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A reference frame is a particular coordinate system chosen to represent physical entities. The notion is most often used in special and general relativity to denote particular coordinates chosen on the spacetime manifold.

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The chronology of taking approximation changes the answer?

The problem is to find the time it takes a particle dropped from a height $h_0$ above the surface of the earth to reach the surface (exactly, not approximately i.e. $g$-value is not constant, in the l …
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which force should come out to be the same in both frames

Suppose that a long cart is moving at a constant relativistic speed with respect to the ground. Sand is falling on it from negligible height(from the same place and zero horizontal velocity with respe …
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The chronology of taking approximation changes the answer?

I've found out where the error was, it was not due to chronology of taking approximations, instead I had done error while approximating $\arctan(\sqrt{\frac{h_0}{R}})$. Let $x=\frac{h_0}{R}<<1$, then …
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