# Earth as approximate inertial frame of reference

In many practical applications one can consider the earth approximately as inertial reference system (though it is non inertial).

Is there any quotable reference, where this claim is supported by a detailed estimation how small the effects are that one neglegts if one considers the earth frame as inertial?

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 – Qmechanic♦ Apr 25 at 19:21

This is only modified at the second order: the spacetime curvature (the Riemann tensor) is nonzero near the Earth. Equivalently, the spacetime curvature prevents us from setting the metric tensor equal to the flat spacetime metric at the second order. We may have the metric schematically of the form $$g_{\mu\nu} (\vec x) \sim \eta_{\mu \nu} + [R_{\alpha\beta\gamma\delta}] [x^\pi x^\rho]$$ So the metric is flat up to corrections that go like $x^2$ where $x$ is the deviation from the Earth's center. These corrections generically manifest themselves as tidal forces; the greatest contributions come from the Moon and the Sun; other planets may matter, too. The non-inertiality of the Solar System as a whole; and the non-inertiality of our local cluster etc. gives increasingly negligible contributions because the tidal forces decrease with the typical distance scale faster than the force itself.