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May 8, 2022, 8:57:16 PMMay 8

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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]]

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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