Changes

The linear density of Newtonian gravitational force acting on dust (force per unit length), which is identically equal to <math>d^2E/d^2r</math>, where <math>r</math> is distance travelled by photons, can be written, using relativistic relation between mass and energy <math>(mass = Energy / c^2)</math> as <math>4\pi G\rho(E_o-E_d)/c^2</math> leading to equation <ref>See [[Essay:Demystified gravitation]] for step-by-step derivation of eq. (1)</ref>  

The linear density of Newtonian gravitational force acting on dust (force per unit length), which is identically equal to <math>d^2E/d^2r</math>, where <math>r</math> is distance travelled by photons, can be written, using relativistic relation between mass and energy <math>(mass = Energy / c^2)</math> as <math>4\pi G\rho(E_o-E_d)/c^2</math> leading to equation <ref>See [[Essay:Demystified gravitation]] for step-by-step derivation of eq. (1)</ref>  

:<math>d^2E/dr = \Lambda E </math> ...... (1)

:<math>d^2E/dr^2 = \Lambda E </math> ...... (1)

Substituting <math>1/R^2</math> for <math>\Lambda</math> and solving the equation with initial conditions <math>E(r=0)=E_o</math> and <math>(dE/dr)(r=0)=-E_o/R</math> (meaning selecting a solution that makes physical sense) one gets  

Substituting <math>1/R^2</math> for <math>\Lambda</math> and solving the equation with initial conditions <math>E(r=0)=E_o</math> and <math>(dE/dr)(r=0)=-E_o/R</math> (meaning selecting a solution that makes physical sense) one gets