Neptune is about 30 astronomical units (au) from Earth.exactly at 327,000 km per second.
If I look at the planet Neptune from Earth, I am not looking at a stationary object.
In my reference, Neptune makes a full 360-degree turn in 24 hours.
I was curious to check at what speed Neptune is moving with respect to my terrestrial frame of reference from which I am observing it and I have discovered that, incredibly, Neptune (with respect to me) is moving faster than the speed of light and
Obviously I am wrong in my calculations which are these.
The space traveled by Neptune is a circumference that has its center in the Earth and a radius of 30 au.
Thus, the circumference traveled (in my reference) by Neptune in the 24 hours is 2*pi*r*30=2*3.14*30=188.4 au long.
In one hour Neptune travels 188.4/24=7.85 au.
In one minute Neptune travels 7.85/60=0.13 au.
In a second Neptune travels 0.13/60=0.00218 au.
Since an au corresponds to approximately 150,000,000 km, Neptune travels 0.00218*150,000.00=327,000 km per second, with respect to me.
Can you tell me where is the conceptual or calculation error?
[[Mod. note -- I see no conceptual or calculation error here.
So, my question is this: Why with our telescopes do we always (and only)
see perfectly spherical celestial bodies and have we never seen one contracted in the direction of motion like the one at the top right of
my animation?
In article <tkvd81$aqr$1@gioia.aioe.org>, Luigi Fortunati <fortunati.luigi@gmail.com> writes:
So, my question is this: Why with our telescopes do we always (and only)
see perfectly spherical celestial bodies and have we never seen one
contracted in the direction of motion like the one at the top right of
my animation?
It is a misconception that spheres look contracted when moving at relativistic speeds:
A. Lampa, _Z. f. Physik_, 27, 138, 1924.
J. Terrell, _Phys. Rev._, 116, 1041, 1959.
R. Penrose, _Proc. Camb. Phil. Soc._, 55, 137, 1959.
I can turn around in a second but the relative motion of the Moon, much faster than the speed of light, doesn't correspond to the notion of
relative motion normally discussed in SR.
It is a misconception that spheres look contracted when moving at
relativistic speeds:
A. Lampa, _Z. f. Physik_, 27, 138, 1924.
J. Terrell, _Phys. Rev._, 116, 1041, 1959.
R. Penrose, _Proc. Camb. Phil. Soc._, 55, 137, 1959.
I can turn around in a second but the relative motion of the Moon, much
faster than the speed of light, doesn't correspond to the notion of
relative motion normally discussed in SR.
Luigi Fortunati <fortunati.luigi@gmail.com> wrote:
[[question about an apparent paradox involving special relativity
and a rotating reference frame]]
I think the underlying cause of Luigi's apparent paradox may be that
special relativity implicitly assues that the geometry of space is Euclidean... but the geometry of a rotating reference frame is non-Euclidean. (The non-Euclidean nature of rotating reference frames results in things
like the Sagnac effect, the Ehrenfest paradox, etc.)
There are interesting and relevant discussions in
https://en.wikipedia.org/wiki/Sagnac_effect
https://en.wikipedia.org/wiki/Ehrenfest_paradox
https://en.wikipedia.org/wiki/Born_coordinates
Phillip Helbig wrote:
Luigi Fortunati <fortuna...@gmail.com> wrote:It is a misconception that spheres look contracted when moving at
relativistic speeds:
A. Lampa, _Z. f. Physik_, 27, 138, 1924.
J. Terrell, _Phys. Rev._, 116, 1041, 1959.
R. Penrose, _Proc. Camb. Phil. Soc._, 55, 137, 1959.
I can turn around in a second but the relative motion of the Moon, much
faster than the speed of light, doesn't correspond to the notion of
relative motion normally discussed in SR.
[[question about an apparent paradox involving special relativity
and a rotating reference frame]]
I think the underlying cause of Luigi's apparent paradox may be that
special relativity implicitly assues that the geometry of space is Euclidean... but the geometry of a rotating reference frame is non-Euclidean. (The non-Euclidean nature of rotating reference frames results in things
like the Sagnac effect, the Ehrenfest paradox, etc.)
There are interesting and relevant discussions in https://en.wikipedia.org/wiki/Sagnac_effect https://en.wikipedia.org/wiki/Ehrenfest_paradox https://en.wikipedia.org/wiki/Born_coordinates
--
-- "Jonathan Thornburg [remove -color to reply]" <dr.j.th...@gmail-pink.com> currently on the west coast of Canada
"!07/11 PDP a ni deppart m'I !pleH" -- slashdot.org page footer, 2022-10-16 "eHpl !'I mrtpaep dnia P PD1 /107" -- slightly more plausible message
given PDP-11 little-endian byte order
Luigi Fortunati <fortunati.luigi@gmail.com> wrote:
[[question about an apparent paradox involving special relativity
and a rotating reference frame]]
I think the underlying cause of Luigi's apparent paradox may be that
special relativity implicitly assues that the geometry of space is Euclidean... but the geometry of a rotating reference frame is non-Euclidean.
There are interesting and relevant discussions in
[[references]]
[...] the rotating coordinate frame is not an inertial reference
frame.
SR only applies in inertial frames.
Velocities in a rotating frame are not real and you can't use SR
with these coordinates.
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