Velocity of light creates ...several truths ?

[frankuitaalst]

A while ago there was a here thread about instant communications. . The thread evolved a.o. to the question of simultaneity and universal time in the universe. I think some of us remember...
At a certain point the following idea came into my mind , which I worked out a little and want the results have discussed here in order to check them if they're right...
The picture below might explain it .

Suppose we have a system of a central star orbited by two coorbital planets which are at 180° , so each being at the exact opposite site of the sun.
Suppose further that there is an inertial observer positioned highly above the ecliptic of the system . When he looks down he sees the planets evolve exactly at 180°.
Also an inertial observer located at the suns surface sees both sister planets at 180° ...
Suppose also that both planetes are tidally locked to the central star , so they both keep the same sides directed towards the sun .
For simplicity let the planets orbit the star without eccentricity . This means that at any given time an observer on each planet always sees the sun at the same point in the sky , all over the year ...

I can imagine the inertial observer highly above thinking : I'm a privileged guy . I can watch this small solar system for all time , but it must be really boring for the people living on these planets : they don't even know they have a sister planet as their sun blocks the light of their sister planet ....

Is this observer right ?
Depends . Depends upon the orbital speed of the planets and the distance towards the sun .
In case of the Sun-Earth system fi. the light of a (hypothetical) sister planet would take about 16 minutes to reach us . In this time our Earth moves by about 28000 km or 16/(24*60) arcdegrees . If the suns diameter would have been smaller or if our planet would rotate faster , it might even be possible that our sister planet becomes visible as at "moves" from behind the suns surface due to the time lag .
We would see the planet "lagging behind" .

Curiously the inhabitants of our sister planet would have the same perception : also our planet "lags behind" , instead of leading .
Consider the confusion if both societies were able to communicate : "you have lag " , "no, it's you having lag " .
While it makes common sense that if one leads the other must lag ...

Who is right ? The intertial observer above ? , the observer at the sun ?, the inhabitants of planet A ? , or those of planet B ?
So one might think about this : Is there such a thing as general truth in the universe ?
( This question had already been answerd ...)

I wrote down some simple equations to calculate the angle of lag ( or deviation from the zero angle ) as a function of v/c .
I expected that as v/c increases up to ~1, the formula would give a special value for the angle , but this doesn't seem to be so .
There's no special value or singularity , as the angle of deviation is about 42,. degrees at v/c~1., rather meaningless .
Even at higher v/c >1 , although fysically impossible, the deviation angle increases...

[frankuitaalst]

To illustrate the formula above I add an animation of the observed postion of the sister planet with increasing v/c . V/C start at 0.1 and ends at v/c=1.

[NEOWatcher]

Suppose further that there is an inertial observer positioned highly above the ecliptic of the system . When he looks down he sees the planets evolve exactly at 180°.

Gee; if they evolved exactly opposite each other, then they wouldn't agree on anything.
(yes; I know you ment revolve)

Anyway; It would depend also on who has what kind of knowledge.

If all the observers understand the speed of light and know they are in a rotating reference frame, then I think they would all agree that the outside observer would be the preferred view.

Otherwise, arguments would arise from just about any misconceptions.

[tommac]

I dont think this works out. Remember that there is also movement away from the sister planet and remember that the light would be perpendicular to the radius of the sun. You would have to be moving very fast around the sun to see the other planet

[NEOWatcher]

I dont think this works out. Remember that there is also movement away from the sister planet and remember that the light would be perpendicular to the radius of the sun. You would have to be moving very fast around the sun to see the other planet

Could you explain that differently? I'm not quite sure what you mean.

I think that "perpendicular to the radius" is confusing me.

My take is... If the orbits were very slow in relaton to the sun, then you would observe the photons being emitted parallel to the radius. As the orbits get faster, then you would see the photons emitted at increasing angles away from parallel.

[frankuitaalst]

Gee; if they evolved exactly opposite each other, then they wouldn't agree on anything.
(yes; I know you ment revolve)

Anyway; It would depend also on who has what kind of knowledge.

If all the observers understand the speed of light and know they are in a rotating reference frame, then I think they would all agree that the outside observer would be the preferred view.

Otherwise, arguments would arise from just about any misconceptions.

Yes , correct , if they do understand the speed of light then they could agree with the external observer .
Contrary : if they believe in a infinite speed of light the might argue until eternity .
( ==> if they believe in instant communications and observations they will argue ....till ...)

[frankuitaalst]

I dont think this works out. Remember that there is also movement away from the sister planet and remember that the light would be perpendicular to the radius of the sun. You would have to be moving very fast around the sun to see the other planet

If the sun had a smaller radius by a factor of 100 fi . they would see the sister planet appear near the sun...

[a1call]

I don't really know if the planets would have line of sight or not, but I can see a potential misconception with the scenario. The scenario seems to consider the frame of reference of the sun absolutely stationary which if so would be false. Considering the equality of all frames of reference my primitive grasp indicates that there might not be a symmetry breaker for the appearance of line of sight. Another point is that the sun has been pointed out on this board in the past to lag as well, again it is important to understand there is no absolute frame of reference.
But then again I totally don't understand relativity.

[NEOWatcher]

I don't really know if the planets would have line of sight or not, but I can see a potential misconception with the scenario.

True; but I think it's ok in this context considering the scales of speed.

[mugaliens]

Who is right ? The intertial observer above ? , the observer at the sun ?, the inhabitants of planet A ? , or those of planet B ?

Yes. They're all correct. However, each is seeing the things not as they exist when the light reaches them, but as things existed when the light left the objects.

So one might think about this : Is there such a thing as general truth in the universe ?

Actually, yes, but only as a mathematical construct.

[John Mendenhall]

Remember that the planets occupy Lagrange points with respect to each other and their sun. I'll have to look it up to see if they're stable.

Good question, Frank.

Regards, John M.

[frankuitaalst]

Remember that the planets occupy Lagrange points with respect to each other and their sun. I'll have to look it up to see if they're stable.

Good question, Frank.

Regards, John M.

Hi John , about the stability : they are stable for some time . After a while the planets will drift of their 180° , come close together , then drift away again . So they will come into a horseshoe orbit .
I've simulated this a while ago with Gravity Simulator .
Here's a llink to such a simulation...
http://www.orbitsimulator.com/cgi-bi...=1175890089/15

[tommac]

a radius (plural: radii) of a circle or sphere is any line segment from its center to its perimeter. ( http://en.wikipedia.org/wiki/Radius )

perpendicular:
In geometry, two lines or planes (or a line and a plane), are considered perpendicular (or orthogonal) to each other if they form congruent adjacent angles. ( http://en.wikipedia.org/wiki/Perpendicular )

http://en.wikipedia.org/wiki/Tangent
In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point (in the sense explained more precisely below).

Could you explain that differently? I'm not quite sure what you mean.

I think that "perpendicular to the radius" is confusing me.

My take is... If the orbits were very slow in relaton to the sun, then you would observe the photons being emitted parallel to the radius. As the orbits get faster, then you would see the photons emitted at increasing angles away from parallel.

[frankuitaalst]

Here's the simulation which I linked to above:
Visualised are Sun in the center , Earth at right , a second Earth at he left , originally at 180° , in a rotating frame to Earth . So Earth keeps its position at zero degrees .
The sister planet stays at its position for many years , but when we give it a small offset it starts to move to Earth , gets close and then moves away again . In the next cycle it approaches Earth from the other side .
This goes on an on ...
Animation was created with GravitySimulator .

[frankuitaalst]

Yes. They're all correct. However, each is seeing the things not as they exist when the light reaches them, but as things existed when the light left the objects.

Indeed . So it is and you're right.
The two inertial observers have the same perception , due to their privileged central postion , whereas the two moving observers have a different perception . Both moving observers have the same perception but disagree with each other .

[a1call]

Let's replace the two Earths with two space ships. Rather than being in orbit around the sun, they are actively kept at opposite sides of the sun at the expense of some fuel.
I think we can all agree that no line of sight between the ships can exist.

My understanding is that from a relativistic point of view the frames of reference of the ships are equivalent/interchangeable with the two orbiting earths.

In other words a spinning frame of reference is relative as there are no Landmarks in Space.

I would very much like to know if any related experiment to OP has been conducted and what the result has been.

[pooria]

Hi frankuitaalst;
it seems that you have not taken the aberration of sun light into account.
Aberration causes the apparent position of the star to change.so the angular seperation of the planet and the star (denoted by alfa=delay angle) will not be derived from your equations.

[frankuitaalst]

Hi frankuitaalst;
it seems that you have not taken the aberration of sun light into account.
Aberration causes the apparent position of the star to change.so the angular seperation of the planet and the star (denoted by alfa=delay angle) will not be derived from your equations.

Yes , thats correct .
It's not a dynamical expression where masses appear . It's rather kinematics , or even simpler :mathematics , in this way : given a certain orbit , what is the apparent deviation due to the lilited speed of light.

[astromark]

So if the light image travel time is 16mins, would the planets see each other?... Yes. right near the limb of the sun, with appropriate filters it would be visible. From both planets. This universe does not do instant... Photons transverse the vacuum of space at C. The third person view of this would see a 180deg opposition as all the light reaching them has traveled the same distance.

[mugaliens]

Hi John , about the stability : they are stable for some time . After a while the planets will drift of their 180° , come close together , then drift away again . So they will come into a horseshoe orbit .
I've simulated this a while ago with Gravity Simulator .
Here's a llink to such a simulation...
http://www.orbitsimulator.com/cgi-bi...=1175890089/15

There's a difference between stability and equilibrium, Frankuitaalst. Objects are all Lagrange points are in a state of static equilibrium. Stability, however, is defined by whether objects which are very slightly displaced from a point of equilibrium will tend to return to equilibrium, or whether they'll tend towards less equilibrium.

A ball balanced on the top of a hill is in static equilibrium, but is dynamically unstable. The slightest nudge in any direction results in increasing acceleration away from that point.

A ball in the center of a valley with higher ground on all sides (think dry lake bed) is both in static equillibrium and dynamicall stable. Thus, after a nudge, the ball will return to its previous position.

Of all the Lagrangian points, the first three are only stable in the plane perpendicular to the line between the bodies, but are dynamically stable elsewhere. Thus, the points are dynamically unstable as a whole.

L4 and L5, however, are dynamically stable. Objects near them will tend towards them, even if slightly displaced away from those points. This only holds if the ratio of M1/M2 > 24.96, where M1 is mass of the sun, and N2 is mass of the Earth. This ratio also holds for the Earth and Moon.

[frankuitaalst]

There's a difference between stability and equilibrium, Frankuitaalst. Objects are all Lagrange points are in a state of static equilibrium. Stability, however, is defined by whether objects which are very slightly displaced from a point of equilibrium will tend to return to equilibrium, or whether they'll tend towards less equilibrium.

A ball balanced on the top of a hill is in static equilibrium, but is dynamically unstable. The slightest nudge in any direction results in increasing acceleration away from that point.

A ball in the center of a valley with higher ground on all sides (think dry lake bed) is both in static equillibrium and dynamicall stable. Thus, after a nudge, the ball will return to its previous position.

Of all the Lagrangian points, the first three are only stable in the plane perpendicular to the line between the bodies, but are dynamically stable elsewhere. Thus, the points are dynamically unstable as a whole.

L4 and L5, however, are dynamically stable. Objects near them will tend towards them, even if slightly displaced away from those points. This only holds if the ratio of M1/M2 > 24.96, where M1 is mass of the sun, and N2 is mass of the Earth. This ratio also holds for the Earth and Moon.

Sie haben ganz recht Mugs. , I mean fully correct .
As in your example of the ball on the top of the hill the planet at the opposite site is in static equilibrium but as the slightest deviation from this position moves it further and further away from it , it is not stable . For reasons of simplicity I mixed the two .
Corresponds with a local maximum in potential energy .

[mugaliens]

Danke! Ich bin froh, wenn ich korrekt bin!