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3,589 miles

Update by ffinybryn:

Seattle is at Latitude 47d36'35" or 47.60972222 degrees of a Great Circle from the Equator.

Assuming a Mean Earth radius of 6371Km:

Distance to Equator is (47d36'35"/360) x 2 x pi x 6371 km

= 5294 km

= 3290 miles

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