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A first principles physics model for the Earth’s magnetopause position R provides an accurate initial approximation as a power law R ~ P^a, where P is the solar wind dynamic pressure. In the approach of dipole Earth’s magnetic field configuration and gas-dynamics solar wind flowing around the magnetosphere the exponent a equals to -1/6. Early satellite measurements in 60-80s had showed that such approximation is valid. However, one study using PROGNOZ satellite data base found a deviation from the “first principle” law of (1/6) with a ~-1/5.3. At present, various studies using huge statistics of 15 thousand magnetopause crossings indicate that probably the exponent a is about of -1/5. We discuss previous and recent results and give interpretation for such deviation.