@PM2Ring Telescope quality. It's actually my goal to make a Newtonian telescope.

@PM2Ring Is it bad form to try to get ahold of those people? Not sure what kind of etiquette is implied on SE.

@Beliod Have a look at the existing answers on Astronomy. Some of them mention excellent books on the topic.

FWIW, when I was in my teens, I helped a friend grind a 6" mirror for a Newtonian scope. But he moved to America before the telescope was finished.

When grinding a telescope mirror, you first grind a spherical mirror. And then you change the grinding process to convert it to a parabolic shape.

Testing.

Alright, it lets me message again!

@Beliod It's called a mirror blank. There are various suppliers, eg telescopemirrorblanks.com Good blanks aren't cheap. 50 years ago, you could save quite a bit of money by grinding your own mirror. That's not the case these days, unless you're grinding a big one. But with practice, you should be able to produce a better mirror than an equivalent commercial mirror.

So it's a good idea to start off making a small mirror. And if it works ok, and you enjoyed doing it, try for something larger.

But keep browsing the telescope-making questions on the Astronomy site. I'm just repeating stuff that's already written there. :)

@Beliod No worries. There is an Astronomy chat room, but it's very quiet. Maybe take a look at some astronomy / telescope forums to see what mirror blank suppliers they're currently recommending.

I guess you could post a comment on one of Florin's answers to ask if he has any recommendations.

How does Github have so much space for so much storage for so many users? I mean, it must cost a lot of money to supply the world with A LOT of free storage.

It's a stupid question, they make enough money to buy storage...

Storage is cheap these days.

That's why all those dodgy sites that allow you to upload copyright material can survive on advertising revenue plus a few paid subscriptions.

Hmm, not like the days where I had to buy 1MB memory cards for my playstation

How does one cross-reference equations in mathjax? I have "\label{}"ed an equation as I would in LaTeX, but I can't reference it using "\ref{}" What am I missing?

I also have a LaTeX problem.

What command needs to be used to type the title of a document so that the title looks like a title?

in MathJax or in LaTeX?

I mean, on this site or in a latex document?

\title{Title Name here} and then later on do \maketitle. But it depends on your document style

How do I make packaging for product? I was thinking of buying cardboard boxes (in the favored color) and then putting some type of custom stickers with the brand name, info and so on. Anyone have better ideas?

I can also spray the texts over the box

but spraying would be difficult and I can't achieve gradient colors etc

Is it possible for two world lines connecting two different events to have different lengths?

I want to say no, then the proper time between two events is just the length of the unique world line that connects them

@Charlie Depends on whether you're in Minkowski space or on an arbitrary spacetime :P

I was thinking in the context of minkowki space

I want to say that since the spatial and temporal contributions are opposite signs, any different world lines will "cancel out", in a way, the extra distance and the total length will be the same

Then there is always a unique geodesic connecting two events - the straight line between them.

Not a unique world line

Ah I see why unique is wrong

the proper time between two events is the length of the unique geodesic

So in this picture, the length of the world line R and G is the same?

In general not

if this is minkowski

but R is a geodesic and G is not

oh

ohh

No, not even in Minkowski. Note that if you draw G a bit more extreme as two pieces at 45° degrees, then it has length 0 because it consists of two lightlike pieces, but R has clearly not length 0.

Ah y eah

So the proper time is the length of a geodesic connecting two events

Not just any random world line we can draw between them

yes (but there are spacetimes where the notion of "proper time between two events" is ill-defined because there is more than one geodesic connecting them)

Are those just spacetimes with a more general metric?

So in GR geodesics are not necessarily unique

I could believe that then, since the sphere doesn't have unique geodesics iirc

Yes, I was just about to give the sphere example

It's both about the metric and about the topology

I see

tyvm

Actually if I could ask one more point, you say "there are spacetimes where the notion of "proper time between two events" is ill-defined because there is more than one geodesic connecting them", but if there exists more than one geodesic connecting two events, aren't they necessarily the same length and therefore there's no ambiguity defining the proper time?

Since if one is "longer" than the other, it's no longer the shortest distance and so no longer a geodesic

@Qmechanic re: physics.meta.stackexchange.com/questions/12986/… (can't comment there since it's locked):

physics.stackexchange.com/posts/561464/revisions shows it was edited before it was closed and migrated to Meta.

Not sure if the last close voter(s) voted to migrate it; it might even be that it got three votes for migration, then it was edited and then it got two other close votes.

@Glorfindel : Ah. Ok. Anyway, no lasting harm done by the meta migration.

@Charlie Again, look at the Riemannian 2-sphere: For two points that aren't antipodes, there are two geodesics with different lengths - one going clockwise around the great circle the points lie on and one going counterclockwise around the great circle.

You can by convention define the distance to be the "shorter" of the two, of course

Then, on a globally hyperbolic spacetime, this makes "Lorentzian distance" a well-defined function between all pairs of points.

Hmm

Ahh, I think I'm confusing myself by trying to think of "shortest distance" in a global sense

I was unhappy that two paths to the same point of the sphere are considered geodesics even though one is longer, but that isn't the point, the only requirement is that the particle is travelling along a geodesic path

So it's better to think of it as a constraint on local motion rather than "you always have to take the shortest path between event A and B"

Yes, exactly!

:D

Local conditions are always best rly

How do I calculate the trajectory of an ellipsoid rolling without slipping or friction on a plane?

I know how to do the case where two of the axes are equal because of symmetry considerations

t seems like quite a hairy problem to answer on chat, but the answer's available on the internet (not that I advise looking it up necessarily)

I tried looking it up but couldn't find it

I think I might be using the wrong search terms

Does this help?

I found this kybernetika.cz/content/2016/2/209/paper.pdf

but I don't understand half the words in it

The link I sent you is what you want, I think :)

I started thinking about this after watching an egg nearly roll off the table

I wanted to know if there's a shape of egg that would allow it to roll infinitely far with no starting momentum

That's a very interesting question..

At the end of the paper I sent you, they have the (horrible!) differential equation that needs to be solved

This link might also be interesting: lockhaven.edu/~dsimanek/scenario/….

hello