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## Main Question or Discussion Point

Hello everyone,

I'll go straight to the question. The gravitational time dilation is equal to

However, the formula for speed of light in gravitational field is equal to

My intuition tells me that these two formulas must be the same, since time dilation must compensate the speed of light change. Am I wrong or there are other parameters that must be taken into account (like length contraction etc). Or maybe the formulas don't describe the same situation (free fall in one case and g-force in the other case).

Thank you

I'll go straight to the question. The gravitational time dilation is equal to

**t**, with_{earth}= t_{space}*sqrt(1 - r_{s}/r)**r**_{s}= 2GM/c^{2}.However, the formula for speed of light in gravitational field is equal to

**v = c(1 - r**_{s}/r).My intuition tells me that these two formulas must be the same, since time dilation must compensate the speed of light change. Am I wrong or there are other parameters that must be taken into account (like length contraction etc). Or maybe the formulas don't describe the same situation (free fall in one case and g-force in the other case).

Thank you