How much mass does an object in low earth orbit need to create visible gravitational effects on the surface?

The question stems from watching a scene from ID2 and seeing the massive alien mothership landing/crashing on the North Atlantic.

What mass would a starship, or any other artificial object constructed in low earth orbit, need to be to start to create noticeable gravitational disturbances for the planet or spatial object it is orbiting?

By 'noticeable', I mean something like higher tides that can clearly be linked to the object in orbit or a slight shift in the orbit of the planet. Not something that only some precise instrument can measure and that scientists can determine through mathematical formulae. Something that would have the leaders of the planet think that it is time to get the construct away.

Is there a general rule, like 'at 10% of the mass of the planet', or does it vary depending upon what you are orbiting? Ie '10% the mass of a planet but 25% the mass of a G-type star'?

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How much mass does an object in low earth orbit need to create visible gravitational effects on the surface?

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