Gravity is Stronger Than I Thought

I’m not a physicist, and I’d always supposed that, while the Earth has a significant gravitational pull because it’s so massive, the gravitational pull between everyday objects must be completely undetectable, or maybe only detectable with modern laboratory equipment.

But I only thought that because I never bothered to actually plug in any numbers.  Using the formula \displaystyle{\frac{G M m}{r^2}} for the force of gravity, you can see that if you have two 1-kilogram objects 0.1 meters apart, the acceleration due to gravity between them is enough to move them by 2.7 millimeters in just 15 minutes.  Wow!

Of course, this makes sense, given that G was measured all the way back in 1798 by Henry Cavendish.  I think I knew that G was measured quite long ago, but I just assumed it was based on some astronomical calculations, or was some sort of indirect inference.  Nope, it turns out Henry Cavendish put some lead balls on a torsion balance and directly measured how much they attracted each other.  Cool!

4 thoughts on “Gravity is Stronger Than I Thought

  1. Interesting! I wonder if conditions could ever be set up, where this motion would actually take place? Or would it always be swamped by frictional effects? Maybe a good experiment to do on the International Space Station? –Tom

  2. Yeah, I found it quite surprising! I think that Cavendish’s original experiment (the link is here: https://en.wikipedia.org/wiki/Cavendish_experiment; it was in the blog post too, but sort of hidden) essentially did just that: the lead balls moved towards each other due to their own gravity. I think you have to be quite careful not just of frictional effects but also other objects around, air currents, and stuff like that.

  3. Yeah, I saw your link to Cavendish. But I was thinking of something more dramatic, like 2 balls actually rolling towards each other. (Or floating towards each other, in Earth orbit.) That IS a pretty amazing experiment Cavendish did though, back in 1797-98, getting a value for G that was only one percent off !

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