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In response to
"If Alaska is about twice the size of Texas, why doesn't the geographic center move north a distance about the size of Texas? and West also? -- nm"
by
rollo
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Here is the best way I can explain it. -- (edited)
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Thinking of the continguous US and the state of Alaska as point masses at their geographical centers. Lebanon, KS and Tanana, AK are close enough for the example.
Now Alaska is about 1/5 the size of the contiguous US, so the weighted distance between the two point masses will be considerably closer to the Lebanon end than the Tanana end. In fact, it will be only 1/6 of the way from Lebanon to Tanana (or 5/6 from Tanana to Lebanon if you prefer).
The distance from Lebanon to Tanana is approximately 2,720 miles. 1/6 of that is about 453 miles, so the addition of Alaska to the lower 48 should move the center of mass about 453 miles along the geodesic between to the endpoints, which places it up by Belle Fourche, SD, north and west of Lebanon by 300 miles in each direction give or take.
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Responses:
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