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Mike Follows
Sutton Coldfield, West Midlands, UK
If a planet were flattened, its own gravity would cause it to collapse back into a sphere. For the sake of argument, let’s assume that this doesn’t occur. Imagine, instead, a flat, pancake-shaped Earth – a wide disc of uniform thickness.
At the very centre, gravity acts straight down. Trees grow upright and hills rise with vertical symmetry. The horizon is level in every direction and, on a clear day, you would see much further than on a globe of comparable size. On our spherical Earth, the horizon likewise appears horizontal to the naked eye, since its curvature is too slight to be detected by an observer at sea level and becomes noticeable only from elevations of about 50 metres or more.
Move away from the centre of a flat planet and the distribution of mass changes as more of it lies towards the centre than towards the rim. Gravity is no longer vertical: it tilts inwards, directed towards the disc’s centre of mass. The further out one travels, the greater this inward tilt becomes, while the overall strength of gravity gradually decreases.
Trees respond accordingly. Through “geotropism”, roots grow along the line of the local gravitational field, and trunks develop in the opposite direction. With increasing distance from the disc’s centre, trees lean progressively outwards. As gravity weakens, they can grow taller and more slender, exceeding the height of those nearer the middle of the planet. Conical hills behave in the same way: their peaks incline outwards and their slopes become slightly asymmetrical, with erosion favouring the inward side. Because the downward pull is reduced, their height increases with distance from the centre.
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On Earth, the horizon appears horizontal to the naked eye, since its curvature is too slight to be detected by an observer at sea level
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Across the broad, flat expanse, the outward-leaning forests and inclined hills extend to the horizon, marking the underlying geometry of the gravitational field. Rivers flow steadily inwards, carrying water and sediment across the plain.
Hillary Shaw
Newport, Shropshire, UK
At the disc centre, you would see a flat horizon with no clues that the planet isn’t spherical. However, walk towards this horizon in any direction and the gradient appears to steepen. Behind, you see a continuous downhill gradient as far as the opposite horizon edge. As you approach the rim, you would see an almost vertical cliff, as the vertical lines to the centre of gravity (just below the disc’s centre) run almost parallel to the disc surface. Your flat world now seems vertical, with the opposite horizon far below you.
Climb onto the rim and things look even weirder. You see a flat, narrow ridge with a horizon fairly close, as it curves away from you, with vertiginous cliffs descending on either side. The rim curves down, but feels flat as you walk along it. If you had a bicycle, you could scoot down the other flat side, racing down at high speed and partly up the other end, and back down again.
All this assumes the disc faces are flat. If there are high hills towards the edge, best avoid these, as they will look like conventional hills from the centre, but as you approach them on that steepening gradient, they will prove to be overhangs from which you might fall back to the disc centre.
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