[latebind (OP)]

Hypothetically speaking, what would happen if we repeat gallileo's experiment, with 2 bowling balls. One bowling ball is normal and one is made from neutron star. Would they really fall at the same rate?

Would'nt the neutron ball fall faster?

[Bored chemist]

The bowling ball and the earth would fall towards the neutron star if it was massive enough.

[syhprum]

If a 1 Kg and 100 Kg ball are both at the top of the tower at the start of the experiment the time taken for the 1 Kg ball to reach the ground will be greater than the time taken for the 100 Kg ball to take the same journey.
This is due to the fact that the as the 100 Kg is falling attracted by the Earth the Earth is also moving up towards it.
Realising that the Earth has a mass 6*10^22 times that of the ball it will be seen that the difference is very small but it is real.
If the 100 Kg ball was replaced by a vastly more more massive one constructed from Neutron star materiel the effect would be much noticeable but the tower would not have enough strength to support it!   

[lyner]

To get a proper answer to this one, you need to specify the quantities involved. Galileo assumed an isotropic gravitational field, for a start.

[Soul Surfer]

Galileo's experiment assumes the normally quite legitimate approximation that the falling object is much less massive than the earth which is providing all the gravitational field.  If you make one of the objects a very heavy object that adds significantly to the gravitational field between the two objects it is bound to fall faster but then the total gravitational field has changed in the experiment.  This illustrates the fact that most experiments involve approximations and if you push things too far the original approximations are invalid and new calculations have to be used.

[Bored chemist]

To get a proper answer to this one, you need to specify the quantities involved. Galileo assumed an isotropic gravitational field, for a start.

He wouldn't have know one of those if he tripped over it.
On the other hand, he was clever enough to know that the generally held opinion at the time (thanks to Aristotle I think) was wrong.
The general belief was that heavy things fell faster than light things.
He considered two balls, one light and one heavy, tied together with a bit of string.
Together they form a heavier object than either of the two balls. So they "should" fall faster. But the heavy ball should also fall faster than the light one. So it should get out in the lead. Somehow, the slower lighter ball would have to push the heavy one in order that the whole lot fell faster than the big one would fall on its own. That doesn't make sense.
Galileo did the experiment to convince the locals who were too entrenched in their dogma to accept the validity of the argument. (that reminds me of another thread somewhere)