Why Density and Buoyancy Can't Substitute for Gravity

(c) 2020 by Barton Paul Levenson

Introduction

Why do Flat Earthers insist there's no such thing as gravity? Because if gravity exists,

1. It would pull anything the mass of Earth into spherical shape. That's why planets are round.
2. It would keep the oceans on the Earth's surface instead of having them flung away by centrifugal force.

The Earth rotates, and Flat Earthers often try to disprove this by pointing out that pouring water on a rapidly spinning basketball or tennis ball gets the water flung off. Clearly, they think, the same should happen to the oceans.

Units

Let's review some basic physics. Newton's first law is: an object remains at rest or moving with a fixed velocity unless a net force is imposed on it. In other words, you can't change velocity without imposing a force. In mathematical terms:

f = m a

where f is force, m mass, and a acceleration. In the SI metric system, mass m is measured in kilograms, and acceleration a in meters per second squared--an acceleration of 1 m s^-2 means velocity increases by 1 meter per second every second. So units of force must be kilogram meters per second squared (kg m s^-2). Force in the SI is measured in "newtons," where 1 N = 1 kg m s^-2. Same thing.

Density

Flat Earthers say density accounts for why things fall, and buoyancy accounts for why some things don't fall (e.g. helium balloons).

Ignore the obvious problems with this, like the fact that the density of the air decreases as you go up (away from Earth's surface). That being the case, things should fall up, since the difference in density is greater going up than going down.

Instead, let's just point out that density in the SI is measured in units of kilograms per cubic meter (kg m^-3). This is not a unit of force. Difference in density? Still kg m^-3. Subtract the density of air (1.225 kg m^-3) from the density of a rock (3,000 kg m^-3) and you've still got a figure in the same units (2,998.775 kg m^-3). Wrong units. Density is not a force.

Buoyancy

How about buoyancy? Buoyancy IS a force! The equation for it is:

f = ρ g V

where ρ is the density of the medium, g the acceleration of gravity--how about that, you need a term for gravity in the buoyancy equation!--and V is the volume of medium displaced. Let's check the units. Density ρ is in kg m^-3. Gravity g is in m s^-2. And volume V is in cubic meters (m³). Multiplying them all together, you get... kg m s^-2, which are newtons, the units of force.

But consider that g term. Without gravity, buoyancy won't work. Put a rubber duck in a three-foot ball of water in zero g, perhaps on the International Space Station, and it will not float to the surface. There's no preferred direction if g = 0.

So density isn't a force and buoyancy depends on gravity to work. And the Flat Earthers are wrong.

Surprise, surprise.