due to the Moon pulling on the Earth. First of all let's assume that the Moons orbital position has no relationship to the Mass of the Moon meaning that the Moon did not get where it is because of its self contained Mass. This suggestion is based on the fact that other much larger planets are farther away from us than the Moon and they have a lot more Mass allegedly pulling them closer to the center of the system.

Newton pointed out that it was the pull of the Earth Gravitation that held the moon in its orbit, without which the Moon would fly off into space. The theory is that the Moon is "falling" towards the Earth but is restrained to its orbit by the speed it travels in its orbit and that speed is due to the Earth's gravitation.

So the thought question becomes "Why is not the Earth's gravitation and its pulling of the Moon that is the cause of the tidal changes we see?" "Also since the water composing the tides is the only part of the Earth that can move in response to Earth's effort to hold on to the Moon is not that bulge to be expected with no contribution by the Moon's Mass?" Possibly you will come up with an explanation no one else ever thought of.

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