Take the Nordtvedt parameter to be

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

The Geometry of Gravity, Ch The equivalence principle under test

Problem

Take the Nordtvedt parameter to be ηN=2×10−4\eta_{\rm N} = 2\times10^{-4}. The differential solar acceleration between the Earth and the Moon scales as Δa⊙=ηN×2.64×10−12 m s−2\Delta a_\odot = \eta_{\rm N}\times2.64\times10^{-12}\ \mathrm{m\,s^{-2}} (this fixed product is the binding-fraction difference times the Sun's acceleration at 1 AU, for ηN=1\eta_{\rm N}=1). The Moon's sidereal orbital period is 27.3227.32 days. ((a)) Compute Δa⊙\Delta a_\odot for this ηN\eta_{\rm N}. ((b)) Estimate the static (non-resonant) displacement this differential acceleration would produce on the lunar orbit, by dividing Δa⊙\Delta a_\odot by the square of the Moon's mean orbital angular frequency nMoon=2π/Torbn_{\rm Moon} = 2\pi/T_{\rm orb}. ((c)) The full lunar-theory result, which accounts for the fact that the forcing is nearly resonant with the orbit, gives an amplitude of 13.1 ηN13.1\,\eta_{\rm N} m instead. Compute this amplitude and compare it with the crude estimate from part (b), stating the approximate amplification factor.

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