2.1.2 Exploring further

In this paragraph we will look at what would happen if the force of Equation 2.1 is the gravitational force of the mass of Earth, hence assuming that somehow the stretching of spacetime by the mass of Earth causes a force equal to the force needed to accelerate an object with the mass of Earth on Earth. Hence if:

where M is the mass of Earth, and from Equation 1.0 we know that:

this yields:

This equation tells us that the stiffness of spacetime depends on the rest mass energy and the radius of the mass itself.
Calculating it for different masses, like for our Sun and the Earth, we obtain different results, which means that the assumption we made is incorrect as we expect k to be the same for all masses.