Sun 500 miles away

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

Moderators: gmalivuk, Moderators General, Prelates

SheffJames
Posts: 24
Joined: Sun Feb 12, 2012 11:32 pm UTC

Sun 500 miles away

Postby SheffJames » Wed Mar 07, 2012 3:20 am UTC

Found this on the good old internets and, after a brief wikipedia, I cant see where the mistake is.

For reference, I know Landover are a parody, I'm not for one second suggesting the sun is that close and, while this isn't homework (Im in my 30s) it is close enough to possibly count. My science just isn't up to seeing whats wrong with it (you know - its hard being a social sciences graduate on this forum :D )

Here is the proof:

To start off with, the sun is hot enough to glow yellow, so we can use Wein's Displacement Law to determine the temperature.

Wein's Displacement Law:
Peak Wavelength in meters = displacement constant / temperature in Kelvin

Yellow light has a wavelength between 570nm and 580nm, so we'll solve for 575nm. Since we are working with nanometers rather than meters, we'll simplify the math by multiplying the displacement constant by 10^9.

575 = 2897768.5/T
575 * T = 2897768.5
T = 2897768.5/575
T = 5039.6° K (8611.6° F)

So the sun is about 5039.6° Kelvin.

Now, the average temperature of the earth is 59° F, or about 288° K. The mean temperature gradient of the troposphere is 6° K/km, so let's solve for the distance.

d = (5039.6 - 288)/6
d = 791.9 km (491.1 miles)

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26830
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Sun 500 miles away

Postby gmalivuk » Wed Mar 07, 2012 3:57 am UTC

It's based on the false assumption that the tropospheric temperature gradient should be linear all the way to the sun. (It's not even linear all the way through the troposphere, which is why they had to use the average there.)
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Copper Bezel
Posts: 2426
Joined: Wed Oct 12, 2011 6:35 am UTC
Location: Web exclusive!

Re: Sun 500 miles away

Postby Copper Bezel » Wed Mar 07, 2012 4:04 am UTC

(Ninja'd by someone with an actual science degree.)

This is coming from an English lit graduate, but I'm pretty sure that the above calculation assumes that the sun and the Earth are flat planes facing one another separated by n miles of troposphere, that the heat energy is carried by that medium, and that the sun doesn't output any visible light. So n then equals 500. But all of the heat we get is of course the result of irradiation, mostly in the visible spectrum, and temperature gradients are meaningless. (Of course, the surface temperature of the Earth is also influenced by other factors, like the fact that our atmosphere is more opaque to the infrared radiation that warm objects radiate than to the visible radiation they receive from the sun and so on, but the calculation actually ignores radiation completely, so there's no sense getting into that.)
So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

she / her / her

User avatar
Proginoskes
Posts: 313
Joined: Mon Nov 14, 2011 7:07 am UTC
Location: Sitting Down

Re: Sun 500 miles away

Postby Proginoskes » Wed Mar 07, 2012 7:07 am UTC

gmalivuk wrote:It's based on the false assumption that the tropospheric temperature gradient should be linear all the way to the sun.


See the "Textbook publishing ills" thread for another example of this same fallacy. An actual textbook problem states that there is a linear relationship between how long a student takes to study for an exam, and what grade he will get on it. Then the (real-life) student is asked how long the student (in the problem) should study to get a 100%.

BTW, in the calculation done by Eratosthenes, why could he assume that the Earth was curved? It could be a flat disk, with the sun very close, and still have the shadows behave the way that they did.

User avatar
KrO2
Posts: 236
Joined: Mon Sep 20, 2010 9:35 pm UTC

Re: Sun 500 miles away

Postby KrO2 » Wed Mar 07, 2012 8:03 am UTC

Re: Eratosthenes. What I have heard (no reliable cite, unfortunately) was that he assumed it was spherical because he could see ships disappearing below the horizon gradually. Wiki just says that he was assuming a sphere shape, so his result would just be "if sphere then 252,000 stadia" not "sphere and 252,000 stadia."
What has me surprised is why the Landover Baptist Church isn't assuming a flat earth.

User avatar
Gigano
Posts: 143
Joined: Mon Apr 18, 2011 8:38 pm UTC
Location: Groningen, The Netherlands

Re: Sun 500 miles away

Postby Gigano » Wed Mar 07, 2012 11:02 am UTC

The result of this calculation and its assumptions pretty much is that the further away from earth you get towards the sun, the hotter it gets. We know that this simply isn't true, because we can measure the temperatures a couple of degrees below zero beyond earth's atmosphere.
Omne ignotum pro magnifico.

SheffJames
Posts: 24
Joined: Sun Feb 12, 2012 11:32 pm UTC

Re: Sun 500 miles away

Postby SheffJames » Wed Mar 07, 2012 11:14 am UTC

Thanks guys, appreciate it.

Incidentally - Landover actually do claim a flat earth - there's an awful lot of proof on their site. But those I can see the problems with :D

mfb
Posts: 950
Joined: Thu Jan 08, 2009 7:48 pm UTC

Re: Sun 500 miles away

Postby mfb » Wed Mar 07, 2012 1:46 pm UTC

I think there is a sign mistake. Actually, temperature is decreasing with increasing height in the troposphere (it is different for other parts of the atmosphere). Which means that, by the same calculation, the sun is below our surface. Maybe it is related to hell?
In addition, about 30-40km above us, we have rain of liquid nitrogen, and 50km above us the universe has to end as there is no temperature below 0K.

User avatar
iChef
Posts: 343
Joined: Fri Oct 15, 2010 9:33 pm UTC
Location: About 5 cm. south of the ring finger, USA.

Re: Sun 500 miles away

Postby iChef » Wed Mar 07, 2012 3:21 pm UTC

Of course the universe ends 50 km above us. That is where the universe ends and Heaven starts. What did you sleep through Sunday school?
Those whom God loves, he must make beautiful, and a beautiful character must, in some way, suffer.
-Tailsteak author of the Webcomics 1/0 and Leftover Soup

iosonologio
Posts: 2
Joined: Thu Mar 08, 2012 11:14 am UTC

Re: Sun 500 miles away

Postby iosonologio » Thu Mar 08, 2012 11:18 am UTC

holy shit. that damn candle in my room is too near. i am going to die


Return to “Science”

Who is online

Users browsing this forum: No registered users and 11 guests