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From: Darren New
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 16:52:14
Message: <4b0c558e$1@news.povray.org>
Warp wrote:
>   I think that getting something to be 6 million times brighter than the
> Sun can be pretty hard...

Note that I said "per square inch."   Sure, if your star is 92x as big as 
the Sun, it's going to be very bright in an absolute sense.

100x the heat of the *middle* of the Sun:
http://www.msnbc.msn.com/id/11732814/

Even the middle of lightning gets 2x as hot as the (presumedly, surface of 
the) star you referenced.

As I say, it's all about square inches.  The *middle* of the sun is 
15,000,000K. The surface is 15,000K. Big difference.

Since a star's surface is essentially a black body, it's pretty easy to 
calculate the temperature of it, and other black bodies the same color will 
be about the same temperature. So the hottest parts of lava are about the 
temperature of the sun's surface, and the hottest parts of a propane flame 
are about the same temperature as a blue star.

-- 
Darren New, San Diego CA, USA (PST)
   You know the kamikaze monsters in Serious Sam
     with the bombs for hands, that go AAAAAHHHHHHHH!
   I want that for a ring tone.


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From: Darren New
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 17:02:30
Message: <4b0c57f6$1@news.povray.org>
Darren New wrote:
> As I say, it's all about square inches.  The *middle* of the sun is 
> 15,000,000K. The surface is 15,000K. Big difference.

Sorry. Should have been 5K, not 15,000K.  Indeed, ignore that whole sentence.

Anyway, Sun's surface temperature: 9800F.

Industrial tools: 25,000F.

http://www.x20.org/industrial/plaz50.htm

For $1300 you can have something >2x the heat of the sun in your hand.


-- 
Darren New, San Diego CA, USA (PST)
   You know the kamikaze monsters in Serious Sam
     with the bombs for hands, that go AAAAAHHHHHHHH!
   I want that for a ring tone.


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From: somebody
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 21:48:27
Message: <4b0c9afb$1@news.povray.org>
"Invisible" <voi### [at] devnull> wrote in message
news:4b0c0220$1@news.povray.org...

> I just noticed the other night that as I passed under a sign telling me
> the motorway exit was in 1 mile, I could already see the green traffic
> lights beyond the exit. And those lights can't be much more than 24cm
> across...

Now calculate the angular extent of most distant star you can see with the
naked eye and explain your mistake <g>.


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From: somebody
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 21:50:50
Message: <4b0c9b8a$1@news.povray.org>
"somebody" <x### [at] ycom> wrote in message news:4b0c9afb$1@news.povray.org...

> Now calculate the angular extent of most distant star you can see with the

Never mind. I should learn to read the rest of the thread.


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From: scott
Subject: Re: Trivial trigonometry
Date: 25 Nov 2009 02:52:42
Message: <4b0ce24a$1@news.povray.org>
> This is what I'm interested in. Are the lights visible from this distance 
> because they glow? Or would any old object be visible from such a 
> distance? (Assuming it wasn't the middle of the night, obviously.)

The fact that it is dark helps a lot, obviously your eye is much more 
sensitive then.

According to this page:

http://math.ucr.edu/home/baez/physics/Quantum/see_a_photon.html

A rod in your eye must receive about 5-9 photons over 100 ms to tell your 
brain that something is there.  That is a pretty damn small amount of light.


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 25 Nov 2009 04:27:23
Message: <4b0cf87b@news.povray.org>
scott wrote:

> According to this page:
> 
> http://math.ucr.edu/home/baez/physics/Quantum/see_a_photon.html
> 
> A rod in your eye must receive about 5-9 photons over 100 ms to tell 
> your brain that something is there.  That is a pretty damn small amount 
> of light.

And THAT is why when it's dark, everything seems "sparkly", I presume.


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From: SharkD
Subject: Re: Trivial trigonometry
Date: 25 Nov 2009 21:09:57
Message: <4b0de375$1@news.povray.org>
On 11/24/2009 11:11 AM, Invisible wrote:
> This is what I'm interested in. Are the lights visible from this
> distance because they glow? Or would any old object be visible from such
> a distance? (Assuming it wasn't the middle of the night, obviously.)


I would guess that stars are significantly distant enough that their 
angular diameter is too tiny to be visible without the aid of the light 
they give off.


--
Michael Horvath
mik### [at] gmailcom
http://isometricland.com


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 06:05:05
Message: <4b13a6e1$1@news.povray.org>
OK, so according to the best data I could get my hands on, Alpha Centuri 
A is about 430 light years away, and is 1.227 times the radius of our 
Sun, so about 853,400 km across. 430 light years is 4.068x10^15 km.

So, if a triangle has sides of 4.068x10^15 km and 853,400 km on either 
side of the right angle, what *the hell* is the small angle?!

By the looks of things, dividing these two distances should give me the 
tangent of the angle I seek.

   853,400 km / 4.068x10^15 km = 2.098x10^-10

   arctan 2.098x10^-10 = 1.2020x10^-8 degrees = 4.327x10^-5 arc seconds

This is a *stupidly tiny number*. If you asked POV-Ray to render this, 
and you sent out a million, billion, trillion rays, every single damned 
one would completely miss such a tiny object. It seems astonishing to me 
that such an absurdly minute object is visible at all - but Wikipedia 
claims it is...


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From: scott
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 06:16:06
Message: <4b13a976@news.povray.org>
> This is a *stupidly tiny number*. If you asked POV-Ray to render this, and 
> you sent out a million, billion, trillion rays, every single damned one 
> would completely miss such a tiny object. It seems astonishing to me that 
> such an absurdly minute object is visible at all - but Wikipedia claims it 
> is...

Good job the real world isn't a backward raytracer then :-)

I suspect even a true point source (ie no physical size) was sending out the 
same amount of light from that distance, you would be able to see that too.


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 06:24:10
Message: <4b13ab5a@news.povray.org>
>> This is a *stupidly tiny number*. If you asked POV-Ray to render this, 
>> and you sent out a million, billion, trillion rays, every single 
>> damned one would completely miss such a tiny object. It seems 
>> astonishing to me that such an absurdly minute object is visible at 
>> all - but Wikipedia claims it is...
> 
> Good job the real world isn't a backward raytracer then :-)

Yeah. Because then we wouldn't be able to see stars... which... would be 
bad... somehow. I'm sure. :-)

I guess it's simply the case that all the light gets focused onto a 
point smaller than a single light sensor, which never the less registers 
that there's some light there. (Also, presumably no lense can ever be 
optically perfect...)

The part that really puzzles me as that even on the clearest, most 
cloudless night, there are, like, maybe 3 stars visible in the entire 
sky. And yet mankind has names for hundreds and hundreds of stars, many 
of which are claimed to be "visible to the naked eye".

I can only presume this must be due to light pollution. (I'm not saying 
that MK's street lighting is inefficient, but... you *can* tell where 
the city is from about 15 miles away just by the fact that one entire 
side of the night sky is glowing at the exact wavelength of the Sodium 
D-line...) Still, even on school caving trips in the middle of nowhere, 
I don't recall seeing many stars in the night sky. I presume they're 
still there, we just can't see them any more.

> I suspect even a true point source (ie no physical size) was sending out 
> the same amount of light from that distance, you would be able to see 
> that too.

Well, photons are quantum, right?

(Interestingly, I'm told it *is* possible to make a light source that 
emits individual photons, one at a time, on que. And that when you do 
this, things like the double-slit experiment still show multiple waves 
interferring and reinforcing - despite this being obviously 
impossible... Wave-particle duality is weird!)


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