Gravitas

Gravity keeps your feet on the ground, as well as just about everything else. I'll not bore you with the Principia or go into the story of Isaac Newton and the apple as I'm sure you have heard it a hundred times or more, but a quick look on Wikipedia will tell you plenty if you have somehow got this far without hearing of the man or his work, however, the (very) basic points of gravity are as follows.

1. Every particle will pull on every other in all directions
2. The more partials in one place (the denser) the stronger the pull
3. Gravity will pull towards the centre of mass
4. The pull gets weaker with distance

Or as Newton put it

"Every point mass attracts every single point mass by a force pointing along the line intersecting both points. The force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses."

Flat earth believers know that gravity can't work on a flat disk-like world. Nothing would work as we experience it in the real world, as already mentioned gravity pulls towards the centre of mass, on a flat pizza like world that would be located just below the North Pole. Standing at the North Pole would be fine and probably feel quite normal but if you were to walk south it would gradually get more and more difficult as if walking up a hill that gets steeper as you go. When you finally reach the South Pol... The rim you will feel like your climbing an almost sheer cliff, the exact inclination felt will depend on the thickness of the disc, but it would be more than noticeable. But this is Not how things appear in the real world, you can walk in any direction and down is always... well... straight down excluding any real incline due to an actual hill or mountain.

So how do flat Earthers explain the difference between real-world observations and the expected results of gravity? Simple gravity does not exist or it's just an alternative name given to an already existing force that happens to hold us down. There are many competing ideas as to how everything is held down and as with most other flat-earth "theories", no one hypothesis seems able to agree on a single answer. I'll cover a couple of them now

 

Accelerating Upwards

This one is as simple as it sounds. The world is a flat disc and it's continuously accelerating in an upward direction at 9.8 meters per second every second (9.8m/s^2). In a very basic way, this means if I was to jump into the air I would be accelerating myself ahead of the ground only for it to catch up with me as I land again. This means the flat earth is moving faster and faster every second of every day, surely this would cause problems? The simple answer is Yes, in one day we would accelerate by 1,894,059 mph (3,048,192 Km/h) and in one week 13,258,413 mph (21,337,344 Km/h). How fast would we be going after one year? Well, it would be a little faster than the speed of light which is just over 670 million mph.

 

Buoyancy

This one is quite straightforward too but also has some odd problems related to it. Heavy things sink and light things float, if you drop a brick in a bucket of water it will sink but wood will float because it's less dense than the water. The same applies to things in air, if it's denser than air it will fall and hit the ground... and that's it.. dance/heavy things fall less dance/light things float. Now that is all true I'll grant you that any physicist or secondary school student for that matter will tell you it's gravity that's doing the pulling and displacing the less dense liquids and gases. A helium balloon will float up because the air pressure underneath is pushing up with more force then the air pressure above and gravity combined are pulling it down, this imbalance in force will cause the balloon to rise. But according to flat-earth believers, that's wrong! Air pressure is what pushes everything down, gravity as we understand it is not required. All the air above our heads is pushing us down to the ground and we call that "gravity", simple right? Yes.. but this is where the problems start. If we go back to our bucket of water with the brick in it and placed it in a vacuum chamber what would stop the water or the brick from floating up out of the bucket? If I went into a pressure chamber shouldn't I feel heavier or at the top of a mountain where the air is thin would I feel lighter? What if I dropped a hammer in a vacuum would it simply float next to my hand without the air to push it down? not sure? I invite you to watch this experiment or buy/build a vacuum chamber and test it yourself. lastly, on this point, I’d like to look at a mercury barometer (left), the mercury in the tube is pushed up into the tube and let fall as the surrounding air pressure changes. If the only force acting on the mercury is air pressure what's pulling the mercury out of the tube and creating the vacuum at the top? Air pressure can only push it cannot pull, the vacuum appears as the tube is lifted into the vertical position so something must be pulling the mercury down and acting against the outside air pressure.

Neither of those examples fully explain what happens in the real world, the same goes for any other explanation other than gravity as understood in modern science. Two body's of mass will pull towards each other even in a vacuum or through any barrier. The force of gravity can be measured and by using the correct apparatus all other forces that could act upon the equipment can be excluded. The Cavendish experiment was the first to measure the gravity between two objects. The experiment used two large lead balls hung from the ceiling and two small lead balls balanced on the ends of a bar, the bar its self hung on a wire. The small lead balls would be pulled towards the large lead balls twisting the wire, this twist was measured and told Cavendish the force acting between the two masses. This experiment is still performed today in labs all around the world, I vaguely remember our physics teacher doing this at school but at the time I found it very boring as it's very, very slow and requires no safety equipment. you can find plenty online about it and anyone with the space and time can perform it, although accurately measuring the results requires high precision and a lot of prep work to exclude any interference. I hope to be doing this sometime in the near future (providing I can sort out a space to do it) and I will walk through my set up and finding hear.

The only conclusion I can come to at the moment is that gravity as Isaac Newton understood it must be real, a force is clearly present and yet nothing else I have seen explains all its property's. There are serval experiments that test it and help to define its laws, if gravity did not exist the experiments they would not work or would produce differing results. 

 

Poe's Law

Recently I come across a YouTube video “New Proof of a Flat Earth: Distance to the Sun? Shorter Version” Sasha appears in the video and talks about measuring angles from the horizon to the sun and how you can make an equilateral triangle which is a triangle in which all three sides and all three internal angles are equal. The video and all Sasha’s videos are done in such a way that its hard to take them or her seriously, I can only assume this is intentional as her channel is labelled as comedy but on the other hand she stats that she is passionate about flat-earth, so is she mocking it? I invoke Poe's Law on this and I will assume she is serious and believes the earth is flat.

On a flat plain, the equilateral triangle would work well, it will give you the exact distance to the sun and as stated in the video it would disprove the sun’s 93 million mile distance. Sasha gives us two places on earth that are the correct distance apart to see the sun at 60° at the same point in time. One is Macapá in Brazil and the other is Malabo in Equatorial Guinea. She also gives us the distance between them as 4134.6 miles, a quick look on google earth and I got 4144.7 miles so a 10.1 mile difference? I’ll use her figures as 10 miles will make little to no difference and is well within any reasonable margin of error. If you work this out using a triangle solver app like this one you will find it gives you a sun height of 3580.67 miles, a long way short of 93 million. Yep that's it the globe earth is done for the world can only be flat…. “Sparkle Sound” 

But wait, wouldn't the curvature of the earth change the angles? Yes and no, from the people standing into two cities measuring the suns altitude there should be no difference but the horizons they are measuring from will be vastly different in relation to each other. Sasha has thought about this and demonstrates how the curvature of the earth will affect the angles. As you can see in the image to the left (grabbed from her video) the 60° measurements taken from our two cities will diverge and simply get further apart the further you are from earth. one thing bugs me about this drawing, where is the working out? how do we know the drawing is correct? I know its hand drawn and it doesn't need to be exact or to scale, but it would be nice to have a little more than just two points marked with time and angle as our only verification. For a start would 4134.6 miles create that much curvature? I had to check this out for my self, time to do some maths!

Ok to test this for my self and demonstrate my finding I decided to test out a new app I found, its called GeoGebra (if you like maths and/or geometry you seriously need to check this app out) and I was pleasantly surprised how easy it was to use. At first I simply tried to replicate the above drawing and found I could manipulate positions of the two cities and the curvature of the earth at will and get the lines diverging, parallel or converging with out changing the 60° angle. this was no good at all I needed to know I was getting all the angles and distances right, so I made a circle and set its circumference to 24901 miles, the same as earth equatorial circumference. Next I set points “A” and “B” to slide along the circumference and the green line that lets us know the distance between the two. I then created another point and placed it 93 million miles away in the direction of the red arrow, this I joined to points “A” and “B” with lines and had the angle between them and the imaginary observers local horizon displayed in green. as you can see in the drawing to the right I used the distance Sasha gave us (within a tenth of a mile) and as you can see the altitude of the sun from our two cities would be incredibly close to 60° and converging on a single point. Infect if we want to get it to exactly 60° we only have to move our observers 2.8 miles closer together giving us a distance of 4131.8 miles.

So in short, if you had two people on a globe earth stand 4131.8 miles apart along the equator, one could watch the sun rise to 60° at the same time as the other watches it set to 60° with the sun that is 93 million miles away. “New Proof of a Flat Earth”? New Proof of Bad Geometry more like.

I’m going to leave you with the worksheet I created in GeoGebra. You should be able to have a little play with it.

Great ball of fire

The sun provides us all with light, warmth and food, keeping our home not just liveable but comfortable, all the sun gods throughout history should be no surprise. But we're not here to talk about gods, today's topic is the sun or more specifically the way it moves or appears to.

As we all know the globe earth spins making a stationary sun appear to move across the sky. At the end of the day, the sun appears to drop below the western horizon, travelling under our feet before risings from the eastern horizon the following morning. On flat earth things are very different, the sun and moon float about 4000 miles above the ground moving in a circle that follows the equator. both shine there light down on earth like spotlights only illuminating half (approximately) of the world at any one time.

I have spent quite some time looking in to this and at first I assumed that the sun on a flat earth would orbit over the top and then underneath much like in the Discworld series of book. If you don’t know about the Discworld books I highly recommend you read one or two and I’m shore you will want to read the rest. The Discworld its self is a flat world ten thousand miles across which rests on the back of 4 elephant's which in turn stand on the back of the giant star turtle Great A'tuin. But let's get back on track. The flat earth is very different from the Discworld, for a start the ocean's don't flow off the edge as the Antarctic stretches all the way around the rim, it also doesn't rest on the back of any animals but its exact nature is subject to debate. Some say its a flat disc, others say its a never-ending flat plain, furthermore some say the earth is covered by a dome called the firmament and then it all starts to get complicated with every theory splitting off into two or three others. For my own sanity, I’m going to ignore some of the more outlandish theory's and stick to the basics that most flatheads can agree on. 

When looking at how the sun would work I kept getting the same thoughts and I decided to do some maths to see if things would look the same as I have witnessed time after time from my own back garden. If you look into the distances involved you will come across some quite contradictory figures, most flat heads believe the sun is somewhere between three and four thousand miles high, but I’ve come across as little as 35 miles. To keep things simple I'm going to use the figures that seem to be the most common and to simplify things further I will be calculating the suns movements as if it's at the equinox. This will give me a sun that is 3000 miles high and 32 miles across. Assuming the equator is half way between the north pole and the rim and that the equators circumference is the same as that of a globe earth the earth's diameter must be 25000 miles.

So just to recap the figures I'm going to use are as follow

• Sun’s diameter : 32 miles
• Sun’s height : 3000 miles
• Earth's diameter : 25000 miles
• The Equator from North pole : 6250 miles

I used MS Excel to do the maths involved, mainly because I’m familiar with using formula in Excel but also it would be easy to send the file to any one who wishes to look at my workings. The following is the work sheet I created to show the flat earth model working, the graph at the top shows a representation of the flat earth as viewed from above with the north pole in the centre. positions “A”, “B” and “C” are lined up along the Greenwich prime meridian. the box on the bottom left displays the figures as well as the time. the box on the bottom right gives information about the sun from each of the points labelled.

Let's have a closer look at position “A” the rest will then be self-explanatory. Position “A” is 1250 miles from the north pole and at this time its 5438 miles from the point which the sun is directly over. Using this distance and the suns height (3000 miles) we can work out the angle above the horizon the sun would appear to be, at this time from “A” it would be 28.88° (I’m not going to go in to the maths but if you want to check it you can do so here). The last bit “Sun Angular Size” is simply how small the sun would look with the naked eye. (not that I recommend looking at the sun with the naked eye as it can do some serious damage however if you feel the urge to, please don't let me stop you)  The sun always stays the same size but due to it being further away it will look smaller, so to work this out all I need is the distance to the sun its self (which works out to be 6210 miles) and its diameter, if you assume its a right-angled triangle you can use the same maths as before.

As you advance time on the worksheet you will see the distances and angles change in accordance with how things would appear if you were stood at any one of the three positions marked on the graph.

the following are examples of different times of the day

The first chart shows you the figures for 6pm this should be sunset, but if you look the lowest angle as seen from “C” the sun is still 13.12º above the horizon. Worse still is the apparent size of the sun, if you've ever paid attention to the sun as it passes over your head it always look roughly the same size and yet the maths says that on a flat earth the time of day will drastically affect how big it looks. As you can see the graph on the far right is set to 12 o'clock midnight yet the sun is still above the horizon, infect using these figures the sun will never go below 9° and will always be visible (unless its obscured by something like a building or a big hill) and it appears to have halved its size compared to 3pm. Point “B” sees the sun seemingly accelerating towards you before slowing down as it moves off into the distance more like what you would expect if you watched a passenger jet fly over. The chart to the right shows the angular size and altitude every hour for point “B”, these numbers fly in the face of anything I would see if I was stood at the equator observing the sun.

All my charts and figures are very well and good but not very visual and unfortunately I'm not all that good at animation, however as I was looking into this I stumbled across the following gif file that displayed exactly what I was trying to. I don't know what distances are used so the numbers are a little different but the results are more or less the same. the software used to create it can be found here. Ill let you scrutinise the picture your self as its mostly self-explanatory

After carefully calculating all the angles and distances on a flat earth the results just don't fit with real-world observations. The sun does does not grow visibly as it approaches noon before shrinking off into the distance. Some flatheads may show you photos or videos of the sun shrinking as it setts but this is an artefact of the lens or the sensor being flooded with light in one spot and struggling to deal with the information, any good photographer will know this and should be able to suggest a way or two to fix it. (an ND filter or small aperture, even the use of HDR may help).

In the real world the sun appears to move across the sky at a consistent speed never slowing as it reaches the horizon, but on the flat earth the sun would appear to slow as it approaches the horizon, a horizon it will never actually meet or dip below. but flatheads have this covered as well, saying perspective will make the sun “set” as it travels beyond the vanishing point, however, a vanishing point is simply an imaginary point on a picture or graphical projection to create the correct visual perspective and so making it seem more realistic. Perspective will only make the sun look smaller it will not make it move out of sight as if setting below the horizon.

in conclusion, the sun from our point of view can not move round in a circle 4000 miles above us, it must stay the same distance from us and we spin creating the illusion of the sun moving across the sky. At 93 million miles any change in apparent size due to earth's spin would be unnoticeable with the naked eye and hard to measure with good equipment. The observable sun does not support the flat earth it sits squarely in the globe earth model. 

Bad Attitude!

A couple of weeks back I come across the following video staring Dave AKA DMurphy25 on Late Nite, in the first minute and a half he talks about gyroscopes and artificial horizons (attitude Indicators as they are called in the aerospace industry). This got my interest, not in the rest of the video but in gyroscopes and artificial horizons.

 

I paused the video at that point and went to google attitude Indicators. I knew what they where and that they had a gyro in them but hadn't put much thought in to how they worked.

“The Attitude Indicator shows rotation about both the longitudinal axis to indicate the degree of bank, and about the lateral axis to indicate pitch (nose up, level or nose down). It utilizes the rigidity characteristic of the gyro. It is gimballed to permit rotation about the lateral axis indicating pitch attitude, and about the longitudinal axis to indicate roll attitude. Once powered up, the indicator is maintain in a fixed position no matter what the aircraft attitude may be.” www.pilotfriend.com

After learning a little more about attitude Indicators I found DMurphy25 to be correct in that they are mechanical (some of the newer ones are more electronic but this is more for digital displays and autopilots) I find it disturbing that the pilot didn't now this. The pilot should know the plains instruments and the false readings some can give in certain instances.

A gyro will maintain its orientation in space this makes it very useful as an artificial horizons, however a gyro can “drift” off its original position if and outside for acts up on it. Procession is when a out side force pushes on the gyro and the force is transferred 90° round the gyros axis. You can test this your self, take a bicycle wheel and hold it upright by its axle so it can spin freely. now have someone spin it nice and fast (preferably a friend as strangers in the street may look at you oddly) now try to turn the wheel on its side you will feel it resits and try to push you round to your left or right. The mechanism that houses the gyro in an attitude Indicator will inevitably produce a small amount of friction acting on the gyro causing procession and over time the attitude Indicator will begin to give a false reading this is called mechanical drift. There is a second kind of drift called apparent drift this is where the plains axis changes as it follows the curvature of the earth but the gyro dose its job and holds its original orientation. (click hear to see a beautiful 1960 Navy Aviation Training Film explaining all this) 

So DMurphy25 is correct again, pilots don't see this "Apparent Drift" but why don't they? Mechanical drift would be a problem no matter what shape earth is, both mechanical and apparent drift are problematic to a globe traveller. Mechanical drift would need to be corrected for and engineers have come up with a couple of ways to correct for drift. they are called attitude arrestors. the following video explains it all far better then I can.

so dose an attitude Indicator prove or disprove a flat Earth?
No, with the attitude arrestor attached and working gravity will keep it pointing to the ground weather you are flying over a globe or a flat earth. The only way to detect the change caused buy flying over the curvature of a globe earth is with a straight up none correcting gyro.

I have to say that the attitude Indicator is busted as a proof for the flat Earth. but experiments with a gyroscope on a plain are worth looking in to. (providing you don't spook airport security or you get proper permission first) 

In the Beginning...

I created this blog as a way to get my thoughts on the whole globe v flat earth debate out there. 

I must admit I am fully on the side of a globe earth, but I'd like to think I can approach this subject from a scientific perspective, letting the evidence lead the way. If I come across something that points to a flat earth that can not be debunked or explained I will still post it and discuss it here. 

My main goal here is to find evidence pointing either way, scrutinise it and see if it stands up to the real world. I say "see if it stands up to the real world" because I have seen a lot of stuff coming from both sides of the debate that looks more like pseudoscience than real scientific method. I have a list of things I have come across that seem... odd and deserve a closer look, this is where I will start.

Ultimately I would like to conduct my own experiments and post the results here but I wouldn't hold my breath for this one as I have limited time and funding.

I apologise if posts are sporadic, I have a full-time job and a young family (a full nights sleep is a distant memory)