The formula for force is

F = ma

The formula for the force of gravity is

Isaac Newton came up with these two formulas in 1687.The force of gravity between the earth and a body on its surface is the weight of the body.

My Gravity Theory

A body weighs less when it is moving.
The rest weight of a body is how much it weighs when it isn’t moving. The formula for rest weight is

Weight is equal to rest weight minus kinetic energy.

The Derivative of Kinetic Energy

The formula for kinetic energy is

What is the derivative of kinetic energy?
For a body that starts from rest and travels with constant acceleration, we have the following formula

Multiplying by ½m

A graph of this equation is a straight line. The slope of the line is ma.
A graph of kinetic energy versus distance traveled for a moving body might be a curve.
A straight line on a graph of kinetic energy versus distance traveled for a moving body has a slope of ma.
The slope of a tangent line on a graph of a function is the derivative of the function.
The derivative of kinetic energy, with respect to distance, is mass times acceleration.

Falling Bodies

What is the acceleration of a falling body?

Newton's Way

The force acting on a falling body is the force of gravity. For a falling body, we have

F = Fg
Ma = GMm/r2
A = GM/r2

My Way

The derivative of rest weight is

DRW =

The formula for weight is

W = RW - KE

The rest weight of a falling body is increasing.
The kinetic energy of a falling body is increasing.
The weight of a falling body stays the same.
For a falling body, kinetic energy and rest weight both change at the same rate.
For a falling body, we have

The positive direction is up. The acceleration of a falling body is downward, so the acceleration is negative.

Wrong

Mass times acceleration is the derivative of kinetic energy. It’s not anything else. Force is a bunch of baloney.
Force was invented by Isaac Newton. Newton never heard of energy. Newton didn’t know what he was doing.

Helmholtz's Gravity Theory

Gravitational potential energy is the integral of the force of gravity. The formula for gravitational potential energy is

Hermann Helmholtz came up with this formula in 1847.

Falling Body

The kinetic energy of a one-kilogram body that falls ten centimeters near the surface of the earth is one joule.

Helmholtz's Way

The value of GM for the earth is 399 trillion meters cubed per seconds squared.
The mean radius of the earth is 6,371,000 meters.
The gravitational potential energy of a one-kilogram body on the surface of the earth is −62,627,531 joules.
The gravitational potential energy of a one-kilogram body at a height of ten centimeters is −62,627,530 joules.
If a one-kilogram body falls ten centimeters near the surface of the earth, gravitational potential energy goes down one joule.
Mechanical energy is equal to kinetic energy plus gravitational potential energy.
As a body falls to the ground, kinetic energy goes up, gravitational potential energy goes down, and mechanical energy stays the same.

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My Way
The formula for rest weight is
RW = GMm/r
The rest weight of a one-kilogram body on the surface of the earth is 62,627,531 joules.
The rest weight of a one-kilogram body at a height of ten centimeters is 62,627,530 joules.
If a one-kilogram body falls ten centimeters near the surface of the earth, rest weight goes up one joule.
Weight is equal to rest weight minus kinetic energy.
As a body falls to the ground, rest weight goes up, kinetic energy goes up, and weight stays the same.

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