[@rogersofnorwich]

@rogersofnorwich asked the Naked Scientists:
   
Could the moon be made denser in order to attract an atmosphere and be made arable? We can worry about tides as and when...

What do you think?

[yor_on]

heh

Transmuting the moon, are we?

[CliffordK]

As you know, gravity is based on both mass and distance to the center of mass, or the center of the planet.

If the moon was made denser without changing the mass, one could potentially increase the surface gravity without affecting the gravity or the tides on the Earth, and without necessitating adding more matter (from somewhere).

So, the density of the moon is about 3.346 g/cm³.
If the same mass was converted to the density of lead 11.34 g/cm³

Then the size of the moon would be much reduced, and thus the surface gravity would be increased.  I don't have the actual calculations. 

However, it would be exceedingly difficult to convert all the matter on the moon to Lead.  Likewise, it would be difficult to generate alloys and compounds that would match the density of lead.

[neilep]

I'm just a sheepy but if we were really able to do this to the moon would it not have catastrophic effects  for life on Earth ?

[CliffordK]

I'm just a sheepy but if we were really able to do this to the moon would it not have catastrophic effects  for life on Earth ?

If you could change the density without changing the mass, it would have little if any effect here on Earth.  The main difference would be less reflected light on those dark, cloudless nights.

Adding mass equivalent to a planet the size of Venus locked into a close orbit would be a whole different story.