Bodies freely fall when dropped from a certain height. But they also have their mutual gravitational forces acting on each other. For small bodies I suppose the effect wouldn't be noticeable, but if heavy bodies having tonnes of mass are dropped from large height, they have to stick or at least come a little closer. Why does this not happen?
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2$\begingroup$ Just to be clear, are you asking about two bodies that are dropped side-by-side, and are you asking why they do not seem to be attracted to each other as they fall toward the Earth? $\endgroup$– Solomon SlowCommented Jun 25, 2021 at 12:32
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$\begingroup$ Yes that is correct sir @Solomon Slow $\endgroup$– SHIKHAR CHAMOLICommented Jun 26, 2021 at 6:56
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1 Answer
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The amount the two masses would approach each other is minuscule and effectively impossible to measure.
Imagine two large bodies being dropped next to each other. The acceleration that one body feels towards the other is (roughly) $a = GM/r^2$, where $G$ is Newton's constant, $M$ is the mass of the other body, and $r$ is their separation.
If we imagine two bodies with 1 ton of mass that are 1 meter apart, this acceleration works out to be $6.67 \times 10^{-8} \text{ m/s}^2$. This is in comparison to the $9.8 \text{ m/s}^2$ with which they accelerate towards the Earth. It's not too hard to show (try it!) that they will move approximately 7 nanometers towards each other for every meter that they fall. This is well below the level of accuracy with which we could reasonable expect to measure, and would be swamped by local non-uniformities in the Earth's field.
As pointed out by Solomon Slow in the comments, it is definitely possible to measure the mutual attraction of masses much smaller than the Earth. The most famous such experiment is the Cavendish torsion balance experiment. But to get a measurable effect from such a small acceleration, you must let the forces act over a long period of time, and the relatively brief window of free-fall from a reasonable height simply won't do.
answered Jun 25, 2021 at 12:01
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$\begingroup$ you probably already know this, but for the benefit of anybody else who might be reading your answer: The force of gravity acting between "small" objects can be measured. Henry Cavendish did it in the late 18th century. en.wikipedia.org/wiki/Cavendish_experiment It's just that, like you said, the force is so small that it would not be practical to try to measure it while the objects were freely falling toward Earth's surface. $\endgroup$ Commented Jun 25, 2021 at 12:36
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$\begingroup$ @SolomonSlow: Good idea for an addition to the answer. Thanks. $\endgroup$ Commented Jun 25, 2021 at 12:42
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2$\begingroup$ So, as Randall would certainly suggest in a what-if column, "Now let's try it with much more massive objects..." $\endgroup$ Commented Jun 25, 2021 at 12:47