The Earth is has a globular shape and sea water level is a plane.
We are on the upper surface of the Earth, then how is sea water level a plane?
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2$\begingroup$ Short answer: It only seems to be flat in the area you can see, because the Earth is a lot bigger than you are. $\endgroup$– SpencerDec 25, 2022 at 20:23
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$\begingroup$ it's not really a plane in the large scale, it's a spherical (well, oblate-spheroid) shell. But locally appears like a plane just like the horizon and walking in a path appears a flat line. Where did someone call sealevel a plane? $\endgroup$– JeopardyTempestJan 25 at 19:31
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1 Answer
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Water level is flat with regard to the balance between several forces predominantly gravity (other smaller effects include baroclinic effects). The direction of Earth's gravity is a combination of gravitational pull and inertia (centrifugal "forces"). The gravitational pull is toward the relative center of mass of the earth-moon system depending on the relative position of the Moon with respect to the local position on Earth's surface.
Simplified sea level for a stationary uniform Earth covered by water. Source
Gravity does change slightly in different areas based on Earth's density (more info in this answer). A good explanation of why water level is "flat" is found here.
The ocean is not like a bathtub. At shorter time scales the water level surface responds as a balance between multiple forces (tides, wind stress, friction, baroclinic torque, ...). The balance is complex and highly local:
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$\begingroup$ Gravitational pull is not towards the Earth-Moon barycenter unless you are much farther away than the distance between the Earth and Moon. From the close-up vantage point of Earth's ocean level Earth's gravity is more dominant over the Moon's and the pull is thus more nearly towards the center of Earth alone. $\endgroup$ Jan 25 at 3:05
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$\begingroup$ The gravitational pull is always relative to the relative position with regard to BOTH Earth and Moon. Of course at the Earth surface the pull of the Earth is much larger, but the gravitational pull is still with regard to the Earth-Moon system. Otherwise you will be missing the tides. $\endgroup$– arkaiaJan 25 at 12:11
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$\begingroup$ Still not directed towards the bartcenter when you are on the surface of Earth. Work out the force resultant. $\endgroup$ Jan 25 at 12:15
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$\begingroup$ True. It will vary depending on the relative position of the point on Earth surface and the Moon. Not the barycenter. Corrected. $\endgroup$– arkaiaJan 25 at 14:05