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Topics - momentia

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1
Flat Earth Debate / Gyroscopes make FE impossible
« on: September 24, 2011, 11:34:43 AM »
Gyroscopes demonstrate both the rotation and the shape of the earth.

Free rotating gyroscopes will conserve angular momentum and always point in the same direction. If you spin up a free rotating gyroscope and point it straight up, you can determine that the earth is rotating, and the angle shown below, or the angle between the angular momentum of the earth and the angular momentum of the gyroscope.

If the earth were flat (rotating or non-rotating), a gyroscope pointed up would always point up. However this is not the case. In fact, the angle between the earth's angular momentum vector and the gyroscope's angular momentum vector is the latitude at which the gyroscope is located. This means that the earths surface is tilted by (90-latitude) degrees from the axis of rotation, which can only occur for a round earth.

The angle I'm talking about is Φ in the below diagram if the z axis is the axis of earth's rotation, and the vector shown is the gyroscope's axis of rotation.


Here's one of many experiments that confirms that the gyroscope procession depends on latitude.
http://www.sciencedirect.com/science/article/pii/S0921452600007535

And you can't blame the procession on mystically torque from the stars either. There are other ways of detecting small rotations. In particular, the sagnac effect: a laser gets split and one beam goes around a circle and interferes with itself. If the ring is spinning around an axis perpendicular to the plane, the laser will be out of sync with itself upon recombination, which can be interpreted as a certain rotational velocity around the axis perpendicular to the loop.

The equation relating the rotational velocity of the earth, wavelength of laser, area of the loop, and perimeter of the loop can be found on the following page:
http://www.fs.wettzell.de/LKREISEL/G/LaserGyros.html
In the top equation, n dot omega is related to latitude as is shown in the lower equation.

This is from a lab that very accurately measures the rotation of the earth.

Here's some more types of experiments measuring the rotation of the earth using inertial frames:
http://prl.aps.org/abstract/PRL/v78/i19/p3602_1
http://prl.aps.org/abstract/PRL/v78/i11/p2046_1

Using the fact that the earth is rotating is also the basis for the gyrocompass:
http://en.wikipedia.org/wiki/Gyrocompass

None of this is remotely possible on a flat earth.

2
Flat Earth Q&A / Mathematics of Perspective
« on: September 22, 2011, 04:58:32 PM »
In the opinion of RE'ers:
FE'ers do not seem to understand the notion of angular resolution, which is exactly what rowbotham's perspective is. They will just say his principle is that lower lines converge before higher lines do, but never give an explanation why this is so. They completely ignore the principle that supposedly gives rise to this perspective.

So, I would like an equation relating any or all of following variables for a distant ship according to Rowbotham's perspective:
H = height of the observer
h = height of the hull that is hidden
d = distance to the ship
m = magnification compared to the naked eye.

Ignore any secondary effects like atmosphere.

Also, don't tell me to read ENaG's explanation myself. I have. I gave my best shot at relating the variables:
Quote from: Rowbotham
The above may be called the law of perspective. It may be given in more formal language, as the following:. when any object or any part thereof is so far removed that its greatest diameter subtends at the eye of the observer, an angle of one minute or less of a degree, it is no longer visible.
    The angular diameter of a distant object (distance = d) with height h is h/d radians.
    a magnification of m will multiply the angular diameter by m.
    and this angular diameter has to be less than one arc minute, or 0.000291 radians for the object to be invisible.

    Thus my FE relation between the above variables is:
    (h/d)*m ≤ 0.000291

Now its your turn FE'ers, what do you think the relationship is? Explain why you think so.

3
Flat Earth Q&A / Angle of polaris from the horizon.
« on: September 14, 2011, 01:54:10 PM »
So, I have always been confused by celestial things in FE. One of the problems I have is polaris's angle from the horizon.
I assume that polaris is directly over the north pole in the north pole centric FE model.
I used the following diagram to determine the FE relation between latitude and the angle polaris makes with the horizon:


φ (or Φ) is latitude, and θ is the angle polaris makes with the horizon.
h is the height of polaris, and R is the radius of the earth.

I then plotted θ as a function of φ for various h/R ratios:


Note that I also plotted θ = φ, which is roughly the observed relation between the two variables. (Personally, I have viewed at latitudes 47N and 34N)
No h to R ratio can account for this.

However, this relation comes naturally for the RE model, where Polaris is  about 433 lightyears away, and sends in light pretty much parallel to the axis of earth's rotation:


What does FE make of this?


4
Flat Earth Debate / Lack of a distance preserving FE map.
« on: September 09, 2011, 10:38:27 AM »
Any FE map will have different distances than the RE map at points due to the lack of a distance preserving map (function) from a Geoid (kind of like a sphere) to a plane.

For example, take the FAQ map. Distances in the southern hemisphere are distorted severely, as shown many times before. So I will ignore it.

Or, take Rowbotham's map with a smaller radius (8402 miles)
on Rowbotham's map, distances at northern latitudes are too small.
Lets say New York to Southampton, using Rowbotham's distance of 3476 miles.

"New York to Southampton 2980[nautical miles] = 3476[statute miles]"
http://www.sacred-texts.com/earth/za/za22.htm

Now according to this map and known latitude and longitude, the distance should be:
>Thork distance: 2472 mi
or about a thousand miles short.

Also, for reference, i get:
>RE distance: 3422 mi


5
Flat Earth Debate / Underwater Cable Connecting South Africa and Malaysia
« on: September 05, 2011, 10:21:52 PM »
So there is this underwater fibre optic cable that is in the Indian Ocean called the SAFE cable system.
This is a cable built by a private company, Tyco Submarine Systems, and its furthest apart terminal ends are at Melkbosstrand and Penang.

According to the website, the total cable length is 13,500km.
Source: http://www.safe-sat3.co.za/ (click on System Information)

The cable length (not geographical distance) from Melkbosstrand to Penang is 11,465 km according to the latency calculator.
Source: http://www.safe-sat3.co.za/ (click on Configuration and enter Melkbosstrand and Penang at the bottom.)

Now, using the standard FE map, where longitude is like the angular coordinate and latitude is like the radial component (equator is half-way to the south rim from the north pole, lines of latitude are equally spaced. Assume earth radius of 20,000km, like the standard FAQ) I calculated the distance between the two cities.

Melkbosstrand is located at 33.723197S, 18.440552E
Penang is located at 5.274213N, 100.467224E

using the following python code, I estimated the distance between the two cities on the flat earth:
'''
import math

def toRad(x):
   return x*math.pi/180

lat1 = -33.723197
lon1 = 18.440552

lat2 = 5.274213
lon2 = 100.467224

dy = (1-lat1/90.0)*math.sin(toRad(lon1)) - (1-lat2/90.0)*math.sin(toRad(lon2))
dx = (1-lat1/90.0)*math.cos(toRad(lon1)) - (1-lat2/90.0)*math.cos(toRad(lon2))

print
print "FE distance: %i km"% int(10000*math.sqrt(dy**2+dx**2))
print
'''

My output was:
>FE distance: 15546 km

This is much further than the entire length of the cable system, and longer than the length of the cable between the two cities.
This FE distance is in fact, this is 4,081 km longer than the length of the cable connecting the cities.
To give you a feel for 4000 km, thats about going from Canada to Mexico and back.

This means that, on a flat earth, the cable would need to be a minimum of 35.6% longer than its true value, and practically longer since the cable is not a straight line; it curves.

There is absolutely no way the company could not notice that they were producing and laying more than 4000 extra km of cable, or even contain this knowledge to high management levels.

How can FE explain this?

6
Flat Earth Q&A / Hurricanes and other tropical cyclones.
« on: August 29, 2011, 03:50:18 PM »
It is well known that tropical cyclones are formed when a low pressure region forms over tropical waters. Due to the Coriolis Effect, the winds going towards the center of the low pressure region are twisted in the direction of the earth's rotation, (clockwise in the south, counter clockwise in the south). Warm air rise in the center, creating more of a low pressure zone in the center, and the storm continues to grow and its angular momentum rises (it gets its angular momentum from the rotating earth). How would hurricanes form on a non-rotating flat earth, given the conservation of angular momentum? How can it gain any angular momentum, and from where? Also, why due hurricanes rotate different directions north and south of the equator?

7
Flat Earth Debate / Sailboat masts.
« on: August 22, 2011, 06:04:16 PM »
There's often talk of sailboats masts appearing over the horizon, but never any pictures. So, I took my binoculars and a camera, and shot these two photos of the same sailboat through the binoculars. One picture was from about 5 feet above the water, and the other was higher, ~20 feet above the water. I took the shots within 2 minutes of each other. After I took the second shot, I looked through the binoculars 30 seconds later at 5 feet and saw the same thing as in the first picture. I.e. the boat didn't move significantly.

One of the pictures is out of focus, yes, but I was in a hurry to get it before the boat disappeared behind an island.
The difference in brightness and zoom between the two photos is due to how the pictures were taken (zoom on camera, and auto brightness/through binoculars.)

5 feet:

20 feet:


note the lack of a hull in the first photo.

now, this is expected on the round earth, but on a flat earth, we should be able to see to hull of the boat in both pictures or in neither picture. (neither if you ascribe to Tom's funky perspective, both oterwise.)

And no, the waves were not high that day, less than a foot.

8
Flat Earth Q&A / Persieds Meteor shower
« on: August 12, 2011, 11:06:43 PM »
Ah, tonight and tomorrow night are the peak nights of the persied meteor shower. I'll be camping out tonight and be watching meteors after midnight.

Anyways, I thought of FE. I searched and found some topics on the subject of meteor showers, but no FE explanation. So, I thought to give it another shot. FE, explain the following two points.
1) Why do certain meteor showers, like the persieds, occur 365 days apart all the time?
2) Why is the meteor/hour rate greatest from midnight to dawn?

In RE, the answers are trivial:
A comet leaves dust behind it, so there is a constant dust stream in the same location that the earth moves through:
1) Since this dust stream is from a comet path which is constant, the earth will pass through it once a year (365 days).
2) Since dawn is always at the "front" of the earth, in terms of the earth's movement around the sun, the meteors are most visible after midnight and the shower is best right before dawn while it is dark enough to still see the meteors.

So, FE, what's up with the annual meteor showers?

More info at:
http://www.imo.net/zhr

9
Flat Earth Debate / FLIGHT PATHS DISPROVE FE
« on: July 18, 2011, 05:42:39 PM »
The white line connects Sydney and Buenos Aires.
Then I drew a line of the same length (you can check) through the north pole.

In this picture, the earth is 40,073 km in diameter.
in this picture, there are 12 latitude lines.
Therefore, the lines line are 40,073 / (2*12) = 1670 km apart.
The length of the pink line is about 15 latitude lines long, so thats 25 050 km (about 25000 km) long.
(info given by FES.)

Using the map provided by FES,
The white is the same length as the pink, so the white is 25,000 km long.
Thus the distance from Sydney to Buenos Aires is 25,000 km.



However, using Quantas route maps (which people fly on every day),
We find the distance covered is 11,780 km.

If you think that they are wrong,
the time it takes the flight is 14hrs, 40 min (14.66 hrs)
(verified by passengers.)
If they flew direct over a flat earth, their planes would have to travel at an average of 1,705km/h, or 1059 mph.
To give a reference, the speed of sound is 761 mph at sea level.
An average jet liner travels at  500-600 mph.
The passengers would know if they went supersonic.
people in the flight path would hear regular sonic booms.

If the plane took a more circuitous route, it would have to go faster.
This means that the earth cannot be flat.

http://www.qantas.com.au/travel/airlines/route-maps/global/en

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