Does the gravity constant change?

[Rader]

Does the gravity constant change slightly over time due to the expansion of the universe?

What would be the consequences to applied science if it did?

 

[meteor]

The general consensus is that it don't change, but there always people trying to go against the mainstream; if not science would be very boring, don't you think?
One of the theories that postulates a variation of Newton Constant in space and time is Brans-Dicke theory.

What would be the consequences to applied science if it did?

You can imagine it: bad. Imagine a varying Newton constant in the vicinity of Earth. How positive can be it for our network of communication satellites?

This paper is interesting as postulates a varying Newton constant
Rippled Cosmological Dark Matter from Damped Oscillating Newton Constant
http://arxiv.org/abs/gr-qc/0409059
Saludos

 

[Chronos]

Not exactly as phrased. Expansion weakens the tug between distant objects merely by increasing distance [gravity follows the inverse square rule like other forces]. Variations in gravity over time would have a lot of pretty weird effects, assuming the variance was more than trivial. Stellar evolution would be goofy, orbits would would be messed up, as meteor noted, even really weird stuff like a black hole unforming - I can't really even imagine what that would look like.

 

[J20gU3]

when the universe was created set values for, speed of light, gravity etc etc were all specific. They may change but it would either pull the planets into the sun or send them flying out into space.