Radiohead lead singer Thom Yorke was at the head of the marchers who had found a moorland footpath on an Ordnance Survey map that led to the perimeter fence of RAF Fylingdales, the early warning station.
They exercised their right to walk the path and got within 400 yards of the pyramid-shaped structure.
"There has never been a big protest so close to it before," said Yorkshire CND spokesman Neil Kingsnorth.
The marchers were escorted by a heavy police presence along the A169 Whitby Road from their base camp at Ellers Beck.
The pyramid building shoots a radar beam 3,000 miles into space to pick up any incoming missiles and is currently being upgraded so that it can track as many as five weapons.
Mr Yorke said: "Since 9/11, the US and Britain can now hide this system under the concept of defence against rogue states. The legacy for our children if this Star Wars system is allowed to happen is absolutely terrifying.
Retaliation
"I don't know how Defence Secretary Geoff Hoon, who has authorised this work, can sleep at night. Apparently, there may be some jobs in it, so that's all right then."
Dave Knight, of the Global Network Against Weapons, praised Mr Yorke for making a stand. "So many celebs don't put their head over the parapet because they are worried it will affect their careers. So congratulations, Thom."
Kate Hudson, chairman of CND, said: "This station is part of the US drive for global domination. In their Vision 20/20 they talk about full spectrum military dominance of land, sea, air and space.
"This system will give the US the capacity to wage a first strike war without fear of retaliation."
A statement from protesters who were simultaneously campaigning at Fort Greely, Alaska, was read out and the Americans in turn read a statement from the Fylingdales group.
The North Yorkshire demonstration was one of 100 around the world during Keep Space For Peace Week, 60 of which were held in the United States.
howard.williamson@ypn.co.uk