thx

it's such a monstrosity

it's basically just me taking the papers I was a part of and stitching them together

@Semiclassical interesting correspondence with one of the early classic scifi stories, frankenstein.

it's an interesting comparison, though I don't think Mary Shelley read Copernicus much

@Semiclassical lol expert plastic surgery is what makes (many) celebrities so beautiful :P

@Semiclassical theres no shame in that and many phd theses are written in a similar fmt, just ran across one recently, trying to remember which

in modern parlance what copernicus did was called connecting the dots™...

What's interesting in retrospect is how effective the Ptolemaic model was, despite it being evidently artificial in certain ways

I think I saw a remark somewhere to the effect that part of the reason it works so well is that the equant approximately captures how the sun serves as a focus for the orbits of the planets

which is worth remembering: the orbits of Newton were not merely ellipses (i.e. not circular) but ellipses with the sun as their focus

reminds me of a semifamous quote, the map is not the territory...

hmm, this is an interesting article: adsabs.harvard.edu/full/2005JRASC..99..120B

punch line being, I think: there's no equant in the Kepler orbits, but if you consider the 'empty focus' then you get a pretty good approximation for the equant

which again points to why the ptolemaic model would've been so effective, namely that it's most artificial feature served as a good approximation of the actual motion

new models are made out of the bits and pieces of old ones, rearranged, even Kepler said so :)

(i guess a second punchline is that the simplest mechanical approximation for Kepler's laws is...the Ptolematic model)

Hey guys you know the lorentz transformations

How do they not contradict eachother?

@JakeRose math

Because the normal and the inverse are both multiplied by the lorentz factor

So shouldnt they both be bigger tha the other? Just going of multiplying by the lorentz factor makes it larger

work out the composition of two inverse Lorentz transform

you'll find out that it's the identity matrix

Only just started matrices in maths so could you give another explanation?

I think the more pertinent point that what enters into the lorenz transformation is the boost velocity $v$

you don't need to use matrices

Just consider this :

to go from a reference from at rest, to one at motion +v, to one at rest again

involves a boost by +v and then by -v

same magnitude of boost velocity in both cases

Then apply a second Lorentz transformation

The + coming from the fact that the speed is the inverse

Then replace $t'$ and $x'$ in this expression

You'll find out that $t'' = t$

and shake until equivalent

and $x'' = x$

yeah

give it a good shake

@Semiclassical dont quite follow that. there are probably fairly simple machines that can generate elliptical paths.

well, note that they're comparing with the devices which were in fact used

ones which involved rather complicated elliptic pulleys in order to work

There's a standard trick to draw ellipses

@Semiclassical ok

Here's the complicated machinery to do it

A string

If you spply the lorentz transform again doesnt that imply that you are jumping to a frame which is stationary relative to the already stationary frame?

@Slereah lol

only problem with that is that I don't know if you get the same time dependence as you'd get for an orbit

i.e. Kepler's second law

was thinking how there exist things called "elliptical gears" but havent looked into it much

to sketch the trajectory is one thing. to display the trajectory in time is another

anyways. the mechanical models you'd use were apparently kinda complicated

and the point the author is making is that a simpler arrangement is one predicated on the fact that the motion around the empty focus (in the Kepler model) is well-approximated by the equant (in the Ptolemaic model)

so you can build a pretty good model for kepler's laws if you use a ptolemaic device

@Semiclassical not sure when the 1st machines with elliptical elements appeared but they might have been possible to create much earlier using the available technology. ie some of it has to be seen as "failure of imagination" so to speak. also shows how our models are influenced by existing technology ("at hand") aka "clockwork universe" etc

of course, that's a good model insofar as it approximates the trajectory

don't give too much shit to the ptolemaic model

It works, and it's about as correct as the copernician one from the point of view of modern physics

Saying that the sun is at the center is as wrong as saying that the earth is

eh. I'd say they were wrong in different ways

what the Ptolemaic model did a very good job of was approximating the phenomena observed

@BalarkaSen Abby Martin works for Venezuela l m a o

whereas the Copernican model has to do some complicated gymnastics to get similar agreement iirc

on the other hand, in the Copernican model you have a notion not just of the individual orbits, but of how they should all fit together into a solar system

Plus really, people get way too mad at epicycles

When they're just Fourier series

I think people just talk about epicycles too much

You don't see people getting mad at engineers for Fourier series

for one thing: yeah, Fourier series

for another, the notion of 'epicycles upon epicycles' is a myth

Yeah I don't think they went beyond just a few

I mean they were observing with the naked eye

You don't need a lot for that kind of precision

as far as I know, the ptolemaic model only uses one epicycle per planet

anything beyond that was rare. the calculations for that were beyond the reach of the time

it's easy to forget just how hard it was to make lots of calculations in those days, before even the invention of logs

That's what grad students are for, @Semiclassical

lol

what would the medieval equivalent of a grad student have been

JOSEPHUS, COMPUTE THE ORBIT OF THE MOON TO 6 EPICYCLES

a scribe?

I think a lot of the people involved were like church people

So use the Church hierarchy to find out

Marginal comment: "Just show him the results of 1 epicycle, he won't know the difference."

they would have needed more epicycles to describe the moons

I think that's what people refer to when they say "epicycles upon epicycles"...?

not really, no

like Galileo saw the moons of Jupiter and thought it wouldn't really make sense to keep making epicycles

first off, at that point in time you really could only see one moon

I'm talking about the point in time we moved beyond the ptolomic model

so no point in constructing epicycles upon epicycles for something you can't observe

eh, maybe. I'm not so clear on the timeline there

@Semiclassical obviously you don't know nerds

lol

During Galileo's time, they still believed in the Earth being the center of the "universe", and one of the motivations of him believing in a Copernican model was the moons of Jupiter afaik

It's even worse, really

Back then people still believed in celestial spheres

to model the moons of Jupiter with the Ptolomic model would require more epicycles

like first level was the planets, second level would be the moons

so epicycles on top of epicycles

:D

@Semiclassical galileo is famous for spotting multiple moons (of jupiter) with a telescope. right?

right

I'm not sure what people did in terms of 'models' for the moons of Jupiter

they must've gotten to that eventually, to be sure

but I've no idea how long that took

For a start people weren't that sure about them existing

Galileo's telescope was fairly shitty back then

Lenses were still in the early days

well he got to name them

at least, people later named them the "Galilean moons" after him

Maybe Jesus of Galilee discovered them

possible

more generally, i'm not sure how the history of observational astronomy progressed

i mean, after a certain point it had gotten very far along mathematically---hence why you could infer the existence of certain planets by looking for perturbations

So at some point they were in a position to do things like model the orbits of Jupiter's moons

but I've no idea when that would be

might be a good question for the History site

That would have to be post-Newton...but I think by Newton's time the Copernican model was more or less accepted?

No

Newton was the one that made the Galilean model accepted by everyone

the copernican model is more of a transitional thing

Guys

With lorentz transformations what are actually doing?

I don't think it 'replaced' the Ptolemaic model so much as it indicated that the Ptolemaic model wasn't the last word on the subject

as far as practical observational astronomy went, I don't know how the transition from Ptolemaic to Newtonian proceeded

Most people didn't really need all that much from observational astronomy

@JakeRose that's a pretty broad question...a Lorentz Transformation is simply a transformation of coordinates in a specific manner

just to know the coordinates of which celestial body at which time

right

With regards to special relativity

and know how to do astrology :P

have you taken a look at the wikipedia article? en.wikipedia.org/wiki/Lorentz_transformation

@JakeRose A Lorentz transformation mathematically describes the change from one frame of reference to another one moving at a different velocity... if that helps

I link not because anything here seems amiss in the room, but because chat moderation has been a topic of conversation around here sometimes.

(Often, admittedly, when I bring it up....)

I think John already posted it and got it on the star board

not to be confused with starboard

...which is going to confuse me now

But yeah, the reminder is good.

@DavidZ Oh. I see now. Do you mind editing John's message so it reads as the question's title, not just the link? (I can't imagine many find the link's text compelling in the way they might that title.)

That reminds me, I got about halfway through drafting a message to somehow post around here--maybe in the meta room, maybe as a meta post--but then life happened and the rooms were humming along pretty nicely so I back-burnered it. But now I feel like I should get back to it. Mind taking a look?

and sure I don't mind taking a look at whatever you've got, if you like