Will the force of gravity between 2 osmium balls overcome friction?

Question

Suppose we have 2 osmium balls.

If we make them big enough and we place them on a low-friciton ground, will they accelerate one toward the other due to gravity?

Even if the math would be useful and helpful , It's not really what this question is asking for.

I'm trying to understand if there is this possibility of seeing 2 objects come together on earth due to the force of gravity between them.

Does earth gravity prevent this from happening at all?

Does anyone has ever clearly observed it?

The only one I know about it's the Cavendish experiment but there balls are suspended, I'm curious if it can happen with balls just rolling on a ground!

Answer 1

The main problem that you'll have here is the friction. For example with sand when I searched it up I didn't see the coefficient of friction go below a value of $0.2$. Taking account of the mass of sand $($which according to a quick google is $6.66\times 10^{-4}$ grams$)$ I calculated the minimum maximum friction $($tad confusing$)$ in this case to be $6.5268\times10^{-6}$ newtons. Using the equation$$F = \frac{Gm_1m_2}{r^2}$$I got the force between the sand and an osmium ball with radius $100m$ to be approximately $4.21\times 10^{-9}$. This is not enough to overcome the friction between the sand and the ball.

If you ignore friction, however then you do get some results. For example, placing a grain of sand $1$ metre away from the ball gives an acceleration of the sand particle of $6.32\times 10^{-6}$. Using the equation $$t = \pi\sqrt{\frac{r_0^3}{8G(m_1 + m_2)}}$$ which is the time that two objects take to travel a distance $r_0$ to each other due to their gravitational attraction. $($A link to a proofs of this can be found here) you can calculate how long it would take the sand to attract towards the osmium ball. Using $r_0$ = $1$ metre we get a time of $441.98$ seconds, which isn't actually that long at all!

I can't think of any examples on earth however say you have an astronaut in the international space station, where gravity is around 90% of what it is on earth and you have two objects weighing 1kg about 0.5 metres away from each other it would only take around 9.5 hours for them to attract. Enough time for objects to attract to each other overnight, for instance.