If Earth was flat, how would gravity manifest?
Mel Earp
Macclesfield, Cheshire, UK
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That is a brilliantly simple question, yet so revealing. To answer this, we need to put to one side how an Earth with a flat side would form. With Newtonian gravity, this would be quite difficult, as any planet or celestial body large enough would tend towards being spherical.
If we ignore this but still assume there is Newtonian gravity, the key driver would be where the centre of mass of this Earth was. The gravitational force on the flat surface would act towards this point.
We can immediately see two effects. Firstly, the distance between a point on the surface and the centre of mass varies and therefore so would the strength of gravity across such a flat Earth. Secondly, the angle at which gravity acts varies too: the directions you feel to be up and down wouldn’t stay the same or be perpendicular to the ground except at the point on the surface directly “above” the centre of mass: the gravitational epicentre.
The edge dwellers of a hemispherical Earth might develop specialised means of locomotion to cope with the gravity
As an example, suppose this Earth were a hemisphere with its inhabitants living on the flat surface. Also assume it was of uniform density and, being “half an Earth”, half the mass of our planet. (You would have to consult the local geologists as to why this is the case.)
In this scenario, the centre of mass is 3/8 of the radius down from the centre of the inhabited disc. This results in the gravity at the edge being about 1/8 of that at the centre, just because of the increased distance from the centre of mass. This is quite some difference. Even more dramatic is the angle: at the edge, you would feel gravity at an angle of just less than 70 degrees from the vertical. You would almost be lying down with respect to the ground to stay “upright”.
It would be very confusing indeed to us, as we are used to the spherical Earth. Your eyes would tell you it is flat, but your inner ear would say you are on a very steep hillside.
At the centre of the disc, the strength of gravity would be just over 3.5 times the strength of our gravity, which is almost constant across the globe. That is despite the mass of this Earth being half that of our planet. This is because you would be so much closer to the centre of mass. At the edge, it would be less than half of our Earth’s gravitational force.
Evolution on a hemispherical Earth would be interesting too. Edge dwellers might develop specialised means of locomotion to cope with the angle of action of gravity. They might well have the characteristics of mountain goats.
Since the strength of gravity would dramatically increase as you moved from the edge to the centre, these creatures probably wouldn’t be able to survive moving towards it.
Circular bands of adaptations might well develop, with much stronger and more powerful creatures in the central ocean and less powerful, but nimble creatures at the edge.
Mike Follows
Sutton Coldfield, West Midlands, UK
We are pulled towards the centre of gravity of whatever object we stand on. For a spherical Earth, which is spherically symmetric, this is downwards towards the centre of the planet.
If we were to move across the surface of a disc-shaped Earth from its centre towards its edge, the direction of gravity would gradually swing away from the vertical, eventually becoming nearly horizontal by the time we reached the edge.
The thinner the disc, the closer to horizontal this force vector will point. In this scenario, buildings would need to be constructed as though on an increasingly steep incline, so that the floors would always remain at a right angle to what we perceived as “down”.
Rather than falling off the edge, we would be able to stand on it comfortably, with the centre of gravity directly beneath us. The truly unsettling situation would be falling back along the surface towards the centre of the disc.
Some believe that a flat Earth is constantly accelerating upwards, as if in freefall, which gives us the perception of downward acceleration and weight.
To create a flat Earth that mimics the sensation of gravity pulling in the same direction everywhere, the distribution of mass would need to resemble something like an hourglass shape in cross-section or two oppositely facing cones joined at their apexes.
Of course, it could be made to have a uniform thickness by adjusting the density distribution to mimic the required mass distribution, but this would be extremely difficult to achieve in practice.
To cosmic rays travelling close to the speed of light, Earth already appears length-contracted and therefore flat.
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