Feasibility of an Experiment about Gravitation Consider a surface with very little friction. We put two solid bodies on it and want to observe gravitational attraction between them.
 Now my question is, what is the least dimensions required for that bodies to show the effects of attraction(can be seen by naked eye)? I missed the shape and dennsity but this is already a rough question.
And, my new question is what should be the mass ratio and shapes of two solids in order to get maximum attraction force, if we have limited amount of material in our hand? I think this is more like a mathematical question but you know, just curiosity.
 A: Generally speaking, gravity is an extremely weak force. It's weaker than the Weak Force and that has "weak" in the name, so you know it's got to be really weak. That said, any reasonably sized masses for this sort of experiment would not be likely to provide enough gravitational force between them to overcome static friction with any surface I can think of that you would have available. Stop: math time.
For simplicity, let's assume you use two masses of the same mass, $m$, separated by a to-be-determined distance, $r$. The force of gravity between them is:
$$F_g=\frac{Gm^2}{r^2}$$
However, the force of friction that each mass has to overcome in order to start moving toward the other is:
$$F_f=\mu mg=\mu\frac{GM_{Earth}m}{R_{Earth}^2}$$
Let's solve for the coefficient of static friction of the surface.
$$F_g>F_f$$
$$\frac{m}{r^2}>\mu\frac{M_{Earth}}{R^2_{Earth}}$$
$$\therefore \mu<\frac{m}{M_{Earth}}\left(\frac{R_{Earth}}{r}\right)^2$$
Plugging in some rough numbers:
$$\mu<(6.8\times10^{-12})\frac{m}{r^2}$$
It should be noted that you have to use standard SI units in this equation (I felt including the metre units in the constant would get confusing with $m$ already there). So what's the largest mass you can reasonably use? 100kg? Probably somewhere in that order of magnitude. And the distance between their center of masses? Even with the densest element, Osmium, the radius of a 100kg sphere would be around $10cm$, which means the minimum $r$ for that case is about $0.2m$. Plugging in the numbers, we find the requirement of $\mu<~10^{-7}$. Herein lies the problem. The lowest coefficient of static friction in a material is about $0.02$ between lubricated titanium boride and BAM (a ceramic alloy). Significantly larger than our $10^{-7}$ maximum.
What does this mean? It means that your experiment will not work on Earth (Earth's mass is the limiting factor here). There isn't a material with low enough friction.
Having said all of this, there is an experiment you can perform to see the gravitational attraction between two small masses. The Cavendish Experiment uses small masses suspended from a wire. This means they do not need to fight against static friction to start moving. They do need to contend with the restoring torque from the torsion in the wire as it rotates, but that won't prevent the masses from moving initially. Essentially, the gravity between the two masses (technically four, but I'll let you read the Wiki article) creates a new equilibrium point where the masses have rotated towards each other. By attaching a laser pointer to the free-to-rotate mass and having it point at a screen far away, you can actually see one mass accelerate and move under the gravity of the other mass. Pretty cool!
A: Sure it's feasible. The question is: is it more practical than say  the Cavendish experiment?  No real world mechanisms are frictionless. So engineering this approach would not be without challenge. Air bearing surfaces have the complication of gas flow disturbing the motion, and anything less than an air bearing would probably have too much friction to be overcome. Sure the greater the masses, the greater the gravitational force, but also more normal force and friction to deal with.
The advantage of the Cavendish approach is it pits a much more deterministic force (torsional spring) against the gravitational force vs the more irregular force of friction.
