# The Flat Earth Society

## Flat Earth Discussion Boards => Flat Earth Q&A => Topic started by: Pythagorus on June 14, 2006, 09:32:20 PM

Title: The Summer Solstice
Post by: Pythagorus on June 14, 2006, 09:32:20 PM
Here's an opportunity to easily prove which theory is correct.  On June 21, the location of the sun can be known with accuracy to be close to the tropic of cancer.  All anyone needs to do is to set a pole perfectly upright when the sun is at its highest and to measure the length of the shadow.  From there the angle of the sun from the horizon can be measured and can be compared to what it should be according to either model.

From my location, the sun should be at an angle of 72.7 degrees if the earth is round, and 68.2 degrees if the earth is flat.

I have also found the angles for a few other cities.
Houston: 83.7 degrees if round, 81.7 if flat
Vancouver: 64.2 degrees if round, 59.3 if flat
Phoenix: 80.0 degrees if round, 77.0 degrees if flat
Knoxville: 77.5 degrees if round, 73.9 degrees if flat

The bigger the pole the more accurate the measurement (2 meters or greater would be nice).  If anyone wants to know the angles for any other locations just post the name (or the coordinates if possible) and I can do the math.
This will be very easy to do and if you truly believe in one theory then its an easy way to prove it beyond a doubt.
Title: The Summer Solstice
Post by: Efimowho? on June 14, 2006, 09:41:29 PM
so0o0o0o i dont get it.
what would you like us to do with these degrees?
Title: The Summer Solstice
Post by: Unimportant on June 14, 2006, 10:07:22 PM
I'd like to point out to other RE'ers that this is exactly the kind of posts we need more of; experiments we can perform ourselves that produce measureable, meaningful results.

Efimowho?:
You measure the height of the pole, and the length of the shadow. Then use your calculator to find Arctan(SL/PH), which will give you an angle in degrees.

If this angle matches the "if round" number, then that suggests the earth is round.
If this angle matches the "if flat" number, then that suggests the earth is flat.

Pythagoras: Could you explain a bit your procedure for finding these values? Also, I'm sure the time of day is important; should we be checking at 12 noon?

And if you've got a second I'd like to know the theoretical values for the Washington DC area.

Again, thanks for the constructive post.
Title: The Summer Solstice
Post by: Pythagorus on June 14, 2006, 11:43:22 PM
Thank you, Unimportant.  The latitude for Washington D.C. is 38 degrees 53' 38" N (the longitude is unimportant but it's 77 degrees 02' 12" W).  That's the middle of the White House lawn to be exact.

The angle should be 74.5 degrees if round, 70.4 degrees if flat.
Using a 2 meter pole, the shadow should be 55.5 centimeters if round, 71.2 centimeters if flat, so the difference should definitely be measurable.

Also, the angle I'm talking about is the angle of solar elevation, not the solar zenith angle, so the equation is instead Arctan(PoleHeight/ShadowLength) just to make things clear.

The time of day to be checking in Washington D.C. is 1:10 PM June 21
This website is useful for measurement times http://aa.usno.navy.mil/data/docs/RS_OneDay.html
If you don't trust the website, you can take a measurement every 15 minutes from 12 PM to 2 PM and use the shortest measurement.

Houstin:  measure at 1:23 PM
Vancouver:  1:14 PM (If Daylight Saving?)
Phoenix:  12:30 PM (non Daylight Saving)
Knoxville:  1:37 PM (Eastern)

--------------------------------------------------------

The procedure for finding angles goes like this:

For the Round Earth angle:
Find your latitude and convert to decimal (i.e. 38.894 degrees washington dc)
subtract 23.439 degrees from that (the tropic of cancer, the sun would be directly overhead this latitude on June 21)
The angle you get is the solar zenith angle.  Subtract it from 90 degrees to get the solar elevation angle.

For the Flat Earth angle:
Take the solar zenith angle (your latitude minus the tropic of cancer latitude) and divide over 90 degrees.  Multiply that number by 10,018.1664 kilometers (1/2 the radius of the flat earth model) to get your distance from the tropic of cancer.  Then do Arctan(4,828/your distance) to get the solar elevation angle.  4,828 km is the height of the sun in the flat earth model.

Once you find the angles, go to the website I mentioned earlier and put in the date (june 21), your location (name or coordinates), and timezone (don't forget Daylight Saving/nonDaylight Saving) to find the sun transit time (the exact minute the sun is at its highest on that day, it will probably be sometime after 1 PM for most states)

At that exact time, set up your pole (2 meters or more recommended) and make sure it is perfectly straight (so that it's close to balancing itself).  Then measure the shadow length and pole height and find a good calculator to do Arctan(Pole/Shadow) to find the actual angle of solar elevation.  If the real angle matches the "round earth" angle, then the earth is undoubtedly round.  If it matches the "flat earth" angle, then the earth is undoubtedly flat.
Title: The Summer Solstice
Post by: Pythagorus on June 16, 2006, 07:19:35 PM
I got too tired of waiting, so I went ahead and took a measurement already.

The angle I got was 25.9 degrees.  I measured at 6:30 PM, June 16.  I guess the sun was close enough to the tropic of cancer to do it.

I calculated the theoretical angles and this is what I got:

Round earth:  26.1 degrees
Flat earth:  31.1 degrees

I just had to do a little extra trig to calculate for the different position of the sun.  So here's your evidence.  Try it yourself if you don't believe me.
Title: The Summer Solstice
Post by: Unimportant on June 16, 2006, 09:49:43 PM
I'll wait until June 21 to do it.
Title: The Summer Solstice
Post by: Pythagorus on June 20, 2006, 08:03:18 PM
The solstice is tomorrow.  I want everyone to try this out.
Title: The Summer Solstice
Post by: god on June 20, 2006, 08:16:34 PM
they won't
Title: The Summer Solstice
Post by: RenaissanceMan on June 21, 2006, 04:55:22 AM
I live very near Washington DC, and today is the 21st. I have my 2 meters plus stick and I've scoped out a flad location to make my measurement.

I'll report back after I make the measurement.

Heh, won't I be shocked if some G-men in a black Suburban try to tell me what the measurement SHOULD be?
Title: The Summer Solstice
Post by: FlatAnus on June 21, 2006, 05:43:33 AM
but dude that's today, and now it's like night time, and it like rained ALL day.....
Title: The Summer Solstice
Post by: RenaissanceMan on June 21, 2006, 06:06:51 AM
Quote from: "FlatAnus"
but dude that's today, and now it's like night time, and it like rained ALL day.....

Dude! Where I live, the solstice occurs at 1:11 pm (local time), which is in 4 hours 5 minutes, and it's sunny here... a perfect day to preform the meaasurement.

It's like... the planet is a SPHERE or something, with some parts dark while other parts are illuminated by the sun!

But... proving my preconceptions is not the purpose of the experiment. The purpose of scientific experimentation is to prove what IS right, not to prove that YOU are right. As such, I'll approach the experiment with an open mind and do my best to record accurate data that can be subjected to peer review.
Title: The Summer Solstice
Post by: FlatAnus on June 21, 2006, 06:16:23 AM
on your bike then! Best of luck, I look forward to seeing what you come up with. You better find out your co-ordinates!
Title: The Summer Solstice
Post by: EnCrypto on June 21, 2006, 10:12:19 AM
What is the formula to find the Arctan?
Title: The Summer Solstice
Post by: Pythagorus on June 21, 2006, 10:28:32 AM
arctan(pole height/shadow length)  which should be the sun's angle of elevation.
Title: The Summer Solstice
Post by: EnCrypto on June 21, 2006, 10:31:50 AM
Quote from: "Pythagorus"
arctan(pole height/shadow length)  which should be the sun's angle of elevation.

Pole height divided by shadow length? Gotcha
Title: The Summer Solstice
Post by: RenaissanceMan on June 21, 2006, 10:58:33 AM
Dang it... I missed it. I had my measuring apparatus all set up, too. But I had to take a phone call.
Title: The Summer Solstice
Post by: god on June 21, 2006, 11:15:20 AM
SUPRISE
Title: The Summer Solstice
Post by: Unimportant on June 21, 2006, 02:22:39 PM
I had to work through lunch today :(
Did anyone get a chance to try out the experiment?
Title: The Summer Solstice
Post by: EnragedPenguin on June 21, 2006, 08:47:14 PM
I wanted to try it out, but it's been cloudy all day.
Title: The Summer Solstice
Post by: Pythagorus on June 21, 2006, 09:33:06 PM
Well, it's not like summer lasts only one day.  Trying tomorrow will yield the same results.  Every midday for the next week would also be a good time to try.
Title: The Summer Solstice
Post by: levilsirfiss on June 21, 2006, 09:34:30 PM
Quote from: "FungusMcUncle"
oh well, another year of stupid, pointless debate...

they make me do tose at school a lot

i dont liek to do debates
Title: The Summer Solstice
Post by: EnCrypto on June 21, 2006, 09:47:17 PM
The pole height was 56 inches, and the shadow length was 20 inches.

I don't know how to get the Arctane, so if someone else could do me the favor...

I'm near Houston, by the way.
Title: The Summer Solstice
Post by: levilsirfiss on June 21, 2006, 09:51:57 PM
wats a Arctane???
Title: The Summer Solstice
Post by: Unimportant on June 22, 2006, 03:14:48 PM
Quote from: "EnCrypto"
The pole height was 56 inches, and the shadow length was 20 inches.

I don't know how to get the Arctane, so if someone else could do me the favor...

I'm near Houston, by the way.

Arctan(56/20) = 70.35 degrees

There you have it folks, scientific proof that the earth is... concalve.
Title: The Summer Solstice
Post by: EnCrypto on June 22, 2006, 03:18:17 PM
Quote from: "Unimportant"
Quote from: "EnCrypto"
The pole height was 56 inches, and the shadow length was 20 inches.

I don't know how to get the Arctane, so if someone else could do me the favor...

I'm near Houston, by the way.

Arctan(56/20) = 70.35 degrees

There you have it folks, scientific proof that the earth is... concalve.

Well, I did take it at 12:00 instead of at 1:10.

And what's concalve? And what's the calculation for Arctan?
Title: The Summer Solstice
Post by: Unimportant on June 22, 2006, 03:25:46 PM
The calculation for Arctan is "punch it in to your TI-89".

Arctan is defined as follows:

Tan(X) = Y

Arctan(Y) = X
Title: The Summer Solstice
Post by: EnCrypto on June 22, 2006, 03:30:31 PM
Quote from: "Smartass"
The calculation for Arctan is "punch it in to your TI-89".

I don't have a TI-89.
Title: The Summer Solstice
Post by: Unimportant on June 22, 2006, 03:54:17 PM
If you don't have a calculator you probably aren't going to be able to calculate the Arctan by hand, sorry :(
Title: The Summer Solstice
Post by: DrQuak on June 22, 2006, 04:51:29 PM
well you perhaps could, you just need to draw an accurate diagram with the length of the pole and the length of the shadow, and join a line between them and get out a protractor.
Title: The Summer Solstice
Post by: 6strings on June 22, 2006, 05:03:46 PM
Quote
If you don't have a calculator you probably aren't going to be able to calculate the Arctan by hand, sorry

Not really, he just needs time on his hands, just perform the following operation until you reach a desired degree of accuracy:

arctan(35pi/180)=(35pi/180)-((35pi/180)^3)/3+((35pi/180)^5)/5-((35pi/180)^7)/7...
Or, of course, you could always just use an online calculator, I'm sure.
Title: The Summer Solstice
Post by: Pythagorus on June 22, 2006, 07:02:57 PM
I guess it is better to measure when shadows are longer, but there's more math to do.

At 12 PM June 21 at Houston, the sun's angle of elevation should be 74.6 degrees if round.  If flat, and using the numbers of the flat earth model, the angle should be 83.6 degrees.

At that time, the sun was at 111 degrees 7' W and at the tropic of cancer.  I figured out the distance between Houston and the point where the sun is directly overhead, and from there I figured out the sun's angle for the round earth.

With the flat earth angle, I also figured out the distance between Houston and the "sun" point except using the figures for the diameter of the flat earth and the height of the sun.