The blue lines are Neap Tides (when the sun is opposite to the moons), with the effects added up in the green.
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Expression 10: "y" left parenthesis, "x" , right parenthesis equals 1.2 5 4sine left parenthesis, StartFraction, "x" Over 4.3 1 , EndFraction , right parenthesisyx=1.254sinx4.31
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Expression 11: "y" left parenthesis, "x" , right parenthesis equals 0.8 7 7sine left parenthesis, StartFraction, "x" Over 22.8 , EndFraction , right parenthesisyx=0.877sinx22.8
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Expression 12: "y" left parenthesis, "x" , right parenthesis equals 0.2 6 6sine left parenthesis, StartFraction, "x" Over 23.6 , EndFraction , right parenthesisyx=0.266sinx23.6
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Expression 13: "y" left parenthesis, "x" , right parenthesis equals 1.2 5 4sine left parenthesis, StartFraction, "x" Over 4.3 1 , EndFraction , right parenthesis plus 0.8 7 7sine left parenthesis, StartFraction, "x" Over 22.8 , EndFraction , right parenthesis plus 0.2 6 6sine left parenthesis, StartFraction, "x" Over 23.6 , EndFraction , right parenthesisyx=1.254sinx4.31+0.877sinx22.8+0.266sinx23.6
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This is the tide that combines the Spring and Neap tides, shown in black. The equation IS NOT PERFECT - it is my partner's best guess. It is best viewed over a period of x=2000 or more to really see what's going on, and best viewed alone.
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Expression 15: "y" left parenthesis, "x" , right parenthesis equals StartFraction, left parenthesis, 1 plus sin left parenthesis, StartNestedFraction, 4 "x" NestedOver 457 , EndNestedFraction , right parenthesis , right parenthesis Over 2 , EndFraction left parenthesis, 1.8 8 5sin left parenthesis, StartFraction, "x" Over 4.3 1 , EndFraction , right parenthesis plus 1.5 0 8sin left parenthesis, StartFraction, "x" Over 22.8 , EndFraction , right parenthesis plus 0.3 6 5sin left parenthesis, StartFraction, "x" Over 23.6 , EndFraction , right parenthesis , right parenthesis plus left parenthesis, 1 minus StartFraction, left parenthesis, 1 plus sin left parenthesis, StartNestedFraction, 4 "x" NestedOver 457 , EndNestedFraction , right parenthesis , right parenthesis Over 2 , EndFraction , right parenthesis left parenthesis, 1.2 5 4sin left parenthesis, StartFraction, "x" Over 4.3 1 , EndFraction , right parenthesis plus 0.8 7 7sin left parenthesis, StartFraction, "x" Over 22.8 , EndFraction , right parenthesis plus 0.2 6 6sin left parenthesis, StartFraction, "x" Over 23.6 , EndFraction , right parenthesis , right parenthesisyx=1+sin4x45721.885sinx4.31+1.508sinx22.8+0.365sinx23.6+1−1+sin4x45721.254sinx4.31+0.877sinx22.8+0.266sinx23.6
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Here is the average Earth tides, for comparison, using a random data point of high tide from NOAA and the time the moon orbits the Earth.
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Expression 17: "y" left parenthesis, "x" , right parenthesis equals 2.4 4sine left parenthesis, StartFraction, "x" Over 27.3 2 , EndFraction , right parenthesisyx=2.44sinx27.32
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Comparing the Earth tides to Homeworld's, we can see that Homeworld has tides that change more frequently and more dramatically than anything on Earth. Earth's tidal curve is smooth - Homeworld's is erratic.