Is proximity a factor in speed of light's relative effect on time

That is, in order for Burt to experience a different passage of time
than Ernie by traveling at the speed of light while Ernie stays in bed,
must he also travel somewhere away from Ernie?

Or, put it this way. Burt goes to visit Ernie, who has suffered an
accident that will leave him in a coma and bedridden the next 20 years.
I know. It's sad. Burt gives Ernie a Mickey Mouse watch as a present
to his old comatose friend. He looks out the open window of Ernie's
room. It's such a nice day outside that Burt decides to hop out the
window to a nice patch of grass about 15 feet away (where he can still
keep an eye on Ernie.) Here he decides to try out his new toy.

Burt's toy allows him to hover just above the ground while moving in a
circle (with a 2 foot radius) at the speed of light. It's okay, Burt's
not hurt. He's a puppet. He hovers and spins above the same patch of
ground for the full hour on his Big Bird watch. During his hour, does
Burt watch everything speed up around him? Do the days and nights fly
by around Burt, the change of seasons subjecting him to flashes of rain,
snow, and summer heat, while comatose Ernie grows older and his Mickey
Mouse watch spins furiously?

The classic example would have Burt do something like take a spaceship
to the nearest star and back, and I understand that when Burt returned
the time he experienced relative to Ernie would have been much shorter.
But in this example, Burt remains within approximately 15' of where
Ernie was the whole time. Is the proximity he had to Ernie during the
time he spent traveling at the speed of light a factor in how he
experiences time compared to Ernie?

Thanks folks!
.

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