Do heavier objects fall faster?

[Blinkz]

Right having a great Saturday night discussion with my house mates. Basically we are talking about mavity. We are assuming no friction, air resistance etc

I think that objects will fall towards each other at the same rate. My thoughts on this is that as the mass of an object increases the gravitational force increases, however the increase in mass also increases the force needed for the same acceleration, using F=ma

However my mate says this is wrong and that heavy objects fall faster. His example of this is the earth and the moon. The acceleration towards the earth is bigger then the acceleration on the moon.....

any thought??

 

[Blinkz]

Like I said guys this is all a theoretical situation, so no air resistance or anything. The acceleration between the objects is relative to each other, not from another observation, if that makes sense.

Any actual proof to the answer would be great!

 

[Blinkz]

I recon if you had a giant empty universe, and only had the earth and an apple, and another giant empty universe, with only the earth and the moon, and in each universe you set them the same distance apart and released them, the moon and earth would collide sooner than the apple and the earth.

yes but the earth and the moon have more mass so even though the force is inceased, the acceleration will not change due to the masses increasing.

I think the pertinent bit of information that is missing is to whether the gravitational force increases proportionally to the mass, if it does then they will fall at the same rate, if the force increases faster then the mass increases then the heavier mass will fall faster.....