This is my working hypothesis - the way I see it as of this moment!! 

Following is an e-mail from  Thomas Gale Moore to Sally. 
Tom's Home page.

"I have been doing some more research on the Moore family and I am virtually certain that you are right and that John Moore was the son of William Moore. I also believe that William Moore came over sometime just before 1652 to patent land that was owed his father, William Moore, who was an investor in the Virginia company. A William Moore is shown as an investor in 1609, the Second Charter. There is no evidence that he came over but many investors who didn't come sent their heirs to get the land.

Below is the first three paragraphs that I [TGM] have re-written to reflect this view. Also I am attaching a chart that shows this though the last two Moores are connect by dashed lines to indicate that I cannot be certain of their connection. 

The first Moore we are sure about was John Moore G9. (See Charts 3) His
father almost certainly was William Moore G10, who received a patent for 300
acres on a branch of the Nansemond River in Virginia on the 6 of December
1652. The records of the Isle of Wight show that in 1667, William Smelley
patented land on the western branch of the Nansemond River adjoining John
Moore. In 1668. Thomas Cullen also is listed as patented 400 acres adjoining
John Moore in the Upper Parish of Nansemond Co. The property being referred to must certainly be the same as that patented by William Moore in 1652. The fact that John Moore owned property on the Nansemond River makes the likelihood very high that William was John's father. 
I believe it is also significant that a William Moore (More) was a member of
the Virginia Company of London. . He is one of the signers of the May 23,1609
Second Charter. Many of those members sailed to Virginia to become planters;
some, however, were only investors. There is no evidence that William Moore
of London ever came to America. 
Nothing is really known about either William Moore of London or the one who
patented land in 1652 beyond what is described above. It is plausible that the
William Moore who was a member of the Virginia Company of London was
father to William Moore (G10) who patented land in 1652. Members bought
shares hoping to earn profits but also possibly land. Profits never materialized
but each share holder was offered land. According to Professor W. Stitt
Robinson, Jr. about one-third of the investors sailed to Virginia to become
planters, another third sent a representative, often their heir to occupy the land,
and the rest either sold the land or failed to exercise their rights. While William
Moore the investor probably never came to Virginia, he could have sent his son
and namesake, who in turn fathered John Moore before 1680. " 

Grandchildren of William Moore