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Tim Duckenfield answered on 13 Mar 2018:
That’s a really good question actually! Earth feels the Sun’s gravity quite strongly – in fact, about 175 times as strongly than we feel the Moon’s gravity. However tides are not caused just by the amount of gravity felt – tides are caused by the DIFFERENCE in gravity felt between one side of the Earth and the gravity felt at the other side. The tides on Earth are caused by the fact that when the moon is overhead (say above the UK), the near side feels 6.8% more of the Moon’s gravity than the far side does (like Australia). This difference of 6.8% causes the seas closest to the Moon to bulge upwards, making tides as the Moon orbits us.
The Sun’s gravity is nearly the same between the near side and the far side – a difference of only 0.017%. So although the actual force of gravity is bigger from the Sun, the difference between sides is small, so the tidal forces are small. Even so the Sun still has some tidal force, which by some quick calculations turn out to be about 3% the tidal force of the Moon – I didn’t know that before answering this excellent question, so thanks!
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