In our terrestrial reference, the Sun travels in 24 hours an entire circumference with a radius of 152 million km, corresponding to a speed
of about 11,000 km/s.
Is it correct to say that this is the speed of the Sun for us?
If the answer is yes, is it correct to say that, again in our
terrestrial reference, Pluto has a much greater speed than that of the
Sun?
[[Mod. note -- Yes on all counts. And in that
attached-to-the-rotating-Earth reference frame, every star other than
the Sun has a coordinate speed which is much larger than the speed of
light. (And that speed would be even larger if you choose coordinates
attached to the minute or second hand of an analog clock!) There's no violation of special or general relativity here because these are
*coordinate* speeds.
In Newtonian mechanics or special relativity, it's easy to see (and experimentally measure) that these "attached to rotating objects"
coordinate systems are in fact rotating with respect to inertial
reference frames. In particular, looking at the motion of a gyroscope, Foucoult pendulum, etc, in the rotating frame will quickly reveal the
rotation. See
https://en.wikipedia.org/wiki/Newton%27s_bucket
https://en.wikipedia.org/wiki/Foucault_pendulum
for some interesting related discussions.
[There is a sad/amusing video on youtube where the cinematographer follows
some flat-Earth believers (who also believe the Earth to be an inertial reference frame) who buy and operate a (fairly expensive) gyroscope to
try to "prove" that the Earth is non-rotating. Their gyroscope promptly detects the Earth's rotation with respect to an inertial reference frame,
and the video shows them spending some time trying to figure out what's
"wrong" with their gyroscope. :) ]
In general relativity one can use any coordinates, including rotating
ones like these... but you need a metric tensor that corresponds to the coordinates you're using, and in a rotating coordinate system the metric
tensor has lots of off-diagonal components which are such as to just
cancel out the effects of rotation when you try to compute the light cone. (Which is as it must be, since light cones are invariant, i.e., they don't depend on the coordinate choice.) So, the speed of light stays constant,
and nothing material moves outside the light cone.
-- jt]]
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