Preprint Article Version 1 This version is not peer-reviewed

# Gravity without Newton's Gravitational Constant and No Knowledge of Mass Size

Version 1 : Received: 11 August 2018 / Approved: 13 August 2018 / Online: 13 August 2018 (08:24:57 CEST)

How to cite: Gaarder Haug, E. Gravity without Newton's Gravitational Constant and No Knowledge of Mass Size. Preprints 2018, 2018080220 (doi: 10.20944/preprints201808.0220.v1). Gaarder Haug, E. Gravity without Newton's Gravitational Constant and No Knowledge of Mass Size. Preprints 2018, 2018080220 (doi: 10.20944/preprints201808.0220.v1).

## Abstract

In this paper we show that the Schwarzschild radius can be extracted easily from any gravitationally-linked phenomena without having knowledge of the Newton gravitational constant or the mass size of the gravitational object. Further, the Schwarzschild radius can be used to predict any gravity phenomena accurately, again without knowledge of the Newton gravitational constant and also without knowledge of the size of the mass, although this may seem surprising at first. Hidden within the Schwarzschild radius are the mass of the gravitational object, the Planck mass (their relative mass), and the Planck length. We do not claim to have all the answers, but this seems to indicate that gravity is quantized, even at a cosmological scale, and this quantization is directly linked to the Planck units. This also supports our view that the Newton gravitational constant is a universal composite constant of the form $G=\frac{{l}_{p}^{2}{c}^{3}}{\hslash }$ , rather than relying on the Planck units as a function of G. This does not mean that Newton’s gravitational constant is not a universal constant, but that it is instead a composite universal constant that depends on the Planck length, the speed of light, and the Planck constant. Further, $\frac{G×1 \mathrm{weight} \mathrm{unit}}{{c}^{2}}=\frac{G}{{c}^{2}}$ is the Schwarzschild radius off one weight unit. So G is only needed when we want to use gravity to find the weight of an object, such as weighing the Earth. This is, to our knowledge, the first paper that shows how a long series of major gravity predictions and measurements can be completed without any knowledge of the mass size of the object, or Newton’s gravitational constant. As a minimum we think it provides an interesting new angle for evaluating existing gravity theories, and it may even give us a small hint on how to combine quantum gravity with Newton and Einstein gravity.

## Subject Areas

Schwarzschild radius; weight, planck mass; planck length; measurement; gravitational constant; Heisenberg