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6:40 AM
@fqq Have you tried modelling matters stackexchange? Thats one of my favourite
 
7:31 AM
I recently wrote a Sage / Python program that uses JPL Horizons data to create interactive 3D plots of trajectories of Solar System bodies. You can specify any target & observation centre that Horizons knows about: (1,169,191 asteroids, 3,778 comets, 211 planetary satellites {includes satellites of Earth and dwarf planet Pluto}, 8 planets, the Sun, L1, L2, select spacecraft, and system barycenters).
There's a link to my program in space.stackexchange.com/a/57832/38535 Of course, a lot of trajectories don't need 3D. Here's a plot of Io as seen from Ganymede.
 
7:45 AM
@imbAF Because before Einstein, everybody thought the weirdness of stuff moving near lightspeed was something to do with electromagnetism. Einstein had the insight that it was due to a geometric connection between space and time (and his former maths teacher Minkowski made the final step of uniting them into spacetime). See physics.stackexchange.com/a/291346/123208
 
 
2 hours later…
9:21 AM
"Morally, the second order approximation should be 'halfway between' the two aforementioned flows."
 
@PM2Ring I don't really know what the Horizons data contains - is your program simulating anything or is it just plotting what the data tells it to?
 
9:41 AM
@ACuriousMind Horizons has the position & velocity data, my program just fetches & plots that data. It uses the normalised velocities as tangents to create cubic Bézier control points. The JPL ephemerides are the basis of the USNO & British astronomical almanacs.
See en.wikipedia.org/wiki/… for a good summary of how JPL produce their ephemerides. Briefly, they integrate the equations of motion, with relativistic corrections. But that requires good data for the body masses and initial locations & velocities. So the generated ephemerides are verified against ground- & space- based observational data. The Chebyshev coefficients are simply the method used to store the generated ephemeride data so that it can be precisely interpolated as necessary. — PM 2Ring 3 hours ago
"The method of special perturbations was applied, using numerical integration to solve the n-body problem, in effect putting the entire Solar System into motion in the computer's memory, accounting for all relevant physical laws [...] As of DE421, perturbations from 343 asteroids, representing about 90% of the mass of the main asteroid belt, have been included in the dynamical model"
 
neat
 
I just learned that Horizons won't let me specify an asteroid as the observation centre. Which is a bit odd, since you can specify a spacecraft, eg STEREO-B space.stackexchange.com/a/56140/38535
Horizons gives you access to planetary system barycentre data from 9999 BC to 9999 AD. Data for the actual bodies covers a smaller time span.
 
10:24 AM
Couldn't find any tool to really visualize special conformal transformations so I made a little one :
 
 
2 hours later…
12:45 PM
Hello everyone, I'm reading Coleman's "Aspects of symmetry". Around page 70 he discuss scale invariance, and states that under a transformation of coordinates $x \rightarrow e^\alpha x$, in order to have a symmetry we need 1) vanishing masses and 2) that fields transform as $f \rightarrow e^{d\alpha} f$, where $d=1$ for bosonic fields and $d=3/2$ for fermionic fields. Anyone can explain me why? Or give me more references?
 
@john the scaling dimension of a field is dictated by it's mass dimension
because if you want the action to be invariant then you at least need the kinetic term for your field to scale with the inverse of what the $\mathrm{d}^nx$ integral measure scales with
the two values you cite are for a scalar and a Dirac fermion in 4d, they are different for different numbers of space-time dimensions
just write down just the kinetic part of the action and apply the scale transformation and you should be able to work out how the specific values come about
 
@ACuriousMind oh ok great, thank you very much
 
 
1 hour later…
1:53 PM
Is there a connection between the jet of a diffeomorphism and the vector field of an isotopy of diffeomorphism?
 
 
3 hours later…
4:24 PM
I have some vague association of ideas in my head to tell me "maybe"
diffeomorphism group is an infinite dimensional Lie group with the vector algebra of TM as a Lie algebra, isotopy of diffeomorphism is a curve in $\mathrm{Diff}(M)$, vectors are defined as jet equivalence of curves, relationship between the jet group and the tangent bundle, jet equivalences can be defined by their evaluation on curves
I am not sure if that is anything tho
also it sounds like it should
 

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