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Can Gravity Exist Without Matter – Proof?

February 19, 2013

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)

Coordinates

a particle has a position, a collection of three coordinates, (x1, y1, z1), which are the components of the position vector of a particle


R = (x1, y1, z1)
(radial vector)

a = (d2x/dt2)
[acceleration = vector made up of the time derivative of the components of the position vector of x1, y1, z1 (2nd derivative of the components of position with respect to time); first derivative of position is velocity = (dx/dt)]

then: F = m(d2x/dt2)

F2= – mg
(force on an object in a flat space approximation has only one component pointing downward, so component of a force in the x2 downward direction is proportional to mass of an object times a constant (g) or gravitational acceleration);

therefore: m(d2x/dt2) = -mg

(d2x/dt2) = -g
(mass cancels out)

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

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2 Comments leave one →
  1. March 7, 2013 4:22 PM

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  2. Polo permalink
    March 14, 2015 1:01 AM

    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).

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