Our moon is about 30 earth-diameters away. In this case
components of forces exerted on any little part of our planet
are very small in comparison with perpendicular components
(on my picture where the moon-earth line is horizontal).
Thus lunar tidal forces (gradient of F) are essentially
horizontal (on my picture). But this would not be so for
an asteroid located only one earth-diameter away from
the center of our planet. Would the vertical force
components reduce the tidal effect? I would expect so.
And I hope we will never have a chance to test this
experimentally for a very massive asteroid. Can this be
tested on a very small scale? For example, in solid tides
mutually induced in two large cannon balls.
Ludwik Kowalski