The gravitational constant is a number. What sets it apart from other numbers is that you can multiply the gravitational constant by the mass and radius of a large body to find the strength of its gravitational field.
Calculating acceleration, force, energy, and other gravitational potentials is simple. Just multiply the constant by the right inputs and out pops the answer. The mathematical formulas go a long way towards helping us understand gravity, but do they explain all there is to know about this mysterious number? Perhaps you wonder why the gravitational constant gives the right answers to so many different questions?
The answer lies in the elementary form of the constant. The gravitational constant is made up of smaller units called Planck units. These units are natural quantities of length, mass, and time.
The gravitational constant has six Planck units–three units of length, one unit of mass, and two units of time. These natural units are arranged in ratios that are useful for calculating gravitational potentials.
We can show the constant using only the elementary Planck units, or we can simplify the constant using the symbol 𝑐 for the speed of light.
elementary form
simple form
The defining characteristic of the gravitational constant is the ratio of Planck length to Planck mass. This is the maximum mass density of a gravitational field, and also the mass density of a black hole.
Formulas use inputs of mass in the numerator and distance in the denominator to determine how diluted a gravitational field is from the maximum mass density potential. The ratios of Planck length to distance and mass to Planck mass produce a dimensionless number that quantifies this reduction in the field’s strength.
Gravitational field strength can be expressed in terms of energy, force, acceleration, and other potentials exerting themselves on a second body. The quantity 𝑐2 which makes up the rest of the gravitational constant is the basis for calculating these physical dynamics.
We can restate gravitational formulas in their elementary form by substituting natural Planck units for the gravitational constant. These formulas show that ratios of length, mass, and time are the real forces governing the strength of gravity and not the composite value of the gravitational constant.
Gravitational acceleration
The traditional formula for gravitational acceleration uses inputs of mass 𝑀 and distance 𝑟.
Combining these inputs with the Planck units making up the gravitational constant produces a formula
This natural formula has two parts:
- The maximum potential of the unit dimensions we are solving for—in this case, acceleration. The maximum acceleration potential is created from the ratio of Planck length to Planck time squared.
- Dimensionless proportionality operators in the ratios of Planck length to distance and mass to Planck mass. The dilution of acceleration potential is determined by these operators.
The following illustration emphasizes the two distinct parts of each natural formula.
Gravitational force
The same formula works for calculating gravitational force. The traditional formula adds the mass of a second body 𝑚 to the previous formula.
Nothing more is required to calculate the force, but inserting a hidden quantity of Planck mass in the numerator and denominator reveals the maximum force potential on the right, and a set of proportionality operators on the left.
The mass density ratios of the two bodies reduce the maximum force potential in the right proportion to quantify the attractive force between them.
Gravitational energy
The formula for gravitational energy requires mass inputs for bodies 𝑀 and 𝑚, and the distance 𝑟 between them.
The formula expresses the gravitational field strength from 𝑀 in terms of the energy potential acting on the second body 𝑚. Revealing a hidden quantity of Planck mass in the numerator and the denominator produces the correct operators and maximum energy potential.
Schwarzschild radius
The Schwarzschild radius measures the distance to the event horizon of a Schwarzschild black hole. The formula does not describe the influence on a second body, so an input of 𝑐2 in the denominator removes 𝑐2 from the gravitational constant. Inputs of 2 and mass 𝑀 complete the formula.
The natural formula modifies the Planck length potential in the right proportion to give the black hole’s radius.
Replacing the gravitational constant with elementary Planck units reveals hidden information about the natural world that is explained by the New Foundation Model of physics. This model gives new meaning to abstract mathematical ideas and explains traditional formulas in terms of the physical unit dimensions length, mass, and time.