[math-fun] Neptune-Pluto orbital resonance
Wikipedia: Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter <https://en.wikipedia.org/wiki/Jupiter>'s moons Ganymede <https://en.wikipedia.org/wiki/Ganymede_(moon)>, Europa <https://en.wikipedia.org/wiki/Europa_(moon)> and Io <https://en.wikipedia.org/wiki/Io_(moon)>, and the 2:3 resonance between Pluto <https://en.wikipedia.org/wiki/Pluto> and Neptune <https://en.wikipedia.org/wiki/Neptune>. In[234]:= MinorPlanetData["Pluto"][EntityProperty["MinorPlanet", "OrbitPeriod"]] Out[234]= Quantity[247.92065, "JulianYears"] In[235]:= PlanetData["Neptune"][EntityProperty["Planet", "OrbitPeriod"]] Out[235]= Quantity[164.79132, "JulianYears"] In[236]:= ContinuedFraction[%%/%] Out[236]= {1, 1, 1, 55, 1, 1, 1, 7} That's a fairly lousy approximation to 2:3. What's going on? —rwg
On Apr 27, 2019, at 1:57 AM, Bill Gosper <billgosper@gmail.com> wrote:
Wikipedia: Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter <https://en.wikipedia.org/wiki/Jupiter>'s moons Ganymede <https://en.wikipedia.org/wiki/Ganymede_(moon)>, Europa <https://en.wikipedia.org/wiki/Europa_(moon)> and Io <https://en.wikipedia.org/wiki/Io_(moon)>, and the 2:3 resonance between Pluto <https://en.wikipedia.org/wiki/Pluto> and Neptune <https://en.wikipedia.org/wiki/Neptune>.
In[234]:= MinorPlanetData["Pluto"][EntityProperty["MinorPlanet", "OrbitPeriod"]]
Out[234]= Quantity[247.92065, "JulianYears"]
In[235]:= PlanetData["Neptune"][EntityProperty["Planet", "OrbitPeriod"]]
Out[235]= Quantity[164.79132, "JulianYears"]
In[236]:= ContinuedFraction[%%/%]
Out[236]= {1, 1, 1, 55, 1, 1, 1, 7}
That's a fairly lousy approximation to 2:3. What's going on? —rwg
In the case of the Jovian moons the average orbital frequencies are very precisely modeled as w_G = w_0 + w_p w_E = 2w_0 + w_p w_I = 4w_0 + w_p where w_p << w_0. What’s going on is that after the approximate common period T_0 = 2pi/w_0 the system of three moons has “rigidly” precessed by the small angle T_0 w_p. Why they like to do that is complicated. Something similar may be going on with Neptune/Pluto. -Veit
Brad Klee kindly offered http://www.orbitsimulator.com/gravity/articles/pluto.html . So 247.92065 "JulianYears" is an oversimplification representing some average over some unspecified period. We need something much fancier than error brackets here, people. Definately. (Note in the following the hassle created by the Union thugs' demotion of Pluto.) On Fri, Apr 26, 2019 at 10:57 PM Bill Gosper <billgosper@gmail.com> wrote:
Wikipedia: Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter <https://en.wikipedia.org/wiki/Jupiter>'s moons Ganymede <https://en.wikipedia.org/wiki/Ganymede_(moon)>, Europa <https://en.wikipedia.org/wiki/Europa_(moon)> and Io <https://en.wikipedia.org/wiki/Io_(moon)>, and the 2:3 resonance between Pluto <https://en.wikipedia.org/wiki/Pluto> and Neptune <https://en.wikipedia.org/wiki/Neptune>.
In[234]:= MinorPlanetData["Pluto"][EntityProperty["MinorPlanet", "OrbitPeriod"]]
Out[234]= Quantity[247.92065, "JulianYears"]
In[235]:= PlanetData["Neptune"][EntityProperty["Planet", "OrbitPeriod"]]
Out[235]= Quantity[164.79132, "JulianYears"]
In[236]:= ContinuedFraction[%%/%]
Out[236]= {1, 1, 1, 55, 1, 1, 1, 7}
That's a fairly lousy approximation to 2:3. What's going on? —rwg
participants (2)
-
Bill Gosper -
Veit Elser