# What is the simplest way to prove the Earth is round?

Assume you've come in contact with a tribe of people cut off from the rest of the world, or you've gone back in time several thousand years, or (more likely) you've got a numbskull cousin.

How would you prove that the Earth is, in fact, round?

• That depends on the definition of "round". – Leos Ondra Sep 17 '13 at 6:38
• At least two thousand years see en.wikipedia.org/wiki/Spherical_Earth#History – Selene Routley Nov 19 '13 at 12:31
• This question appears to be off-topic because it is most appropriate on earthscience.stackexchange.com – BMS Dec 24 '14 at 22:59
• Numbskull of a cousin? or a Flat Earther? If you're arguing with the latter, then he probably does not believe that the Earth is flat. He probably wants to demonstrate his own cleverness by confounding you with fallacies that you don't know how to disprove. – Solomon Slow Feb 28 '17 at 21:34
• If I were forced to debate a Flat Earther, I would ask about the alleged conspiracy. If the Earth really is flat, then everything you've been told about how ships and airplanes navigate long trips is a lie, and every ship's officer and aircraft pilot is in on it. Ditto for some huge number of people working with space technology, and ditto for all of the astronomers. They've been keeping us in the dark for centuries. How have so many people kept so big a secret for so much time? What motivates them? – Solomon Slow Feb 28 '17 at 21:55

The shadow of the Earth on the Moon during an eclipse and the way masts of ships are still visible when the hulls are out of sight are the classical reasons.

• actually, with a telescope or another telescopic sight, you can show the mast again. It's perspective. – Carlos Carlsen Feb 28 '17 at 17:41
• @ sorry - poorly worded – Martin Beckett Feb 28 '17 at 20:33
• @CarlosCarlsen the telescope doesn't make your view line curved, you'll still only see the masts. Beware of mirages though: they can totally mess up the observations. – Ruslan Oct 23 '17 at 6:45
• Funny that people are so strict affirming wrong things. Actually every student knows that no, you can't see around a corner. Perspective does not help. Perhaps meantime you mount and aim the telescope the ship got nearer :) – Alchimista Dec 14 '17 at 10:52
• @CarlosCarlsen If what you say is true, than gradual zooming in on a ship partially below the horizon would gradually bring the ship up. And zooming out would submerge the ship back under the horizon. This could be recorded on a video. But I have never seen such a video. I have seen videos where flat-Earthers claim this is documented, but in all these videos there is just a ship still completely above the horizon, where zooming in and out only makes it smaller or bigger. No submerging/reappearing of the hull is happening. – mpv Oct 15 '18 at 13:38

Simplest, you say? There are two that strike me as being simple to demonstrate. Luckily someone on the internet has already spent some time to help us here to make these easy to illustrate:

# 1. Shadows differ from place to place

Eratosthenes carried out this experiment to determine the circumference of the Earth, already assuming its spherical shape; incidentally, the proof of such being consequential of the procedure.

However, a demonstration can be achieved by a simple, local experiment (as opposed to having a party venture to a distant enough point):

Take a piece of card (A3, or so), attach two obelisks to the card by their bases and, with a light source, produce shadows - now, slowly bend the card so that it becomes convex (that is, the side with obelisks attached bulging out) and watch the effect.

# 2. You can see farther from higher

There are numerous other ways of demonstrating that the Earth is round, or curved, at least, from analysing the center of gravity to simply observing the other round objects that are visible in space; but I believe these illustrations to be the simplest to comprehend.

Images sourced from SmarterThanThat

• #1 assumes that the sun is arbitrarily far away, and #2 can give conflicting results at long distances due to atmospheric refraction – Nick T Aug 5 '16 at 22:35
• #2 is not true. The horizon always comes up to your eye level. So the distance you can see cannot be attributed to the higher you are up. – Java_User Jul 6 '17 at 13:40
• @Java_User that'll only mean you're looking down. What if you try to look along your local horizontal, e.g. using a bubble level? You'll see that the horizon is a bit lower. And the higher you get, the lower the horizon appears to be. – Ruslan Oct 23 '17 at 6:54
• #1 can't prove it with two points, but it can with three. Place an observer at the equator at noon on the equinox (sun directly overhead), and two other observers 1,000 and 2,000 miles north respectively. Have all three measure the angle to the sun at the same time. If the earth is a sphere, there is provably no solution that can be found for the measured angles that allows a flat earth and a relatively nearby sun. – dgnuff Oct 17 '18 at 21:20

Another way is the triple-right triangle:

1. You move in a straight line for a long enough distance
2. Turn right 90° degrees, walk in that same direction for the same distance
3. 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" an incomplete square.

Source: http://www.math.cornell.edu (add /~mec/tripleright.jpg to find the image)

• "Walk"? At some point, you'll have to swim. :) Which might be a welcome change from a year of walking... – cHao Apr 4 '14 at 4:18
• What is the minimum distance for each side? – Fractional Apr 14 '14 at 15:43
• @RedSirius I asked that very question some time ago. :) – Alenanno Apr 14 '14 at 17:17
• What's a practical way to ensure one is both turning through exactly 90 degrees and proceeding in "straight" lines? – Todd Wilcox Feb 2 '16 at 18:50
• 3/4 finished square – dibs Oct 28 '17 at 8:51

If the person in question is from a temperate latitude, take them to the tropics to feel the heat of the noon sun, preferably trapped out on a sailboat without water. Point to the very high sun and make your point when they are the most miserable. Next, take them to a very high latitude. As they freeze and become exhausted at 3:00 AM while out walking the tundra, point out the low, non-setting (or non-rising) sun, and re-iterate your point in their heightened state of misery. Through suffering and a sense of pride, the object of your demonstration will now likely feel that they have "been there" and "seen it" with "their own eyes". If convinced, that person will gladly proselytize the "truth" of aforementioned roundness of said planet, and will confront the heretics who do not believe.

I think that there are no simple answers to provide "proof" of anything. "Proof" is relative, much in the way "truth" is relative. If simple means "without using science or technology" then you are without hope, as the receiver of the "proof" must accept the truth of the methodology.

Photos from space are photoshopped.

Ships at sea look below the horizon because Osirus/Neptune/Odin/Jesus/Bhaal does not wish man to see to infinity (which also proves that the heavenly bodies are not very far away).

Sticks in the dirt and shadows prove nothing unless you accept that other bodies are permanent, in orbital motion, and far away (at which point the person will already believe that the planet is round).

Don't try to prove anything. You can't. Instead, "Demonstrate and educate", because all you can do is convince, not prove.

• +1, the power of 'torture' ? ;) Fernão de Magalhães paid with is life to prove that the Earth is round. (in eng. is Ferdinand Magellan) – Helder Velez Jun 28 '11 at 2:01
• Proof also connotes finality. Once something is proven, it need never be considered again. – user11266 Feb 20 '13 at 15:32
• @HelderVelez no he did not. People already knew the earth was round back in his time. He was hired to gather evidence that some people were invading some other people's territory on the pacific, by measuring the coordinates of said territory. He died because he picked a fight he shouldn't have, for stupid reasons, and took an arrow to his chest, not for saying what everybody already knew to be true. His story, as written by Pigaffeta, is interesting enough, but as others have said the ancient greek already know about the curvature of our planet. – Thermo's Second Law Mar 27 '17 at 13:18

Sitting for a while by the seashore ought to make it clear the Earth isn't flat, even if you don't happen to see a ship go over the horizon. The edge of the discworld Earth would have to be just a few miles away, and there's no way that the entire, circular world would fit inside the circle that the ocean horizon seems to make.

Humans have not just known the Earth was spherical but actually have been measuring its radius for thousands of years. http://en.m.wikipedia.org/wiki/History_of_geodesy

Besides the going back in time option, you could just show your "numbskull cousin" a picture of the Earth taken from the moon like the one below.

• Like the approach, side stepping an academic approach. Also you could show them picture/video from the ISS or this great video of James May taking a trip in a U2 spy plane where you can clearly make out that the Earth is round from 13 miles up: youtube.com/watch?v=x6cZLfK4Zjk – Fergal Jun 27 '11 at 11:22
• I just find that sometimes when you are going for "simplest way", you have to tailor it to the audience. Some audience members aren't going to understand the math or the academic approach and a different way to show them is necessary. – Annika Peterson Jun 27 '11 at 16:23
• What if your "numbskull cousin" doesn't believe in the moon landing? It's all fake! – jkeuhlen Dec 24 '14 at 20:53
• That photo wasn't actually taken from the moon, it was taken by Apollo 17 while on its way to the moon -- about 5 hours from launch - 2 hours after leaving Earth's orbit on the way to the moon. Though there are plenty of spectacular photos of the Earth from the Moon, plus some of moon and earth taken from beyond the moon – Johnny Oct 26 '16 at 20:42
• @Java_User why should thrust depend on an atmosphere? Newton's third law posits that "For every action, there is an equal and opposite reaction." So all you have to do to produce thrust is to throw mass in the direction opposite to the direction you want to go. You can test this by throwing stones from a small boat on a quiet lake. – Georg Patscheider Oct 18 '18 at 15:25

You can build a simple pendulum and observe how it rotates as the day progresses. You can then put a pendulum on a stick or something that you can rotate yourself in order to demonstrate that when you rotate the stick, the pendulum will continue to swing in the same direction. This shows that the direction of movement of the pendulum will change relative to its base only if its base is rotated.

Pendulums can also be used to measure your latitude (its direction will change at different rates for different latitudes), and to measure the local value of g (the amount of time it takes to go through one cycle, or its period of oscillation, will vary with gravity).

• Doesn' t this merely prove the Earth rotates? – Andrew Jun 24 '11 at 10:21
• @Andrew D'oh! I'm tired and assumed they meant the same. I guess by extension it proves the earth is round, assuming you're not doing this experiment at one of the poles. – Carson Myers Jun 24 '11 at 11:04
• It's also surprisingly hard to build a decent Foucault pendulum. It is necessary to insure that the suspension is torque-free, which is not easy. – dmckee --- ex-moderator kitten Feb 26 '12 at 22:45
• @dmckee torsion-free suspension is only part of the problem. I have seen the experiments described here from close up. Sir Brian Pippard was arguably a very, very good experimental physicist... but he was stumped. Well - he made a great pendulum, just not great enough to look for confirmation of the Thirring-Lense effect – Floris Jan 27 '16 at 20:49

The occurrence of noon (i.e. meridian passage of true Sun) isn't simultaneous for two observers situated along an east-west line. Hmmm...okay perhaps even simpler. Sunrise and sunset aren't simultaneous for those two observers.

I think the simplest way is to have two sticks of same size put both of them perpendicular to the surface of the earth in the mid day sunshine and the gape between them is to be few miles and exact time mesure the angle of elevation or mesure the size of the shadow so both will be differ! By several exams in a sysmetic order we can find that the earth is round.

There's a video on youtube of a island a few miles away such that when you see the island from an elevation, you can see further to its base than you can when you see the island from the shoreline ( a demonstration of answer 1 above). I think this is the simplest way given that now we have zoom ability, anyone can do this kind of experiment on a clear day from any shoreline viewing something a few miles away.

Classically, the gravitational force experienced by a mass $m$ above the Earth is given by the familiar,

$$F=G\frac{Mm}{r^2}$$

where $M$ is the mass of the Earth. In other words, a mass will experience a force which continually decreases as it distances itself away from the Earth. Now suppose the Earth was a flat infinitely$^{\dagger}$ large plane in $\mathbb R^3$ which is infinitesimal, with mass density $\sigma$ (per unit area, not volume). The gravitational potential $\Phi$ satisfies the Poisson equation $\nabla^2 \Phi = 2\pi G \sigma \delta(z)$, assuming the plane is at $z=0$.

The solution is given by $\Phi(z)= 2\pi G \sigma |z|$. The gravitational force is $-\partial_z \Phi$, which is always pointing towards the plane. Another feature is that the gravitational force is constant with magnitude $2\pi G \sigma$. In other words, no matter how high one is above the plane, the same forced is experienced. To be more realistic, if the plane had some non-zero thickness, the force would still be constant, but whilst inside there would be a 'jump' as depicted:

Hence, to determine if the Earth is flat, one would simply have to conduct an experiment to see how the gravitational force scales as one increases altitude. One will find $F \sim r^{-2}$ approximately, as expected, confirming the Earth is round. Of course, for sufficiently small variations in $r$, one may be fooled into thinking $F$ is constant since the change is minute, but it is measurable.

$\dagger$ For convenience, it is taken to be infinitely large; the conclusions remain the same, but the force will of course be different, since it will be dependent on $x$ and $y$ as well.

• I like this answer because it is one the knowledge - impaired cousin can easily understand – WoJ Dec 22 '15 at 6:21

If you're in the northern hemisphere, walk to the south and notice how Polaris sinks lower and lower each night until it disappears below the horizon. If he can handle more info point out how the stars before you are getting higher and the stars behind you are getting lower. Of course then you'll need to explain their east to west motions too.

• Very curious answer – SaudiBombsYemen Feb 28 '17 at 22:21

Here's another way, which only works in the Southern hemisphere - at least that is the case if you use the Flat Earth Society's map of the world, where Antarctica is a ring of ice around the works, and the North Pole is at the centre.

When flying from Sydney to Santiago or Pretoria, you regularly get close enough to Antarctica to see it. If the earth were flat, that would mean a huge waste of fuel. Only on a spherical world does this kind of trajectory make sense. On a flat earth, the shortest distance from Sydney to Santiago is via the North Pole, Sydney to Pretoria takes you across the Himalayas.

Of course this depends on airlines trying to save fuel - if all of them are in cahoots with NASA and all the other conspirators who claim a spherical earth, then all bets are off...

• Having been through a discussion in a radio show with a FE'er, I can tell you that this argument — as well as any other argument — does not prove anything to them. The extra fuel spent is nothing compared to all the resources outside the Southern Ring of Ice that are being hidden from us. – pela Jul 7 '18 at 11:11

Showing a picture of the earth from space seems like the simplest way to prove that the earth is round, but first of all you would need to convince this tribesman that this photograph is taken from far up in the sky. This can be done by taking a video of the earth from takeoff to orbiting the earth. That way he can see the connection between the world around him and the blue dot on a black background as representing the same thing, the earth.

Seeing a plane disappear behind the horizon. If the earth wasn't round (i.e. flat) the plane would be visible for a longer time than if it was round, assuming it would be visible for a long time.
Of course, the earth could also have another, more exotic form, like a banana, kiwi, pear, or pine apple. Or maybe have a book form. So you have to make a distinction between two forms only: sphere-like or flat.

1. Watch live ISS footage. Neither Hollywood nor any software can produce this raw footage at such level of realism.

2. See planes flying live. See for instance how you can go from NY to London, then from London to Tokyo, and the from Tokyo to NY, always going eastwards. If still in doubt, try it yourself.