What is π?
2r/t This will remind us that the numerator is not really a velocity squared and that v is not an orbital velocity by the current definition. That is, it is not equal to 2 π r/t. Pi only applies if the tangential velocity is equal to r/t. But in orbits and most physical problems, this will not be true. The centripetal acceleration and the tangential velocity are independent motions. They are not necessarily related, much less equal. That is why we don’t find the value of pi for the acceleration in gravitational fields. In these cases, given the equation:a = x^{2}/t^{3}2r/t x ≠ r Therefore a ≠ π x ^{2}/t^{2} ≠ 2πr/ta ≠ 2π ^{2}r/t^{2}As I showed in my other paper, the correct equation is a = √ v _{o}^{2} + r^{2} ) - rWhere v _{o} is the tangential velocity. If we let v _{o} = x/t a = √ [(x ^{2}/t^{2})+ (r^{2}/t^{2})] - r/ta ^{2} + 2ar/t = x^{2}/t^{2}r/t = (x ^{2}/2at^{2}) – a/22r = at ^{2}r/t = (x ^{2}/4r) – a/2a = (x ^{2}/2r) – 2r/tSince the wrong equation has been used throughout history and is still being used, this must once again compromise our calculated values for orbital "velocity". For instance, if we calculate an orbital velocity for a satellite using the equation a = v ^{2}/r, we must either get the wrong number for a or for v. The reason our current values mostly work in calculations is that they are at least consistent. We make the same mistake in all calculations (and always have)—this makes it possible to compare one calculation to another and find correct proportions. This allows us to put satellites in successful orbits despite using faulty math and equations. Our engineers have gotten very good at making any necessary corrections to equations, since they are much practiced at it. If one equation doesn't work, they just use another, or tweek the old equation until it does work. To be even more specific, a = v ^{2}/r works in experiment because v = 2πr/t works in experiment. The equation v = 2πr/t is a very useful number to us even though it does not really express the orbital velocity, or any velocity. It is more useful to us than the actual orbital velocity or the actual tangential velocity, both of which aren't really that interesting in experiment except as theoretical numbers. The number 2πr/t is a number we can use, and if we mislabel it as a velocity, well, who cares as long as we mislabel it the same way throughout the centuries? Engineers aren't paid or trained to care about such things, but theoretical scientists understand that such mistakes ultimately lead to ruin. In the short term they may lead to simple engineering failures, which is bad enough. But in the long term they always lead to theoretical dead-ends, since a sloppy equation is the surest of all possible ways to stop scientific progress. A correct equation is almost infinitely expandable, since its impedance is zero. Future scientists can develop it in all possible directions. But a false or imprecise equation can halt this development indefinitely, as we have ample proof. Mislabelling variables is not a semantic or metaphysical failure. Is it failure of science itself.
We have discovered several important things. 5) In orbits and all other circular motion v ≠ 2πr/t. Something may equal 2πr/t, but it isn't a velocity. 6) There is no such thing as orbital velocity. There is only tangential velocity. The curve described by an orbit is not a distance, nor is it a velocity. It has the dimensions m ^{2}/s^{3}, just like the circumference.I would like to thank Mike Newman, a reader who suggested to me in an email that pi might be an acceleration. This led me to compare the circumference equation to the orbital equation and discover their equality. This probably would not have occurred to me if I had not already proved that a = v^{2}/2r in another paper.You may now read my second paper on π which will disclose other even more shocking secrets of circular motion. *If you want to understand this fully you will have to read my paper on the calculus. If this paper was useful to you in any way, please consider donating a dollar (or more) to the SAVE THE ARTISTS FOUNDATION. This will allow me to continue writing these "unpublishable" things. Don't be confused by paying Melisa Smith--that is just one of my many |