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By Ryan Prosser

Updated: 11:32 EDT, 12 September 2023

Members of the infamous Flat Earth Society are steadfast in their opinion that our planet is a disc, and that naysaying astronauts have been ‘bribed’ or are ‘mistaken’.

But a team of scientists from the University of Zurich is inviting them to disprove their latest statistical model, which shows (yet again!) that the Earth is indeed round.

The model predicts the time it takes to fly between two cities after inputting the distance between them.

It shows that if you fly north from Perth, Australia for seven hours, you’ll land in Hong Kong, while a westbound flight of the same length would see you land in Mauritius.

However, if the Earth were flat, that seven-hour westbound flight would only get you half the way to Mauritius.

‘It was important for us not to favor a model a priori, but to find a relatively simple method to prove whether the Earth is a disc or not,’ said study author Dr Michael Wolf.

For the last 50 years, we’ve been able to view pictures of the Earth from space, which might seem like all the proof you need to see that our planet is in fact round.

But the awareness of how easily images can be doctored and the growth of internet conspiracy theories appears to have fuelled a resurgence of belief in a flat Earth.

Those who subscribe to the flat Earth model believe that the Earth is a disc, with the North Pole at the centre and Antarctica stretching around along the edge.

Lines of longitudes are represented as spokes going outwards from the center, and lines of latitude are concentric circles.

This differs from the spherical Earth model, where lines of longitude connect the north and south poles vertically, while lines of latitude run horizontally around the globe.

One of the best documented methods for determining the Earth’s roundness is thought to have been first performed 2,000 years ago by the ancient Greeks.

They put sticks in the ground in different locations hundreds of miles apart, and compared the shadows they cast at the same time during the day.

They found that when the sun was directly overhead in one place there was no shadow, but at exactly the same time at the other location there was one.

If the Earth were flat then both sticks should show the same shadow, or lack of, because they would be positioned at the same angle towards the sun.

The ancient Greeks found the shadows were different because the Earth was curved and so the sticks were at different angles.

They then used the difference in these angles to calculate the circumference of the Earth, and managed to get it within 10 per cent of the value known to be true today.

For the new study, published as a working paper by the Social Science Research Network, the Switzerland-based team wanted to find another way to check if this was correct.

Dr Wolf said: ‘Statistics is the ideal method for answering a number of controversial questions. 

‘It is a purely mathematical science and does not depend on basic physical assumptions or ideological paradigms.’

He adds that many of the proofs relied upon by the Spherical Earth model are not accessible to the lay person, so the emergence of conspiracy theories is not surprising.

The distances between two cities on a line of longitude – like Perth, Australia and Hong Kong, China – are the same whether you believe the Earth is a globe or a disc.

Plus, the time it takes to fly between two cities is indisputable, regardless of beliefs.  

The team therefore created a model that, when given a distance between two cities on a line of longitude, gives the correct flight time.

Next, they inputted the distance between two cities along an east-west line, like Perth and Port Louis, Mauritius.

Due to how the Flat Earth and Spherical Earth models interpret the shape of the planet, they both give different values for the distance between these cities. 

But the statistical model only gave the correct flight time for between two cities on an east-west line when the Spherical Earth distance was inputted.

This therefore serves as a proof that the Earth is indeed round.

The authors wrote: ‘If the Earth was flat, Perth–Mauritius should take twice as long as Perth–Hong Kong, which it does not. 

‘The fundamental contradiction is that, under the flat-Earth model, flight durations observed on an East-West axis far away from the North Pole are incompatible with flight durations observed on a North-South axis.’

Dr Wolf added: ‘The really amazing thing about this method, however, is that it can be used not only to prove that the Earth isn’t a disc (i.e. that there is a curvature), but also to determine the value of the curvature.’ 

According to the Spherical Earth model – determined by physical measurements and unattainably complex calculations – the planet has a curvature of π/20,000 km.

The research team used the indisputable flight times between cities on an east-west line to get a value almost identical to this from a similar model to their first one. 

Dr Wolf said: ‘It is the first time that the value of the Earth’s curvature could be determined using a method that makes do with high school mathematics knowledge, classical statistical tools and publicly available data.’