Proving the Earth is round at home
I am looking for practical ways to prove the Earth is round using materials accessible to the average person. I have zero interest in disproving Flat Earth folks.
I am inspired by Dan Olson's (Folding Ideas) excellent video where he is able to do this measuring the curvature of a lake near his home that has a very specific geography that lends itself to this sort of experiment. I've seen all sorts of ways to prove this measuring shadows and poles, using gyroscopes, etc. and wanted to know if there are any practical guides for proving once and for all that the Earth is round for yourself relying on nothing more than experimentation.
What I'm not looking for:
- Math relying on flight times/charts
- Video/picture evidence
- Deductive proofs built on agreed upon premises
- Expensive tests
- Extremely time consuming projects
- Underwhelming results (relying on a probabilistic argument for a round Earth from the evidence.)
What I am looking for:
- Practical experiments
- Things I could potentially do without spending much money
- Tests that aren't largely comprised of accepting someone else's research
- Potentially math-heavy evidence
- Results that are strong and conclusive
I've thought of finding some easy to test version of Eratosthenes' proof using two poles. I've also thought about using a balloon and sending something to space like what is done in this Tom Scott video. Nothing seems well documented in such a way as for me to be able to follow it at home.
TL;DR: I think it would be a meaningful experience to have the power to prove the Earth is round by myself, for myself. I can only compare this desire to the desire a child with a telescope has when wishing to observe Saturn or Mars themselves for the first time. It's not to prove anything or to settle doubts, but for the personal value of independently observing this astronomical fact oneself.
If you're willing to drive a bit you should be able to use Eratosthenes method, this guy did it with a bike :
https://www.youtube.com/watch?v=YaPa4esJJx4
Foucault's pendulum hits your brief pretty much perfectly, I'd say.
A Foucault pendulum proves the Earth rotates (as long as you don't set it up on the equator). A pendulum on a rotating discworld would precess in the same way.
You could move your pendulum a significant distance north-to-south and observe the change in rate of precession, I guess. That's probably convincing that the world is curved in some way; going from those observations to concluding that it is (roughly) spherical is definitely getting into some complicated geometrical math.
My thinking was as simple as "set up pendulum, time the precession, check own latitude on map, confirm the proportionality" - but it's definitely fair to point out the distinction in what that's actually showing, and maybe taking the latitude as an input isn't in the spirit of the post. Call it a verification of existing data, more than a proof, perhaps!
I think that the two sticks method of Eratosthenes (mentioned by @Staross) cannot be beat for simplicity, repeatability, and actual proofiness which many "proofs" often lack. It's the one that feels the most rigorous to me. However, there are a number of other great indicators that the earth is round that you could do to build up understanding; if you're open to doing multiple things on a budget, then perhaps doing many of the things mentioned would be possible?
In addition to a foucault pendulum mentioned by @Greg and considering the phases of the moon as mentioned by @nsz (both of which I recommend doing if you have the means to do multiple things) there are some other fun experiments you can do.
One of my favourite simple indicators requires the use of a tall building with a good elevator. It's also a way to experience the sunset twice in one day.
More broadly this can be used to observe further along the circumference of the earth while being higher up; ie you don't need a building and a sunset to do this, but you can do so with a high place and a low place that are quite close together.
You can also use Gravity to "prove" the spherical nature of planets, though this is often hand-waved away by flat earthers because it's seen as assumption of the antecedent. If Earth were flat, then the weight that we experience from gravity would fluctuate base on our distance from the centre of mass. Since moving a distance laterally does not change your weight, moving laterally cannot change the distance you are from the centre of mass.
A note about the sunset one: It is possible to do it on an eastward facing beach at sunrise as well - while standing up you wait for the smallest sliver of the sun to be above the horizon, then you lay down low to the ground and now the sun isn't visible again. We used to do this as kids growing up on the seaside when going to see the sunrise.
I was wondering how the sunset is supposed to look in a flat earth model and I stumbled upon that pretty cool method that uses the reflection of the sun on water :
https://www.researchgate.net/profile/Robert_Vanderbei/publication/228958090_The_Earth_Is_Not_Flat_An_Analysis_of_a_Sunset_Photo/links/0c960514b687116b2f000000.pdf
Probably the easiest and most straightforward way is to just look at the Moon, observe it's illuminated side change shape throughout the month, then have a think what shape could cause such an effect, keeping in mind a single lightsource, the Sun.
EDIT: Peel half of an orange then rotate it while looking at it with one eye closed (to remove parallax), you should see the phases of the moon!
Here's the leap, extrapolate that earth will most likely have the same or at least similar shape. Is there a good explanation why it shouldn't? To back it up, try explaining time-zones. If you've done any travel you'll have first had experience of their effect. What are the possible shapes earth can take that make time-zones possible? Try getting a call with someone a few time zones away, see the sun set twice in one day. Try explain the phenomenon.
While I enjoy what you've written and think it's a great piece of learning, I don't think it actually proves anything about the Earth; it presents compelling evidence that your hypothesis should be "the Earth is round" but not proof that the Earth is round.
Edit: I expanded a bit on this in a comment below - I think this is an important experiment, and I'm wondering if @RNG would consider doing multiple experiments to build up the proof about the earth.
Edit 2: In addition to being a delightful thought experiment, the bit with the orange is also scrumptious if done right.
Works on the Great Lakes, too. Probably other large lakes out there. Not sure of the math, but off the top of my head, I'd guesstimate anything more than 40-50 miles across would be big enough.
Much less than that in fact. The distance to the horizon is only ~5km (~3mi) for a 2m person standing on the ground (ignoring some details that change the exact numbers but not the general idea). Of course that means that you could just barely see another 2m tall person who is standing 10km away since both of your heads would be just barely above the curvature of the intervening Earth. Now, ships are a lot taller than people, but even from 50m up the distance to the horizon is only 25km/15mi, so even on a lake just 20 miles across the hardest part of demonstrating the effect is probably finding a boat tall enough that you actually need the whole 20 miles.
I wrote about this sort of thing here:
https://www.solipsys.co.uk/new/TheRadiusOfTheEarth.html?tj22tl
I give a talk in which I compute the distance to the Moon, and then as part of that I show how you can compute the size of the Earth using nothing more than a stopwatch, a ruler, and a clear view of the horizon. The simple version starts with that link, then there's a more refined version, and then a further refined version. As a bonus the series also includes how to compute your latitude just by watching the Sun rise or set.
I was pretty sure I'd posted those, but maybe I didn't.
I'm very open to mathematical arguments! I won't shy away from even quite complex ones. If there is a methodology you think I can do cheaply and accurately, I'd love to give it a shot. My point where I first bring up math is to avoid reliance on using flight charts or times to build my proof.
Additionally, I am very open to building some Arduino-based gizmo to go into space (I'd assume I'd just need a GPS, a balloon, and a SIM/LTE radio?) This is sort of what I'd like to do as part of that Tildes project thing.
A very direct way would be to observe a lunar eclipse, during a lunar eclipse you can see the shadow of the Earth on the Moon and see that it is round for yourself. E.g. the photos here
It requires some planning, but there are usually about two lunar eclipses a year that you can observe from any location. Here is a list of upcoming ones.
Despite requiring planning ahead of time, there isn't any math or equipment required, it is just a direct observation of the shape of the Earth's shadow. Granted, one could argue that the earth was a flat round disk and things were perfectly aligned, but if you observe several lunar eclipses, you'll see them at different times of the year, in different parts of the sky, and you could of course observe them from different parts of the Earth and you'll always see a nice round shadow.
As summarized in an often misattributed Magellan quote:
One of the problems with proofs that demonstrate Earth's roundness or rotation is that they do not preclude the possibility of a flat Earth in the way that something like Eratosthenes' proof does (which demonstrates curvature more than mere roundness.)
All that aside, a lunar eclipse does demonstrate that the sun is at times on the other side of the Earth, projecting the Earth's shadow onto the moon, which directly conflicts with most of the Flat Earth cosmology I've seen.
This is an old thread but it prompted a thought.
As you mentioned most of the DIY experiments only prove local curvature. Proving an object is a topological sphere requires global rather than local data. The best global data available is the collection of all GPS coordinates.
So we could ask how would spherical GPS coordinates would work on a disc? We can stereographically project a punctured sphere to a disc, but this means the boundary of the disc would be "the same place." If we do the same operation without removing a point from the sphere we end up getting an infinite plane as the origin of our projection is "infinity."
Reducing this as an experiment: buy a global atlas and glue it together. It will be a sphere unless you decline to glue the most external edged together. I'm sure there is a flat earther explanation for this but it probably means accepting we live in a pacman maze.