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1) C14 is assumed to be in equilibrium, otherwise C14 dating is invalid. Measurements contradict this assumption, yet it is used anyway.
As others have already explained, this is false. 14C is nearly, but not exactly, in equilibrium. But this does NOT invalidate 14C dating! It would affect dates to some extent (but no more than about 15%) if there were no calibrations from tree rings or varves. But with calibration methods, we would get accurate dates even if the 14C were far from equilibrium.
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2) Moon's motion is controlled by precise mathematical equation involving mass and gravity - you have to assume catastrophism, not uniformitarianism, to explain how the moon's path was once different. My point being that you assume catastrophism or uniformitarianism when your model requires it, you don't adapt your model to match either assumption.
I can't tell whether you are referring to the recession of the moon or the origin of the moon?
The recession of the moon (and the lengthening of the day) depends on tidal friction. Continental drift predicts that this is not constant. In the past, when there was a much smaller area of shallow oceans near the equator, the moon's recession was much slower. There is no "catastrophism" here.
As presently understood, the origin of the moon was due to "catastrophism" (collision of a Mars-sized object with the early earth). This is the theory which best fits the data.
The above reveals a common YEC misunderstanding of "uniformitarianism." We have evidence that scientific laws are universal and time-independent; otherwise we would not call them "laws." We often assume that scientific processes (as opposed to "laws") proceed at a constant rate, unless and until the evidence indicates differently, at which point we try to work out the time dependence of the process. In neither case do we simply "assume catastrophism or uniformitarianism" to fit a "model."
Edited by kbertsche, : No reason given.