- #36
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In the restframe of the Earth, i.e., our usually used frame for experiments, we have an approximately inertial frame and we can take the gravitational force of the Earth into account in the approximation of ##\vec{F}_G=m \vec{g}## with ##\vec{g}=\text{const}##. Equivalently you can switch to a freely falling frame within this approximation of a constant gravitational force. Then you are really in an inertial frame.
This is, however of course, an approximation, and the Earth-fixed frame is not an inertial frame, because of the rotation of the Earth around its axis, leading to nice phenomena like Foucault's pendulum.
Today the best realization of a real inertial frame is to use a freely-falling reference frame, where the cosmic-microwave background radiation is at rest, i.e., is really homogeneous and isotropic (neglecting the otherwise very important fluctuations of its temperature at the order of ##10^{-5}##), but that's another story.
This is, however of course, an approximation, and the Earth-fixed frame is not an inertial frame, because of the rotation of the Earth around its axis, leading to nice phenomena like Foucault's pendulum.
Today the best realization of a real inertial frame is to use a freely-falling reference frame, where the cosmic-microwave background radiation is at rest, i.e., is really homogeneous and isotropic (neglecting the otherwise very important fluctuations of its temperature at the order of ##10^{-5}##), but that's another story.