Subject: Is escape velocity dependent on mass of captive object?

Please help settle a friendly wager borne of long forgotten studies- 
My neighbor says that the earth's escape velocity is a constant 11 
km/s, regardless of the mass of the body escaping, at least up to the 
point where the captive is equal in mass to the captor. To prove his 
point he asks, assuming the moon was at rest on the surface of the 
earth, "Is the mass of the moon significant to change the velocity 
required for escape from the earths' gravity well to <.05 or <.01?"

Since I believe the moon's gravity would increase the velocity 
necessary to separate the two, my question is "Is the escape velocity 
for any two bodies the sum of their separate escape velocities, 
computed assuming the escape of an object with an insignificant 
gravitational force, i.e. in this case, earth 11, moon 2 for a total 
of 13 km/s?

Though I am really rusty  on my algebra, my guess is that an object 
1/100th the size of the earth or larger would increase the escape 
velocity by 1% or more - Anything smaller than that would be 
insignificant.

Please help us. Are either of us anywhere close to being right in our 
approach to this question?

Thanks for your help.

Re: Is escape velocity dependent on mass of captive object?