# Can Gravity Exist Without Matter – Proof?

This is a follow up to “Can Gravity Exist Without Matter?” To read the first installment go to: http://tinyurl.com/BarryOnEnergy003

According to Newtonian and Galilean Gravity:

→ →

F = ma

(force for this discussion is a three vector equation, where space is space and time is time and not united in space-time; the force on an object whatever it is, component by component, is equal to the mass times acceleration)

a particle has a position, a collection of three coordinates, (x_{1}, y_{1}, z_{1}), which are the components of the position vector of a particle

→

R = (x_{1}, y_{1}, z_{1})

(radial vector)

a = (d^{2}x/dt^{2})

[acceleration = vector made up of the time derivative of the components of the position vector of x_{1}, y_{1}, z_{1} (2^{nd} derivative of the components of position with respect to time); first derivative of position is velocity = (dx/dt)]

then: F = m(d^{2}x/dt^{2})

F_{2}= – mg

(force on an object in a flat space approximation has only one component pointing downward, so component of a force in the x_{2} downward direction is proportional to mass of an object times a constant (g) or gravitational acceleration);

therefore: m(d^{2}x/dt^{2}) = -mg

(d^{2}x/dt^{2}) = -g

(mass cancels out)

Therefore: gravity is dependent on the 2^{nd} derivative of the components of position with respect to time and not on mass?

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Your conclusion is wrong since a = g= (G.M)/R^2; thus, (d2x/dt2)= G.M/R^2, hence, there is still a term including mass (M).