Philip, apologies for my delay in replying.
You are correct in saying that your ancestor and Cook served on the same ship, but they did not serve together. The muster of the Mary shows that Cook served for most of the sailing season, from 8 February to the 5th October 1750. But the Master had to take on extra crew to make one more trip to London, and George Robinson was one of the sailors taken on for that last voyage. He enrolled in London on 30 November, and embarked at Whitby on 5th December 1750.

II believe James Cook was seaman on the Mary the same time as my 3x Great grandfather George Robinson aged 17 from Whitby 8/2/1750-5/12/1750 Whitby to London

I also am intrigued by cook naming islands with Cumbrian names .william brougham monkhouse his surgeon and Jonathan were from Carlisle Cumbria as was a previous surgeon known to cook John crosier surgeon of hms dolphin and William crosier surgeons second mate on cooks ship Pembroke were also born at dalston Carlisle.

Good luck with your studies Ron. What is needed is a directory of those locations and geographical features that were named by Cook, with an explanation of why he named them so. I am puzzled by your reference to Cumbrian names, as Cook spent his boyhood in North Yorkshire and never lived in Cumbria?

I will be visiting Whitby & Great Ayton early June seeking information on Capt Cook's journeys along the eastern Australian coast. He named many islands adjacent to the Qld coast all with Cumbrian names. In retirement I would like to achieve a degree in history majoring on the journeys of Capt Cook if possible. My family originally lived I Great Ayton until late 19th century when they moved to Durham.