I just bought an electronic copy of Miles book from Amazon.
I did consider the hardback but as there is no index, and kindle e-books are searchable, I went the high tech route. My fiancee kindly downloaded it to the Kindle e-book reader I bought her for Christmas. Now I just have to prize it from her fingers long enough to read Mles’ highly entertaining and thought provoking material.
The first edition of the paperback is on back-order from Amazon UK here.
There are only two copies of the hardback left, an astute investment at £24.22 if you ask me.
As you will now see, the solution to this problem is so simple that it makes three centuries of physicists and mathematicians look like bumblers. I looked at that sequence of numbers for about half a minute before I saw it was based on the square root of 2. The “law” has been in the wrong form since the beginning, and so no one was able to see the proper sequence.
Currently, the sequence goes like this:
4, 7, 10, 16, 28, 52….
But it should be written as
4, 5√2, 7√2, 11√2, 20√2, 36√2….
Which can be written as
(22 + 1)√2
(22 + 1 + 2)√2
(22 + 1 + 2 + 22)√2
(22 + 1 + 2 + 22 + 32+ 42) √2
If we want to express this with Mercury as 1, then we just divide by 4.
[(22 + 1)√2]/22
[(22 + 1 + 2)√2]/22
[(22 + 1 + 2 + 22)√2]/22
[(22 + 1 + 2 + 22+ 32) √2]/22
Which expands to:
√2 + (1/22)√2
√2 + (1/22)√2 + (2/22)√2
√2 + (1/22)√2 + (2/22)22 + (22/22)√2
√2 + (1/22)√2 + (2/22)22 + (22/22)√2 + (32/22)√2
Which simplifies to:
You will say, “Great, you expressed Bode’s Law in terms of √2. So what?” Well, the so-what is that it ties directly into my correction to Newton’s equation a = v2/r. I have shown that the equation should read a = v2/2r, since our current expression of the orbital velocity is not a velocity. Yes, a = v2/r works if v = 2πr/t, but 2πr/t isn’t a velocity. It is a curve over a time, which isn’t a velocity. It is just a heuristic ratio that we like because it is easy to measure. But since the orbit curves, it must be an acceleration, and that acceleration is expressed by the equation,
aorb = 2√2πr/t
Physicists couldn’t look at it without scales on their eyes, since they had bought the “gravity only” interpretation. Laplace “solved” the perturbation equations 230 years ago, and no one has had the gumption to look closely at them since then. Mathematicians failed to solve this, too, and we may assume it is because they got deflected in about 1820, or 190 years ago, by new maths. They weren’t interested in simple algebra like I do here: they wanted to use curved fields and infinities and complex numbers and quaternions and lord knows what else. Actually solving a simple problem of mechanics was beneath them. It really makes you wonder how anything ever gets done.
In physics and math, nothing much does get done, as I have shown. The history of physics and math has not been a wonderland of brilliance and fast progression; it has been a shocking wasteland of deflection, misdirection, and complete incompetence, and it is only getting worse. I expect the response to my papers to continue to be vicious, since there is nothing more reactionary than a field of sinecures. It will be like trying to overthrow the Aristotelians or the French Academy or any other nest of nepotism and privilege and corruption. But they had best put on their waders, because the water is high. I am coming right at them, and I am used to deep currents.