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Each increase by one magnitude corresponds to a release of energy 31.6 times that released by the lesser earthquake.Since 7 is 3 magnitudes higher than 4, the magnitude 4 earthquake has roughly 1/31554th the energy of the magnitude 7.Each increase by one magnitude corresponds to a release of shaking amplitude 10 times that released by the lesser earthquake.Since 7 is 3 magnitudes higher than 4, the magnitude 4 earthquake has 1/1000th the shaking amplitude of the magnitude 7.The amount of energy changes much more rapidly with magnitude than the amount of shaking amplitude. This is a commonly made error.
The main difference is brightness: a twelfth magnitude star is brighter than a fifteenth magnitude star. Magnitude is a logarithmic scale, so each step in magnitude represents a difference in brightness of about 2.5 times. This means a twelfth magnitude star is approximately 12.5 times brighter than a fifteenth magnitude star.
The absolute magnitude of a star is a measure of its true brightness if it were placed at a standard distance of 10 parsecs from Earth. To calculate the absolute magnitude from the apparent magnitude (m) of 6, you would need to know the star's distance. Without this information, we cannot determine the absolute magnitude.
The magnitude difference between two stars can be calculated using the formula: Magnitude difference = 2.5 * log10(Intensity1 / Intensity2). In this case, the magnitude difference between Sirius and Polaris would be 2.5 * log10(24.2) ≈ 1.94.
The brightest stars were traditionally magnitude 1; the weakest that could still be seen with the naked eye, 6. This system has been formalized and refined; as a result, there are now not only magnitudes with decimals, but also negative magnitudes for the very brightest stars and planets. For example, Venus has a magnitude of approximately minus 4.