3. In this problem we estimate the mass deficit due to gravitational attraction, an effect that is intrinsic to relativi

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3 In This Problem We Estimate The Mass Deficit Due To Gravitational Attraction An Effect That Is Intrinsic To Relativi 1 (96.06 KiB) Viewed 36 times

3. In this problem we estimate the mass deficit due to gravitational attraction, an effect that is intrinsic to relativity theory. The mass-energy equivalence means that mass is not an invariant property of matter, and the effective mass is the rest mass modified by the energy content of the object, so if the energy changes by AE then the mass changes by AM = AE/2. Apply this idea to spherical bodies that are in equilibrium between their gravitational attraction and the repulsion of internal pressure. In this case, an equilibrium state implies that 2 Ekin + U, = 0, where Ekin is the total kinetic energy and U, is the gravitational potential energy. (a) Find an expression for the total energy Etot in terms of U, and therefore estimate it in terms of the total mass M, radius R, and constants. (b) Use the relativistic mass energy relation to find an expression for the fractional mass deficit AM/M due to gravitational equilibrium. (c) use your answer in part (b) to estimate a numerical value of AM/M for the Sun (you can look up its mass and size) and for a typical neutron star with mass 1.4 M. and radius R= 13.5 km. Are relativistic effects important in either case?