I'll admit, I have an insanely persistent desire to get behind some of the more out-there theories when it comes to stuff like this - like the X-Files, I really really want to believe this thing could really be 13,000 years old.

Unfortunately, the guy who originally came up with the source info that supposedly traced the Black Knight's radio signal to the Epsilon Boötis system ended up recanting his own statement because of errors in his measurements: "Duncan Lunan took data from Norwegian radio researchers who believed they had found an unusual signal... Once Lunan realized the data he was studying was flawed, however, he immediately withdrew his conclusions." For various technical reasons, he couldn't definitively claim the signals had come from the Epsilon Boötis star system.

Basically there were indeed confirmed recordings made by Tesla and later by the Norwegian scientists of LDE radio reflections...but there are multiple possible explanations for them, most of them having to do with strange effects in the Earth's ionosphere.

Regarding Gordon Cooper's sighting: certainly compelling, but we should keep in mind that Cooper actually reported seeing UFOs on several different occasions, and yet strangely enough, his transcripts from the Mercury mission do not include references to the Black Knight. And as for the object itself - the close-up images posted here, and the most frequently cited evidence for the existence of a genuine "extrasolar satellite," were taken from the space shuttle orbiter Endeavor during the STS-88 Mission in 1998, which began construction on the International Space Station. During the mission, a thermal blanket (specifically a Trunnion Pin Thermal Cover) had become dislodged during an EVA and drifted away into space. People who have studied NASA video footage of the Endeavor astronauts working with the thermal blanket point out its similarity in feature to the Black Knight - as it tumbled towards Earth it seemed to change shape in the photos (the backgrounds of the different photos correspond to a downward trajectory; you can see the object drifting towards the upper cloud layer).

NORAD apparently briefly picked up the thermal blanket on radar, but its orbit decayed so fast that it burnt up in about a week.

(Disclaimer: my dad worked for the space program at Lockheed Martin and I have kind of a casual obsession with NASA and related things.)