How to quickly or easily prove the world is spherical?

Question

A relative of mine has recently introduced me to the modern flat earth theory, which she believes in. Setting aside for the moment that it is ridiculous, and that sending up some balloons with cameras on would provide evidence to the contrary, how could one evidence that it is in fact spherical from ground based observation?

I immediately thought about citing the observations of Aristotle and measurements of Eratosthenes, something that one can do themselves, but of course they have an answer for that regarding curving light to explain variation of the sun's elevation with latitude. Also refraction backed up by observations of ships on the horizon appearing to be above the horizon (due to refraction) and so light-based observations of a curved body of water are out. To make it even harder, the belief has been adjusted to allow for a flat earth that curves slightly but is not spherical, so objects gradually disappearing over the horizon aren't proof and neither is observing the curvature from a plane! For every argument there is a counter argument, and I, as a layman, don't know how to prove e.g. that the light isn't curving as described.

Without getting into countering non-scientific flaws such as the massive amount of government-level collusion that would be needed to maintain this conspiracy, how might one go about demonstrating it or designing a practical experiment for which the conclusion cannot be refuted. Is this even possible when someone can claim e.g. light curving through the atmosphere in a particular way, without having to back it up? I'm not familiar enough with scientific theory to know how one establishes certainty, or if it is based on a balance of probability (i.e. more proof of one theory than of the contrary).

Note: This is a thought exercise only, I do not expect to actually convince my relative while she is going through a personal crisis for which this is one of many symptoms, that is a separate issue. She holds a degree in aeronautical engineering so it isn't caused by a lack of intelligence.

Answer 1

I'm sorry that this answer will be unsatisfactory and, strictly spoken, off topic, but I want to give it anyway.

The answer is: You can't. Don't waste your time. Your relative has developed a paranoia. Not only is this not an isolated earth science issue; it is not even an issue with science at all. Instead, she has dismissed our common everyday frame of reference wholesale. She must assume a lot of things along with a flat earth:

• As you say, a massive conspiracy dating back hundreds of years, involving governments as varied as absolute monarchies, Hitler's and Stalin's regimes and modern democracies. This conspiracy involves government fraud on a large scale, and a secret cooperation between all governments in the world. This renders all of our commonly accepted news meaningless, including news about economics and politics.
• No moon landing, of course. No ISS. No astronautics as we know it whatsoever. Half of NASA's employees are liars, the other half are being lied to like everybody else and duped into performing an elaborate cargo cult.
• Meteorology and climate models are based on the concept of a solar system with a near-spherical earth. Their predictions are therefore meaningless.
• Relativity, and physics in general, is wrong (light bends, the direction of gravity towards the edge of a flat earth is obviously not as it should classically be, whatever).
• If the earth is not a round body shaped by gravitation, all cosmological theories about the formation of star systems, and thus cosmology as such, must be wrong. (That also follows from her rejection of the Relativity Theory.) Then she'll have a hard time with the age of earth as well as the fossil and geological record (oh, all of geology is wrong as well!). Why don't you ask her who created the earth?

This belief of an alternate reality behind the scenes is paranoid. It also lets other conspiracy theories latch on with ease:

• Climate change is not happening, or is not happening the way we are being told, or is not happening for the reasons we are being told.
• Ask her about chem trails. They may be needed to adjust a few things. And since all commercial aircraft pilots are undercover government agents anyway lest they betray the fact that they actually do not cross the poles on certain intercontinental flights, they can as well produce chem trails on the side.
• Ask her if the lying government also keeps people intentionally sick (maybe with the chem trails!) and suppresses simple, cheap medicines.
• On a more unappetizing note, because major players in the sciences and finance system are Jews, there is an overlap with classical anti-semitic conspiracy theories (who else would secretly rule the world?).

Whatever you come up with will be countered with a new idea; you give a few examples of that pattern in your question. Occam's razor alone would do away with such complicated nonsense.¹ It was sufficient to convince the catholic church, eventually.

xkcd illustrates this nicely:

A paranoid person is actually not really interested in science. A scientific answer is simply inadequate: It does not address the issue! (An example for an adequate answer is "If the earth were flat, all your horoscopes would be wrong!").

One possible psychological trigger for the paranoia is when one learns that long-held supposed truths are actually wrong. Developing scepticism as a response is in order, but the pathological response is to suddenly see all of reality differently, like in an ambiguous picture:

Let me add that there are plenty of reasons to be sceptical, because there is so much bad science out there -- most nutritional advice of the last 50 years is nonsense, for example, and most cancer screening did more harm than good. To me, that is an incentive to work towards better science; for others, it's a stumble which makes them see the world differently when they look up from it.

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_{¹ Occam's razor is actually the answer to your question, which only makes it to a footnote in my answer. Assuming roughly spherical bodies which follow gravity's pull in free fall makes a lot of observations fit very elegantly. It is difficult to come up with a *single* (or a handful of single) irrefutable proofs; defending its alternate reality, the paranoid mind is inventing counter-arguments to any single argument. But comparing the two theories *in toto* makes the judgement irrefutable. It is, in essence, the difference between the Ptolemaic and Copernican models of the world, and the jury is not out any longer: Copernicus' model is constructed "procedurally" on the basis of a few basic principles. Ptolemaeus' model, by contrast, needs many arbitrary, intricate rules for the movement of celestial bodies. Occam's razor shaves all that away.— This combining of many observations into a theory is how the scientific method works in practice. Single contradicting observations do in practice *not* immediately disqualify a theory, how ever much the mathematicians among us would prefer that. This could be seen as a generalization of Truzzi's principle: Extraordinary claims need extraordinary proof.}

Answer 2

To answer my own question based on the useful comments here, my favorite methods were:

1. The earth's shadow cast on the moon during an eclipse. It is easy to observe and the flat earth counter argument is so insane that if it is offered you should just walk away.
2. Shadows differ from place to place. The same experiment as Eratosthenes but you can carry this out locally with a piece of large card, 2 obelisks and a light source casting a shadow. Now bend the card and observe the change in shadows. The same effect could then be observed on the earth's surface. The counter argument of curved rays of light is weakened by the fact you can reproduce it locally.
3. triple-right triangle: You move in a straight line for a long enough distance Turn right 90° degrees, walk in that same direction for the same distance Turn again to the right 90° degrees and walk again the same distance After this you'll end up at the starting point. This is not possible on a flat surface since you'd just be "drawing" a half-finished square. Not sure how practical this is as you'd have to walk a long way!
4. Although not technically about the earth being flat, in a flat earth theory the sun orbits, or at least moves over the earth. A simple way to discount this is observing parallax with surrounding stars.
5. It is not too difficult to prove the earth curves at least, such as by observing more objects over the horizon the further you go up. And even measuring the curvature is not difficult. Thus I believe a person could drive the length of the African continent, observing the curvature and measuring the straight line distance, and modelling that alone would show the earth curves beyond what could be acceptable on a flat earth, without all the water running off the edge!
6. One I haven't seen mentioned yet is showing that the flat earth map cannot work. In a flat earth, apparently, the north pole is at the centre and south pole is a ring around the outside. Pick a land mass close to the south pole, and another on the opposite side of the map. The distance you would need to travel to reach one from the other by e.g. flying east around the map would be enormous and not congruent with the flight times or shipping times in real life.
7. Earth is warmer near the equator, for obvious reasons in a non-flat world but the counter argument would have to be pretty imaginative.
8. Sunrise and sunset do not happen at the same time for everyone on earth. The difference in timezones, which can be observed by taking a trip to different countries, cannot reasonably be explained by a curved but nearly flat earth.
9. Experiments with gravity, but flat-earthers reject the complication of gravity (things drop just because). So I avoided this one, but it would be a compelling way to demonstrate why people on the other side of a spherical earth are not on their heads.

Answer 3

Skype.

Skype someone at least 10 time zones away. Ask them to point the camera at the sky.

Proven.

This actually works really well for a psychological reason as well. Its easy to deny abstract arguments, its difficult talking to someone and denying what they claim is their experience.

Answer 4

Just after sunset, call a friend some number of time zones to the west and ask them where the sun is in their sky. Or, just before sunrise, call a friend some number of time zone to the east and ask them where the sun is in the sky. Then, think about why the sun is at different heights for you and for your friend. The more time zones this experiment crosses, the harder it will be to explain this as a feature of a flat earth.

Answer 5

The simplest method I can think of is to observe a hand-held global positioning system ('GPS'), which shows the position of visible satellites, directly overhead, and at various angles from the vertical. Once satellites disappear over the horizon, they reappear again exactly in accordance with an orbital trajectory around a sphere. Secondly, go to Google Earth - a composite of satellite photographs - and take a spin around the world. At all points the Earth appears as a globe. How is this possible if the Earth is flat? Thirdly, there are more than 100,000 commercial flights per day, which can be tracked on sites such as Flight Aware. Not one of these flights has ever seen an edge to the Earth. How come, if the Earth is flat? Fourthly, the sun and all the planets and dwarf planets have all been examined by probes and found to be spherical (more or less). On what basis should one expect the Earth to be any different? Fifthly, apart from minor purturbances caused by local geology, the Earth's gravity is pretty much uniform everywhere. How can this be possible in a flat Earth where the mass distribution would be very heterogeneous?

There are many more possible tests, but as you say, one can't change the minds of such people. 'Flat Earthers', like creationists and climate change deniers, have already made up their mind, and don't want to be confused by the facts.

Answer 6

Major problems with sunlight\energy\temperatures for the "southern Hemisphere". The Flat Earth Society offers this suggested map of a flat Earth and a rough idea of how seasons would work:

But because of the larger radius of the SH Summer circle, the sun would have to move faster to complete a circle in 24 hours during December. That would mean less sunlight per area in the southern hemisphere (or putting it another way, the same amount of solar energy is given onto a larger area in the southern hemisphere, meaning less energy per location). And that means colder temperatures.

For that matter, that larger circle should mean the sun moving through the sky more quickly there, and thus shorter days despite being nearer to the central path?

The one option to keep seasonal temperatures balanced would be moving the sun closer to give more heat, but that would mean even shorter daytimes. And either would cause more asymmetry in seasons, day length, etc at the Equator and between the summer and winter comparisons.

Answer 7

If you can get one dumpy level (surveyor level), it is very easy.

Place the dumpy level in one flat area and take the level from one point and transfer to another one. Try to do it as far as possible. At this stage it is suppose that you have 2 points on the same level.

Then place the dumpy level as close as you can to one of this points and transfer again.

You will get a deviation of 1.5 mm at 100 meters.

Why? The Earth is an spherical body so the gravity is radial. The gravity in one point have no the same direction that the gravity at 100 meters...

How can you explain this gravity deviation on a flat body?

The funny issue is that it happens in the complete planet... How flat-Earth defendors can explain it?

Yo can do the same issue with a laser level, even, with a hand level and one laser pointer.

On a flat earth, pendulus will maintain its normal direction, on a rounded Earth, this normal direction is changing as well as the difference of elevation between 2 points, as the pendulus become tilted.

Regarding this 1.5 mm every 100 meters... Mathematics: 100 meters * Atan (100 m / 6370000 m). Assuming an average radius of 6370 km for Earth, every 100 meters at the surface you are tilting the gravity 1.5 mm from the gravity 100 meters away in any direction. This phenomena it is registered in the whole planet.

Answer 8

There are some recommendations in the following videos:

• The Nightly Show - Neil deGrasse Tyson Slams Flat-Earth Theorist B.o.B
• Neil deGrasse Tyson Rips Kyrie Irving's Flat Earth Nonsense | TMZ Sports

and especially

• Neil Tyson Demonstrates Absurdity of "Flat Earth"

which includes suggestions like repeat Eratosthenes' experiment using three wells instead of two

watch an eclipse

or watch a ship sail off into the distance slowly drop below the horizon.

Answer 9

We can see the Moon's shape, right? We can see the Sun's shape too, right? And lots of other planets through telescopes? Does any of those looks flat to anyone? I guess not! Then, thinking further, I guess Earth cannot be flat...

Answer 10

How's the weather?

The circulation of winds around high and low pressure centers is driven by the Coriolis force, which occurs on rotating bodies. This of itself dies not exclude a flat Earth, for the Coriolis force can occur on a rotating disc (and that model actually does account for the stability of the Lagrange-point objects in space that are now known to follow the orbits of most planets). But the Coriolis force on a rotating disc is uniform in magnitude and direction, and weather observations on Earth disagree with both claims. The apparent dependence of wind circulation on latitude and the reversal that occurs when you move from the Northern to the Southern Hemisphere are instead more consistent with a rotating sphere.