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From: Invisible
Subject: Trivial trigonometry
Date: 24 Nov 2009 10:13:37
Message: <4b0bf821$1@news.povray.org>
A little math help here? Wolfram Alpha is being bloody awkward at me...

A triangle has 3 sides. Suppose that one angle is 90°. Suppose that one 
side is 1 mile long, and the other side is 24 cm long. What are the 
other two angles??


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From: Neeum Zawan
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 10:27:39
Message: <4b0bfb6b@news.povray.org>
On 11/24/09 09:13, Invisible wrote:
> A little math help here? Wolfram Alpha is being bloody awkward at me...
>
> A triangle has 3 sides. Suppose that one angle is 90°. Suppose that one
> side is 1 mile long, and the other side is 24 cm long. What are the
> other two angles??

	That depends on whether one of those sides is the hypotenuse.

-- 
"Graphic Artist seeks Boss with vision impairment."


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From: scott
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 10:28:56
Message: <4b0bfbb8@news.povray.org>
> A little math help here? Wolfram Alpha is being bloody awkward at me...
>
> A triangle has 3 sides. Suppose that one angle is 90°. Suppose that one 
> side is 1 mile long, and the other side is 24 cm long. What are the other 
> two angles??

Google "(24 cm / 1 mile) in degrees".

If you want more accuracy then it's going to depend on whether the 1 mile 
side is the one opposite the 90 degrees or not.

Google:

"asin(24 cm / 1 mile) in degrees"

or

"atan(24 cm / 1 mile) in degrees"


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 10:45:44
Message: <4b0bffa8$1@news.povray.org>
>> A little math help here? Wolfram Alpha is being bloody awkward at me...
> 
> Google "(24 cm / 1 mile) in degrees".

Ah, good old Google calculator. It may not know how to compute the 
Riemann zeta function, but it at least manages to do common math 
operations. :-D

Apparently it's 0.00854446724 degrees, which is about 30 seconds. That's 
some pretty fricken tiny angle!


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From: Fredrik Eriksson
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 10:46:12
Message: <op.u3worblq7bxctx@bigfrog.bredbandsbolaget.se>
On Tue, 24 Nov 2009 16:13:36 +0100, Invisible <voi### [at] devnull> wrote:
> A little math help here? Wolfram Alpha is being bloody awkward at me...
>
> A triangle has 3 sides. Suppose that one angle is 90°. Suppose that one  
> side is 1 mile long, and the other side is 24 cm long. What are the  
> other two angles??

http://en.wikipedia.org/wiki/Right_triangle#Trigonometric_ratios_in_right_triangles



-- 
FE


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 10:56:16
Message: <4b0c0220$1@news.povray.org>
Invisible wrote:

> Apparently it's 0.00854446724 degrees, which is about 30 seconds. That's 
> some pretty fricken tiny angle!

According to Wikipedia:

"20/20 is the visual acuity needed to discriminate two points separated 
by 1 arc minute—about 1/16 of an inch at 20 feet."

So I guess 30 seconds (0.5 minutes) could plausibly be within the range 
of normal human vision then.

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...


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From: Warp
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:00:54
Message: <4b0c0336@news.povray.org>
Fredrik Eriksson <fe79}--at--{yahoo}--dot--{com> wrote:
> On Tue, 24 Nov 2009 16:13:36 +0100, Invisible <voi### [at] devnull> wrote:
> > A little math help here? Wolfram Alpha is being bloody awkward at me...
> >
> > A triangle has 3 sides. Suppose that one angle is 90°. Suppose that one  
> > side is 1 mile long, and the other side is 24 cm long. What are the  
> > other two angles??

> http://en.wikipedia.org/wiki/Right_triangle#Trigonometric_ratios_in_right_triangles

  This is basic trigonometry which is taught in high schools in most places.

-- 
                                                          - Warp


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From: scott
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:01:17
Message: <4b0c034d$1@news.povray.org>
> "20/20 is the visual acuity needed to discriminate two points separated by 
> 1 arc minute—about 1/16 of an inch at 20 feet."
>
> So I guess 30 seconds (0.5 minutes) could plausibly be within the range of 
> normal human vision then.
>
> 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...

Hmm, I can see an object perfectly fine with an angle of 10^-9 degrees.

Being able to see something and discriminate between two points is 
different.


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:05:42
Message: <4b0c0456@news.povray.org>
Warp wrote:

>   This is basic trigonometry which is taught in high schools in most places.

I did say "trivial", didn't I? ;-)

My education didn't include this information. Also, I have no idea how 
many centimeters there are in one mile.


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From: Warp
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:07:46
Message: <4b0c04d2@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> 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...

  Lights can be seen much easier than other details.

-- 
                                                          - Warp


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From: Warp
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:09:31
Message: <4b0c053b@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> My education didn't include this information.

  Did your education include anything?

> Also, I have no idea how many centimeters there are in one mile.

  Nobody is expected to remember factors and numbers, but you are expected
to be able to do the conversion when you know the factors involved.

-- 
                                                          - Warp


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:11:31
Message: <4b0c05b3$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...
> 
>   Lights can be seen much easier than other details.

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.)


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:16:23
Message: <4b0c06d7@news.povray.org>
>> My education didn't include this information.
> 
>   Did your education include anything?

Long division?

Lots and lots of long division?

Like, for years on end?

Let's face it, I went to a school for stupid people, after all. My exam 
results are apparently unprecidentedly high for somebody at that school 
- and I only got a B and two Cs.

>> Also, I have no idea how many centimeters there are in one mile.
> 
>   Nobody is expected to remember factors and numbers, but you are expected
> to be able to do the conversion when you know the factors involved.

Trouble is, while it's easy enough to look up some numbers and do a 
calculation, it's somewhat more tricky to figure out whether your answer 
is actually right (or total gibberish). Hence I asked for assistence. ;-)


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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:20:01
Message: <web.4b0c06c86ad665b96dd25f0b0@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> Warp wrote:
>
> >   This is basic trigonometry which is taught in high schools in most places.
>
> My education didn't include this information.

If you sat GCSEs, it did. Of course, if you haven't really used it since then
it's easily forgotten :)


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From: Darren New
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:43:33
Message: <4b0c0d35@news.povray.org>
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.)

Would you still be able to see it if you intentionally blurred your vision? 
Sure, because the blur makes it bigger, not smaller.

The question is whether you can tell two lights on the same pole apart.

You can see stars that are millions (or more) light years away. That doesn't 
mean you can tell whether it's a binary star or not.

-- 
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: Invisible
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:46:45
Message: <4b0c0df5@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.)
> 
> Would you still be able to see it if you intentionally blurred your 
> vision? Sure, because the blur makes it bigger, not smaller.

And fainter.

> You can see stars that are millions (or more) light years away. That 
> doesn't mean you can tell whether it's a binary star or not.

Sure, they're quite far away (!!), but they're also rather large (!!!), 
and absurdly bright. ;-)


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From: Warp
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 11:51:29
Message: <4b0c0f11@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> > You can see stars that are millions (or more) light years away. That 
> > doesn't mean you can tell whether it's a binary star or not.

> Sure, they're quite far away (!!), but they're also rather large (!!!), 

  Try to calculate how many arc-seconds large the farthest visible stars are.

-- 
                                                          - Warp


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From: Darren New
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 13:16:19
Message: <4b0c22f3$1@news.povray.org>
Warp wrote:
>   Try to calculate how many arc-seconds large the farthest visible stars are.

If my math is right, the closest star would have to have a diameter of about 
4100 times as big as our sun to look the same size as a 24cm street light 
does one mile away.  (Am I the only one that wonders how we managed to mix 
cm with miles?) And that's the *closest* star.

No, I don't remember why I started calculating that.

-- 
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 13:16:38
Message: <4b0c2306$1@news.povray.org>
Invisible wrote:
> Sure, they're quite far away (!!), but they're also rather large (!!!), 
> and absurdly bright. ;-)

Yep. It would be interesting to figure out how big vs how far away it would 
have to be. I mean, the moon is much smaller, the sun is much larger, but 
they both look the same size. Actually, I guess it's linear, so it isn't too 
hard to calculate.

By the way, I'm pretty sure stars aren't all that bright. I think it's just 
because they're large that they seem bright. I.e., per square inch, I don't 
think they're a lot brighter than what you can build on earth easily. 
(Brighter than street lights, certainly.)

-- 
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: Warp
Subject: Re: Trivial trigonometry
Date: 24 Nov 2009 13:29:08
Message: <4b0c25f4@news.povray.org>
Darren New <dne### [at] sanrrcom> wrote:
> By the way, I'm pretty sure stars aren't all that bright. I think it's just 
> because they're large that they seem bright. I.e., per square inch, I don't 
> think they're a lot brighter than what you can build on earth easily. 
> (Brighter than street lights, certainly.)

  I think that getting something to be 6 million times brighter than the
Sun can be pretty hard...

http://en.wikipedia.org/wiki/Cygnus_OB2-12

-- 
                                                          - Warp


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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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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 06:35:01
Message: <web.4b13acc76ad665b96dd25f0b0@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> OK, so according to the best data I could get my hands on, Alpha Centuri
> A is about 430 light years away

Um, I'm pretty sure that should be 4.3 lightyears.

http://en.wikipedia.org/wiki/Alpha_centauri

That will make your numbers a little more sensible. There are very few naked-eye
stars that are as far as 400 lightyears - only highly luminous giants like
betelgeuse.

:)


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 06:38:51
Message: <4b13aecb$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
> 
> Um, I'm pretty sure that should be 4.3 lightyears.
> 
> That will make your numbers a little more sensible. There are very few naked-eye
> stars that are as far as 400 lightyears - only highly luminous giants like
> betelgeuse.
> 
> :)

EPIC FAIL. >_<

Maybe I should just go away and live in a box somewhere. :-S


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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 06:40:01
Message: <web.4b13ad866ad665b96dd25f0b0@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> 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.

Entirely. There are over a thousand stars visible to the naked eye.

http://en.wikipedia.org/wiki/Naked-eye_stars#Naked_eye_in_astronomy

There is nothing like spending a couple of hours on your back in a field with a
truly dark sky - it feels like there are far more than mere thousands visible!

:o


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 06:45:53
Message: <4b13b071$1@news.povray.org>
Bill Pragnell wrote:
> Invisible <voi### [at] devnull> wrote:
>> 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.
> 
> Entirely. There are over a thousand stars visible to the naked eye.
> 
> http://en.wikipedia.org/wiki/Naked-eye_stars#Naked_eye_in_astronomy
> 
> There is nothing like spending a couple of hours on your back in a field with a
> truly dark sky - it feels like there are far more than mere thousands visible!
> 
> :o

But where do you have to go? Outer Mongolia?

(Also... where the hell *is* that anyway?!)


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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 07:15:01
Message: <web.4b13b6596ad665b96dd25f0b0@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> But where do you have to go? Outer Mongolia?

Well, I bet the skies are great there(!), but at least 50 miles from a large
town or city would do in the UK. Simply making sure you can't see an artificial
light source directly by eye will make a big difference. Coastline works well
because you've only got to worry about distance from towns in half as many
directions. Wilderness such as moorland or mountains works best of course
(although steep hills will obstruct part of the sky), but I'm sure you could
find somewhere suitable within a short drive of MK. Also, winter is best because
the cold air holds less moisture and is therefore clearer. Try to make sure the
moon isn't up either, it can produce a surprising quantity of light pollution,
especially when full!

Oh, and pick a cloudless night ;-)


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From: scott
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 07:47:26
Message: <4b13bede$1@news.povray.org>
> 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.

http://www.astro-travels.com/pictures/Europe-Light-Pollution.jpg

On the above map my house is on the border of a green/yellow region and I 
can make out a huge number of stars on a clear night, the Milky Way is also 
just barely visible on a really good night.  I don't know exactly where MK 
is on that map, but it looks a bit red/orange around there :-(

Don't forget you need to go outside for at least 20 minutes or so for your 
eyes to get fully adjusted to the dark, initially it might look like only a 
dozen or so stars are visible, but after a few minutes you will see hundreds 
more.

BTW if you're interested, one of the brightest "stars" in the sky at the 
moment is actually Jupiter.


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 07:54:37
Message: <4b13c08d$1@news.povray.org>
>> 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.
> 
> http://www.astro-travels.com/pictures/Europe-Light-Pollution.jpg
> 
> On the above map my house is on the border of a green/yellow region and 
> I can make out a huge number of stars on a clear night, the Milky Way is 
> also just barely visible on a really good night.

Aren't we *in* the Milky Way?

> I don't know exactly 
> where MK is on that map, but it looks a bit red/orange around there :-(

I would suggest that MK is the small red dot just NW of London. (Or if 
it isn't, it's in that general direction.)

> Don't forget you need to go outside for at least 20 minutes or so for 
> your eyes to get fully adjusted to the dark, initially it might look 
> like only a dozen or so stars are visible, but after a few minutes you 
> will see hundreds more.

We drove to and from work through lots of wilderness, and at this time 
of night it's quite dark even at 5PM. Many of the roads aren't lit.

I don't recall where we get dragged to on our school caving trips, but 
we seemingly had to drive for many hours along winding rounds lined with 
dry stone walls before reaching the nearest building with electricity.

> BTW if you're interested, one of the brightest "stars" in the sky at the 
> moment is actually Jupiter.

Any ideas what the visual angle for that is? ;-)


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From: scott
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:06:19
Message: <4b13c34b$1@news.povray.org>
> Aren't we *in* the Milky Way?

Yes, and it's quite a flat disc, so looking out from Earth along the plane 
of the disc you see a lot more stars than looking out perpendicular to it, 
this looks like a brighter band going across the sky.

>> BTW if you're interested, one of the brightest "stars" in the sky at the 
>> moment is actually Jupiter.
>
> Any ideas what the visual angle for that is? ;-)

Wikipedia tells me the radius is 71500 km, Stellarium tells me it's 5.224 AU 
away from us, so googling "2*71500 km / 5.224 AU in degrees" gives 0.01 
degrees.


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:15:39
Message: <4b13c57b$1@news.povray.org>
>> Aren't we *in* the Milky Way?
> 
> Yes, and it's quite a flat disc, so looking out from Earth along the 
> plane of the disc you see a lot more stars than looking out 
> perpendicular to it, this looks like a brighter band going across the sky.

I will admit I don't know much about the geometry of our galaxy, but I 
was under the impression that the disk is hundreds of billions of light 
years "thick", it's just that it's quadrillions of light years across as 
well. The point being, the disk is many million stars thick, and so we 
should see them in just about every direction we look.

>>> BTW if you're interested, one of the brightest "stars" in the sky at 
>>> the moment is actually Jupiter.
>>
>> Any ideas what the visual angle for that is? ;-)
> 
> Wikipedia tells me the radius is 71500 km, Stellarium tells me it's 
> 5.224 AU away from us, so googling "2*71500 km / 5.224 AU in degrees" 
> gives 0.01 degrees.

So... about 36 seconds of arc. Man, that's pretty small.


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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:20:01
Message: <web.4b13c6376ad665b96dd25f0b0@news.povray.org>
"scott" <sco### [at] scottcom> wrote:
> > Aren't we *in* the Milky Way?
>
> Yes, and it's quite a flat disc, so looking out from Earth along the plane
> of the disc you see a lot more stars than looking out perpendicular to it,
> this looks like a brighter band going across the sky.

This is a pretty awesome photo of the whole thing:

http://en.wikipedia.org/wiki/File:Deathvalleysky_nps_big.jpg

Not exactly what you'd see with the naked eye but it gives you the idea.

> >> BTW if you're interested, one of the brightest "stars" in the sky at the
> >> moment is actually Jupiter.
> >
> > Any ideas what the visual angle for that is? ;-)
>
> Wikipedia tells me the radius is 71500 km, Stellarium tells me it's 5.224 AU
> away from us, so googling "2*71500 km / 5.224 AU in degrees" gives 0.01
> degrees.

Jupiter and Saturn are particularly easy to pick out, because they're big enough
to be actual discs rather than points like regular stars. And if you can hold
binoculars steady enough you'll just about see Saturn's rings.


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:22:00
Message: <4b13c6f8$1@news.povray.org>
Bill Pragnell wrote:

> This is a pretty awesome photo of the whole thing:
> 
> http://en.wikipedia.org/wiki/File:Deathvalleysky_nps_big.jpg
> 
> Not exactly what you'd see with the naked eye but it gives you the idea.

This is awesomer:

http://en.wikipedia.org/wiki/File:Perseid_Meteor.jpg

Here in the name of God does the night sky actually look like this?!


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From: scott
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:23:21
Message: <4b13c749$1@news.povray.org>
> I will admit I don't know much about the geometry of our galaxy, but I was 
> under the impression that the disk is hundreds of billions of light years 
> "thick",

It's much smaller than you think:

http://en.wikipedia.org/wiki/Milky_way

> So... about 36 seconds of arc. Man, that's pretty small.

It's still one of the very few objects in the sky that allows you to 
actually see its shape with a good pair of binoculars or a small telescope 
though.


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:40:52
Message: <4b13cb64$1@news.povray.org>
>> I will admit I don't know much about the geometry of our galaxy, but I 
>> was under the impression that the disk is hundreds of billions of 
>> light years "thick",
> 
> It's much smaller than you think:
> 
> http://en.wikipedia.org/wiki/Milky_way

Heh, "only" 100,000 light years across and 1,000 light years thick. 
Well, that's the trouble when you start dealing with Really Huge 
Numbers, see?

There's a reason why would talk about 4 Terabytes rather than 
4,000,000,000,000 bytes - it's frighteningly easy to get the number of 
digits wrong! ;-)

Obligatory XKCD:

http://xkcd.com/558/


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From: scott
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:40:59
Message: <4b13cb6b$1@news.povray.org>
> This is a pretty awesome photo of the whole thing:
>
> http://en.wikipedia.org/wiki/File:Deathvalleysky_nps_big.jpg
>
> Not exactly what you'd see with the naked eye but it gives you the idea.

I always wonder how they get these type of photos.

I mean this must be a pretty long exposure to get that detail?  But since 
the Earth is rotating, either the ground or the sky is going to get motion 
blurred.  Is this a photoshop of two images, or can they really get a photo 
like that in one shot?


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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:45:00
Message: <web.4b13cb7d6ad665b96dd25f0b0@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> This is awesomer:
>
> http://en.wikipedia.org/wiki/File:Perseid_Meteor.jpg
>
> Here in the name of God does the night sky actually look like this?!

Well, that's an even longer exposure than the one I posted (you can tell by the
way the stars are slightly elongated), so no, that's not exactly what you'd see
by eye either. But similar!

A shame there's only one meteor visible there, I was expecting more...


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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:45:01
Message: <web.4b13cc0c6ad665b96dd25f0b0@news.povray.org>
"scott" <sco### [at] scottcom> wrote:
> > I will admit I don't know much about the geometry of our galaxy, but I was
> > under the impression that the disk is hundreds of billions of light years
> > "thick",
>
> It's much smaller than you think:
>
> http://en.wikipedia.org/wiki/Milky_way

I always remember galactic vital statistics by knowing all the lyrics to this:

http://en.wikipedia.org/wiki/Galaxy_song

:-)


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:47:45
Message: <4b13cd01$1@news.povray.org>
> I always remember galactic vital statistics by knowing all the lyrics to this:
> 
> http://en.wikipedia.org/wiki/Galaxy_song
> 
> :-)

Is that something like the song about the table of elements?


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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:55:01
Message: <web.4b13cdfb6ad665b96dd25f0b0@news.povray.org>
"scott" <sco### [at] scottcom> wrote:
> > This is a pretty awesome photo of the whole thing:
> >
> > http://en.wikipedia.org/wiki/File:Deathvalleysky_nps_big.jpg
> >
> > Not exactly what you'd see with the naked eye but it gives you the idea.
>
> I always wonder how they get these type of photos.
>
> I mean this must be a pretty long exposure to get that detail?  But since
> the Earth is rotating, either the ground or the sky is going to get motion
> blurred.  Is this a photoshop of two images, or can they really get a photo
> like that in one shot?

I'm not sure. The fact that it's a nearly-complete panorama makes it even more
complicated - I guess it must have been unwrapped from a fisheye.

I'd think it was a single shot. I bet you could get away with up to a minute of
exposure, and it's very wide angle so any movement would be less noticeable.

Any expert photographers here want to comment?


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From: Bill Pragnell
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:55:01
Message: <web.4b13ce426ad665b96dd25f0b0@news.povray.org>
Invisible <voi### [at] devnull> wrote:
> > I always remember galactic vital statistics by knowing all the lyrics to this:
> >
> > http://en.wikipedia.org/wiki/Galaxy_song
> >
> > :-)
>
> Is that something like the song about the table of elements?

Similar, but more catchy ;-)


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From: Invisible
Subject: Re: Trivial trigonometry
Date: 30 Nov 2009 08:56:40
Message: <4b13cf18$1@news.povray.org>
>> Is that something like the song about the table of elements?
> 
> Similar, but more catchy ;-)

Heh. I still enjoy listening to TMBG exclaim that "the Sun is a mass of 
incandescent gas". ;-)

BUT EVEN WHEN IT'S OUT OF SIGHT THE SUN SHINES NIGHT AND DAY!


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