Lord knows how you came up with this. -Bill On Fri, Jul 7, 2017 at 5:46 AM, fabio.sav...@nonvedolora.it < fabio.sav...@nonvedolora.it> wrote:
> Hi, I just finished a work that has engaged me in the last two weeks. > > For those are interested about the Kepler's laws, it > > --- > New Outlook Express and Windows Live Mail replacement - get it here: > http://www.oeclassic.com/ > > is an orrery to show the true anomaly starting from the mean anomaly. > > The mathematical formula expresses the mean anomaly as a function of the > eccentric anomaly, function of the true anomaly (the true anomaly is the > angle of the vector ray that sweeps out equals areas during equal intervals > of time) > The problem is that the first formula is not reversible. There are some > iterative mathematical methods to get the eccentricity anomaly from the > mean one, with several steps up to the desidered approximation, or it is > possible the resolution into an infinite series of terms but not a direct > formula. > > Here math limps. But what can not be achieved with a formal language can > be at hand by changing the language, so suggests Godel. > So I designed a gear structure to get the mean anomaly from the eccentric > one, like the formula, ma the movement of the gears, unlike the formula, > can work contrariwise. > I attached an image of an orrery, for the moment it is virtual, where > turning a knob with a costant angular velocity, the mean anomaly, you get > the movement of a planet on an elliptical orbit, following the Kepler's > laws. > The turquoise planet follows the true anomaly and the one outside the > zodiac follows the mean anomaly. > This orrery is setted with an eccentricity of 0.7216, far higher than he > Earth's one (0.0167086), to point out the gear's dinamic and the elliptical > movement. > I also upload a video on youtube: https://youtu.be/Y5eSOfd5Imk > > This work is the entrance door to calculate the eot with gears instead to > use the customary cam, this is the target for some future gnomonic projects. > > ciao Fabio > > Fabio Savian > fabio.sav...@nonvedolora.it > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > >
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