Im not sure if youre serious.
A multi-ton object would not have any appreciable gravitational pull. The largest man-made objects ever created do not create an appreciable gravitational field. Using the calculator here:
An asteroid with a mass of 4*10^18kg at a distance of 1km from a Saturn 5 rocket fully loaded (Mass of 4 * 10^7kg) would feel an acceleration of 0.000000001 m/s^2, and would accelerate the rocket at a rate 10 orders of magnitude higher. The only noticeable effect would be the rocket being pulled into the asteroid, barely altering its course before joining it.
That completely ignores how insanely expensive even that minuscule experiment would be.