Gravity with dependent time

As I’ve noted several times, the physics of the observer takes duration as the dependent variable and measures the corresponding length or other variable. This fits well with the finding that gravity is an approximately constant acceleration, g, which equals 9.81 m/s².

What is gravity in the context of an independently chosen distance and dependent time? Assuming a zero initial distance and zero initial velocity, from the equations of motion we have:

r = ½ gt².

Inverting that equation results in:

t = √(2r/g) = (2r/g)1/2.

The lenticity, w, is the derivative of the time with respect to the distance:

w = 1/√(2gr) = (2gr)–1/2.

The relentation, b, is the derivative of the lenticity with respect to the distance:

b = –1/√(8gr³) = –(8gr³)–1/2.

This means that

b²r³ = 1/(8g) = (8g)–1,

which is a constant.