Stradageek wrote: ↑11 Aug 2022, 7:44am
........... I only have so many (and a diminishing number of) brain cells
If you want some real brain teasers try working out why Dark Matter/Energy is deemed to exist, why Mercury is a regular naked eye morning star only when viewed from the Southern hemisphere or how the 'slingshot' effect is used to accelerate satellites traveling to the outer solar system.
Like your/my 'timing' conundrum I believe there comes a point where you need a mathematical equation to 'prove' it but a) I much prefer to visualise the answer and b) my maths is not up to it.
Aaah. .... that old conundrum. The inverse ratio between age and number of brain cells remaining!!!
Some more brain teasers - why does matter require the Higgs Boson in order to have mass? what's going to happen when a real life example of a "worm hole" is identified? why does the scientific method produce far more questions than answers and, yet, is considered "rational progress to understanding"?
I could go on "ad infinitum". But, there again, where on earth (or not on earth) is infinity, except in our minds?
I'm satisfied with Brucey's explanation, even though it only explains one specific static situation in the diagram. I take his word for it that the same reasoning applies if (for example) the planet pinion in the diagram were rotated by 90 degrees. I'm pleased that my thoughts were the same as his (the advance of the teeth on the planet compared to the sun) even though I overcomplicated the reason for this.
As for delving into the reasons as to why it works with prime numbers ....... I'll get back to you when I've worked out why the hare never did catch the tortoise!!
Nice to talk to you.
Geoff