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Equation 3 · How We Know What Is Inside a Planet

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I∗I^{*}

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I∗I^{*}

Symbol I^*

I∗I^* is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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What a moment-of-inertia factor rules out is more reliable than what it establishes. It is a single number, so it cannot distinguish a small dense core under a light mantle from a larger, less dense core under a heavier one; infinitely many radial density profiles share the same I∗I^{*} . But it will refuse an entire class of models outright. For Mercury, MESSENGER radio tracking combined with spin measurements gave C/MR2R^{2} = 0.353 ±\pm 0.017 together with a ratio of mantle-plus-crust moment to total moment of 0.452 ±\pm 0.035 , a combination consistent with a solid silicate outer shell over an iron-sulfide layer, a liquid iron-rich outer core and possibly a solid inner core [ 7 ] . Seven years…
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What a moment-of-inertia factor rules out is more reliable than what it establishes. It is a single number, so it cannot distinguish a small dense core under a light mantle from a larger, less dense core under a heavier one; infinitely many radial density profiles share the same I∗I^{*} . But it will refuse an entire class of models outright. For Mercury, MESSENGER radio tracking combined with spin measurements gave C/MR2R^{2} = 0.353 ±\pm 0.017 together with a ratio of mantle-plus-crust moment to total moment of 0.452 ±\pm 0.035 , a combination consistent with a solid silicate outer shell over an iron-sulfide layer, a liquid iron-rich outer core and possibly a solid inner core [ 7 ] . Seven years later, a longer tracking arc revised the normalised polar moment to 0.333 ±\pm 0.005 [ 9 ] . The revision is worth dwelling on: the earlier value was not wrong within its stated uncertainty, but the interior models it supported shifted materially when the uncertainty shrank by a factor of three.

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