Gravitational Mass and Inertial Mass The physical property of mass has two distinct aspects: gravitational mass Mg and inertial mass Mi. The gravitational mass produces and responds to gravitational fields. It supplies the mass factors in Newton's famous inverse-square law of gravity (F = GM g M ′g r 2 ) . The inertial mass is the mass factor in Newton's 2nd Law of Motion (F = M i a ) . These two masses are not equivalent but correlated by means of the following factor [1]: Mg = χ Mi

where χ can be expressed by ⎧ 2 ⎡ ⎤⎫ ⎛nW⎞ ⎪ ⎢ ⎥⎪ χ = ⎨1 − 2⎢ 1 + ⎜ r 2 ⎟ −1⎥⎬ ⎜ρ c ⎟ ⎪ ⎢ ⎥⎪ ⎝ ⎠ ⎣ ⎦⎭ ⎩

where nr is the refraction index , W is the density of electromagnetic energy and ρ the density of rest inertial mass. Usually, the value of

W

⎛nW ⎜ r ⎜ ρ c2 ⎝ M g ≅ Mi .

is very small, and the factor

very smaller than one. Consequently, χ ≅ 1 and results

⎞ ⎟ becomes ⎟ ⎠

[1] De Aquino, F. (2010) Mathematical Foundations of the Relativistic Theory of Quantum Gravity, Pacific Journal of Science and Technology, 11(1), pp. 173-232. For more details see: www.frandeaquino.org

Gravitational Mass and Inertial Mass

Published on Oct 1, 2011

About the distinction between gravitational mass and inertial mass

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