A spherical star has mass kg and radius m

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Relativity & Gravitation · The equivalence principle and gravity as geometry

Relativity and Gravitation, Ch Gravity as curved spacetime: redshift and local inertial frames

Problem

A spherical star has mass M=3.0×1030M = 3.0 \times 10^{30} kg and radius R=5.0×108R = 5.0 \times 10^8 m. Light of a sharp spectral line leaves its surface and is received by a distant observer at rest far from the star, where the gravitational potential is taken as zero. Use G=6.674×10−11 N m2 kg−2G = 6.674 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}, c=2.998×108 m s−1c = 2.998 \times 10^8\ \mathrm{m\,s^{-1}} and Φ=−GM/r\Phi = -GM/r outside the star, and work to first order in Φ/c2\Phi/c^2. Ignore any motion of the star and of the observer. ((a)) Find the gravitational redshift zz of the line. ((b)) What recession speed would produce the same first-order redshift? ((c)) By how many seconds per year (a year is 3.156×1073.156 \times 10^7 s) does a clock resting on the star's surface fall behind a clock at rest far away?

Browse the problem library