Sun 500 miles away

[SheffJames]

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 )

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)

[gmalivuk]

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.)

[Copper Bezel]

(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.)

[Proginoskes]

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.

[KrO2]

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.

[Gigano]

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.

[SheffJames]

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

[mfb]

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.

[iChef]

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?

[iosonologio]

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