I've been away from the weekend so have have only been able to do theoretical research.
I haven't really tried to decode the message but have instead approached the problem by looking at it from the other direction. Both UAs and UPs point to Merope 5C. This appears to indicate that this is the context or reference frame of the message. This is seems to be quite widely accepted. The questions I asked myself were these: What characteristics of Merope 5C could be universally agreed and understood by any advanced species? By referring to these characteristics what other useful information could be described?
The most obvious universal characteristics of Merope 5C are its orbital characteristics. Many people have been looking at these.
A positional system for the surface of Merope 5C
It is possible to build a method for locating a point on the surface of 5C with reference only to it's orbital characteristics. A point on a sphere can be described by two angles, azimuth and elevation. This requires having two key references, a pole to give the angle of elevation and a meridian to give angle of azimuth. Angles can be described universally using radians. However we need to know the direction in which the angles operate.
We can easily derive poles from the orbital characteristics of Merope 5C. There are two simple options. We can define the poles as being perpendicular to the orbital plane (orbital poles). Or we can use the axial rotation of the body (axial poles). These are not the same because Merope 5C has an axial tilt of -15.78º.
Illustration of of orbital and axial poles of the Earth:
We can also derive a common prime meridian. Merope 5C is tidally locked and this means that the same side always faces Merope 5. Because the orbit is circular there is no libration to cause the body to oscillate from side to side. Axial tilt does cause a vertical oscillation of 31.78º over the cause of it's year of 6.6 D. However this doesn't causes us a problem for defining the meridian. If you were to extend an imaginary line from the centre of M5 to M5C and mark that point and then extend a line through that point across the surface to the poles then you have described an obvious and natural meridian. Because the oscillation is only vertical it doesn't matter at which point of the orbital year you do this or which poles you choose: The axial poles will pass through the orbital poles as it oscillates.
The equator will be described by a line across the surface equidistant to the chosen poles.
Implications
Any message(s) describing a location on the surface of Merope 5C using such a method would be expected to contain the following information:
A clock for Merope 5C
Again, we can create a clock from orbital characteristics. This is much simpler. Being tidally locked the day and year of Merope 5C are identical at 6.6 D. The direction of movement of the body in it's orbit gives us the direction of the angle that describes the time. All we need to know is where the zero point is.
The most obvious zero point is the ascending node (the point where the orbit of M5C passes upwards through the orbital plane of M5). The problem with this is that M5C crosses the orbital plane on M5 twice during it's orbit. Which of these crossings is our zero point?
The other obvious zero points would be the periapsis (nearest point of orbit) or the apoapsis (furthest point of orbit). For a circular orbit such as that of Merope 5C there should be no periapsis or apoapsis. However as has been noted many times the system map describes the argument of periapsis is given as 138.32º. I'm not sure why this is.
It should be noted that such a clock can only only give us a time within the 6.6 D orbit of Merope 5C. To create a clock for a longer time period we would have to use the orbit of Merope 5 around Merope itself.
Implications
Any message(s) describing a time using the orbit of Merope 5C would be expected to contain the following:
Further notes and observations
It is quite possible that both a time and location could be described in any message.
There are other methods of describing surface location and time using orbital elements. These were the easiest and most obvious to me.
It's more than 20 years since I've done any geometry in anger. Excuse any incorrect terminology and feel free to correct my a language or any errors.
To be honest I think this may all be a bit too complex.
In my research I came across a couple of interesting resources:
Degrees to radians conversion chart
This video of Möbius Transformations illustrated using a Reimann Sphere shows a very familiar image. It's also rather beautiful. I really hope it isn't related to the message because it would suggest our puzzle was created by the guys at Frontier who code the renderer and is far more complex than we imagined:
[video=youtube;0z1fIsUNhO4]https://www.youtube.com/watch?v=0z1fIsUNhO4&spfreload=10[/video]
I haven't really tried to decode the message but have instead approached the problem by looking at it from the other direction. Both UAs and UPs point to Merope 5C. This appears to indicate that this is the context or reference frame of the message. This is seems to be quite widely accepted. The questions I asked myself were these: What characteristics of Merope 5C could be universally agreed and understood by any advanced species? By referring to these characteristics what other useful information could be described?
The most obvious universal characteristics of Merope 5C are its orbital characteristics. Many people have been looking at these.
A positional system for the surface of Merope 5C
It is possible to build a method for locating a point on the surface of 5C with reference only to it's orbital characteristics. A point on a sphere can be described by two angles, azimuth and elevation. This requires having two key references, a pole to give the angle of elevation and a meridian to give angle of azimuth. Angles can be described universally using radians. However we need to know the direction in which the angles operate.
We can easily derive poles from the orbital characteristics of Merope 5C. There are two simple options. We can define the poles as being perpendicular to the orbital plane (orbital poles). Or we can use the axial rotation of the body (axial poles). These are not the same because Merope 5C has an axial tilt of -15.78º.
Illustration of of orbital and axial poles of the Earth:
We can also derive a common prime meridian. Merope 5C is tidally locked and this means that the same side always faces Merope 5. Because the orbit is circular there is no libration to cause the body to oscillate from side to side. Axial tilt does cause a vertical oscillation of 31.78º over the cause of it's year of 6.6 D. However this doesn't causes us a problem for defining the meridian. If you were to extend an imaginary line from the centre of M5 to M5C and mark that point and then extend a line through that point across the surface to the poles then you have described an obvious and natural meridian. Because the oscillation is only vertical it doesn't matter at which point of the orbital year you do this or which poles you choose: The axial poles will pass through the orbital poles as it oscillates.
The equator will be described by a line across the surface equidistant to the chosen poles.
Implications
Any message(s) describing a location on the surface of Merope 5C using such a method would be expected to contain the following information:
- an indication of whether to use the orbital or axial poles (the axial poles seem the most likely)
- an indication of of the direction of the zero angle of elevation (this could be either pole or the equator)
- an indication of the direction of the angle of elevation (which way is positive)
- (possibly) some confirmation of how to describe the meridian
- (possibly) an indication of the direction of the angle of azimuth (I would expect this to be the direction of rotation)
- the angle of elevation (probably in radians, and possibly as multiples/fractions of pi)
- the angle of azimuth (probably in radians, and possibly as multiples/fractions of pi)
A clock for Merope 5C
Again, we can create a clock from orbital characteristics. This is much simpler. Being tidally locked the day and year of Merope 5C are identical at 6.6 D. The direction of movement of the body in it's orbit gives us the direction of the angle that describes the time. All we need to know is where the zero point is.
The most obvious zero point is the ascending node (the point where the orbit of M5C passes upwards through the orbital plane of M5). The problem with this is that M5C crosses the orbital plane on M5 twice during it's orbit. Which of these crossings is our zero point?
The other obvious zero points would be the periapsis (nearest point of orbit) or the apoapsis (furthest point of orbit). For a circular orbit such as that of Merope 5C there should be no periapsis or apoapsis. However as has been noted many times the system map describes the argument of periapsis is given as 138.32º. I'm not sure why this is.
It should be noted that such a clock can only only give us a time within the 6.6 D orbit of Merope 5C. To create a clock for a longer time period we would have to use the orbit of Merope 5 around Merope itself.
Implications
Any message(s) describing a time using the orbit of Merope 5C would be expected to contain the following:
- the zero point of the orbit of M5C
- an angle from that zero point describing the time (probably in radians, and possibly as multiples/fractions of pi)
Further notes and observations
It is quite possible that both a time and location could be described in any message.
There are other methods of describing surface location and time using orbital elements. These were the easiest and most obvious to me.
It's more than 20 years since I've done any geometry in anger. Excuse any incorrect terminology and feel free to correct my a language or any errors.
To be honest I think this may all be a bit too complex.
In my research I came across a couple of interesting resources:
Degrees to radians conversion chart
This video of Möbius Transformations illustrated using a Reimann Sphere shows a very familiar image. It's also rather beautiful. I really hope it isn't related to the message because it would suggest our puzzle was created by the guys at Frontier who code the renderer and is far more complex than we imagined:
[video=youtube;0z1fIsUNhO4]https://www.youtube.com/watch?v=0z1fIsUNhO4&spfreload=10[/video]
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