Measurement of the gravitational constant $G$ in free fall is there a reason why an accurate measurement of $G$ cannot be performed by measuring the distance and rotation period between 2 orbiting 1 kg masses in free fall?
Using a simple estimation for 2 Pt spheres of 1 kg each (radius 22 mm) separated by 4 radiae centre-to-centre I estimate a period of 20500 s or about 5.7 hours. Could it be performed in ISS?  Could the sources of error be managed so that the accuracy of torsion balances is surpassed?
 A: Two platinum spheres in free space might orbit each other in six hours, but near the Earth they would orbit Earth every 1.5 hours.  In practice you would be measuring their orbits around the Earth, which interact with each other in surprising ways.
Many years ago I was adjacent to an effort to design such a satellite-based gravity experiment. (If it ever had a website, it's long gone.)
The idea was that small test masses would be released in a cavity in a satellite in low-Earth orbit, so that their primary interaction was mutual gravitation.  It turns out that mutual attraction would not make them orbit each other; instead they would undergo what's known as horseshoe orbit interaction, and be repelled from each other in the accelerated reference frame of the satellite.
I would guess that if you wanted your two bodies to primarily orbit each other, you would have to move them far enough from Earth that their mutual period is much briefer than their orbital period around Earth.  You might be able to do your six-hour experiment in a geostationary orbit, with a twenty-four hour period, or you might have to go higher.  You might compute the size of the Hill sphere for your test masses for different Earth orbits.
Furthermore, everything about doing a space-based gravitation experiment was at least ten times harder than you might have expected.  In low-Earth orbit, my friends learned that their mutual-gravitation experiment was going to be sensitive to things like the location of sufficiently large herds of cattle relative to the orbital path.  That's probably a reason why the GRACE mission happened before Gravity Probe B, and why my friends' GPB-beating experiment never happened at all.
A: You would not want to do this in the ISS.  It would need to be in a vacuum, and the gravity from the station and the people moving around inside could have an effect.  Placing it a couple of hundred yards away might work. Out there you might need to worry about the gradient of the earth's field.  In terms of measurements, getting an accurate distance between the masses could be a limiting factor.
