Re: Kepler
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 > > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Kepler
Hello Fabio, This is a beautiful animation and clever mechanical design! I can’t say that I completely understand either. What software did you use to compose and animate the gears? Thank you for sharing your work. It was definitely a worthwhile use of two week. I wish I could say I’ve accomplished as much in that time. Best wishes, John > On Jul 7, 2017, at 5:54 AM, 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 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
Re: Kepler
wow! Mechanics beats math. Kurt Am 07.07.2017 11:55 Vorm. schrieb "fabio.sav...@nonvedolora.it" < fabio.sav...@nonvedolora.it>: > 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 > > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Kepler
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
