I posted this already in the bugs forum, but I'm posting it here for discussion and figured that other explorers might be interested in it too.
Description
I've done some analysis of the ring systems I've scanned so far in Elite Dangerous and the data confirms what I've seen visually in the game - that most ring systems around planets and brown dwarfs are unrealistically large in extent. If you want to skip the explanation (if you're a dev then I hope you won't!
then hop down to the Solutions section at the bottom of this post. If you want further info then just let me know!
In this post I'm going to present what I found, some technical background, and some suggestions for fixing it. I'm putting it in the Bug forum because it appears to be a bug (or oversight) in the Stellar Forge system creation. FDev have made a big deal about realism in the game so I hope this explanation gives them a way to fix at least this flaw in the system generation. I'd really appreciate some acknowledgement that they're aware of the issue and can incorporate a fix for it soon (I've also found several other errors in the Stellar Forge output which I'll post later on).
---------------------------------
Definitions (for the purposes of this article):
Roche Limit: The Roche Limit is the distance from a massive body within which an orbiting body is physically disrupted by tidal forces.
This distance is defined by the density of the central body and the density of the satellite (or the material that comprises the satellite). There are several formulae that can be used to define the Roche limit, depending on the rigidity of the satellite - the most relevant and realistic one is that which accounts for fluid deformation of the satellite, which allows it to be deformed by tidal forces. The roche limit for rigid, solid bodies is within this fluid limit, so the fluid limit can be considered to be a valid outer limit at which a body would be broken up by tidal forces. It is important to note that the Roche Limit of satellites with different compositions would be different around a given planet, since it depends on the density of the satellite material.
The fluid Roche Limit formula is as follows: Roche limit ={(2.44)*((Planet Density/Satellite Density)^(1/3))}
The constant of 2.44 is assumed to be correct for this purpose, but it should be noted that some sources give other values between 2.4 and 2.5 (depending on the specific derivation used). The density of the planet and satellite are in kg/m³, the Planet radius and Roche Limit are in metres. The density of the planet can be calculated using the values in the journal.log files - we know the planet mass in Earth masses (1 Earth mass = 5.9742e24 kg) and we know the radius is metres (so we can calculate the volume using V = 4/3*pi*(radius^3), and the density is mass divided by the volume. The calculated Roche limit is expressed in units of the planet's radius - multiplying this by the radius of the planet in metres will give the Roche Limit distance from the centre of the planet in metres.
The satellite density is determined by associating a density value with the RingClass given in the journal.logs. The densities below assume a solid body with no spaces or voids - realistically, many asteroid-sized objects could have voids in them and may be as low as half the stated density.
Icy: 1000 kg/m³.
Rocky: 3500 kg/m³
Metal-Rich: 5500 kg/m³
Metallic: 8000 kg/m³
Plugging these numbers into the Roche Limit formula, we can see that satellites made of less dense material will be torn apart further away from the planet than those made of denser material - i.e. the Roche Limit is further from the planet for low density materials than for high density materials.
From this, we can arrive at two more definitions:
Ring System: A Ring System is a collection of material orbiting a body within its Roche Limit. Massive objects cannot form within a ring system because they would be disrupted by tidal forces.
Accretion Disk: An Accretion Disk is a collection of material orbiting a body beyond its Roche Limit from which massive objects (satellites) can form.
The key difference between a ring system and an accretion disk is the Roche Limit. Within the Roche Limit, tidal forces would disrupt satellites of a given density and would break them up into fragments that form ring systems. These are generally long-lived features since they are usually maintained by impacts within the ring system.
Beyond the Roche Limit, tidal forces would not disrupt satellites of a given density - any debris beyond this distance is free to coalesce (accrete) into larger bodies. This is how planets form in protostellar disks, and how moons form in protoplanetary disks. If an satellite was somehow broken up (e.g. by a giant impact) then at least some of the debris could become an accretion disk around the central body that could then reform into new satellites. Since planet/satellite formation and giant impacts by their very nature occur in very young systems, these are the most likely places to find accretion disks - after a relatively brief span of time, all of the material in the disks forms into satellites or is dispersed.
Hill Spheres: For added complication, there is a potential outer limit for the extent of Accretion Disks - the Hill Sphere. This is the volume where the planet's gravity dominates over that of the star that it orbits.
Hill Sphere = a(1-e) * {(planet mass/3*star mass)^(1/3)}
where a=semi-major axis of planet orbit, e=eccentricity, and the masses are in kg.
This can be calculated using the data known for each planet and its primary star. The actual zone of stability is within about 1/3 of the Hill Sphere - beyond this distance other influences reduce the stability of orbits (though retrograde orbits between 33% and 100% of the Hill Sphere may be stable). In practical terms, it would be best to assume that the maximum size of an Accretion Disk would be 33% of the calculated Hill Sphere distance for that planet. Also, the hill sphere of a planet is usually larger in extent the further the planet is from the star - thus, planets orbiting very close to a star (within 1 AU) would not have huge accretion disks that were millions of km in radius. This must be determined on a case by case basis.
It is important to note a few specific cases to clarify these definitions:
1) While most of Saturn's rings are within its Roche Limit, it does have rings beyond the Roche Limit - the E Ring, and the Phoebe Ring. However, these rings are actively maintained by geyser eruptions on Enceladus (in the case of the E Ring) and micrometeorite impacts from Phoebe for the ring there. They are also composed of much smaller particles than the main rings (dust to pebble-sized). If the processed that maintained them were to cease, these rings would disappear rapidly.
2) The so-called "Super Saturn" J1407b (http://earthsky.org/space/huge-distant-planet-has-rings-200-times-bigger-than-saturns) has often been touted as a "giant ring system" and therefore used as justification for over-sized rings in Elite Dangerous. However, looking at the details it should be obvious that this is actually an Accretion Disk and not a true "ring system" - the disk is around a brown dwarf star that is only 16 million years old, and satellites are forming in the disk.
Now that these have been defined, we can determine the Roche Limits for the worlds in Elite Dangerous. The source data can be extracted from the journal.logs saved by ED.
---------------------------------
Data: I have scanned 227 ringed objects - terrestrial objects, gas giants, and brown dwarfs. I calculated the Roche Limits using the planet density and the assumed RingClass density (listed above) and compared that with the Outer Limit distance of each ring system of those bodies.
The half-density values (due to spaces and voids reducing the density of the satellite) were used to simulate an extreme outer limit for the ring system size.
One system was under 100 million years old and had four ringed planets. These rings were beyond the Roche Limit of those planets, but that was acceptable since they could be considered to be Accretion Disks.
Using the solid density values, I found that 194 out of the remaining 221 ringed objects (88%!) had rings that extended beyond their Roche Limits. Using the half-density values (assuming satellites that were not solid and contained gaps and voids in them) I found that 179 out of the 221 ringed objects (81%) had rings that extended beyond their Roche Limits.
In practical terms, the Roche Limits of most terrestrial bodies and gas giants were between 2 and 5 planetary radii for Icy Rings, and 1 to 4 planetary radii for Metallic Rings. Brown Dwarfs are significantly denser objects and their rings can extend out to between about 5 and 8 BD radii as a result (though they would not be icy due to the heat from the brown dwarf).
In some cases (for solid metallic rings) he Roche Limit is within 1 planetary radius - this means that satellites with that density would not be torn apart before they hit the planetary surface, and so rings made of that material would not be able to exist around that planet.
---------------------------------
Solutions: I think the simplest solution would be as follows:
Regardless of system age, if any planets or satellites orbit within the Roche Limit (or have orbits that enter the Roche Limit) then they should either be removed or replaced by rings.
If the age of the system is over 100 million years old:
1) If the inner radius of a ring is beyond the Roche Limit, then remove that ring completely.
2) if the ring has not been removed in (1): if the outer radius of a ring is greater than the Roche Limit for the Ring Material then reduce the Outer Radius to the same distance (or just within) the Roche Limit.
If the age of the system is less than 1 million years old
1) if the ring system is larger than the Roche Limit then it can remain as an Accretion Disk. If the outer radius of the Accretion Disk is beyond 1/3 of the planet's Hill Sphere then reduce the outer radius to this distance. This is the only circumstance in which huge disks that have radii of millions of km are possible.
2) Ring systems with an outer radius smaller than the Roche Limit remain unchanged as Ring Systems.
---------------------------------
Discussion: Given the radii of even the largest planetary object (around 70000 to 80000 km) and the fact that the Roche Limit of most planets is within 5 planetary radii, it should be apparent that ring systems should not be found anywhere near 1 million km from the planet, let alone beyond it. While Brown Dwarfs are denser objects, they are also usually smaller than this maximum radius so their more extensive rings systems wouldn't extended much further in terms of absolute distance from the BD (also, Icy rings would be extremely unlikely around BDs given the heat that they emit - though they could possibly be found around the coldest Y dwarfs if they were created long after the BD formed).
While this precludes extensive ring systems for older systems, the "over-sized ring systems" that we currently see in the game would be totally acceptable around bodies in young systems that are less than 100 million years old. These would be identified as Accretion Disks and their greater rarity would make them much more impressive when encountered.
Description
I've done some analysis of the ring systems I've scanned so far in Elite Dangerous and the data confirms what I've seen visually in the game - that most ring systems around planets and brown dwarfs are unrealistically large in extent. If you want to skip the explanation (if you're a dev then I hope you won't!
then hop down to the Solutions section at the bottom of this post. If you want further info then just let me know! In this post I'm going to present what I found, some technical background, and some suggestions for fixing it. I'm putting it in the Bug forum because it appears to be a bug (or oversight) in the Stellar Forge system creation. FDev have made a big deal about realism in the game so I hope this explanation gives them a way to fix at least this flaw in the system generation. I'd really appreciate some acknowledgement that they're aware of the issue and can incorporate a fix for it soon (I've also found several other errors in the Stellar Forge output which I'll post later on).
---------------------------------
Definitions (for the purposes of this article):
Roche Limit: The Roche Limit is the distance from a massive body within which an orbiting body is physically disrupted by tidal forces.
This distance is defined by the density of the central body and the density of the satellite (or the material that comprises the satellite). There are several formulae that can be used to define the Roche limit, depending on the rigidity of the satellite - the most relevant and realistic one is that which accounts for fluid deformation of the satellite, which allows it to be deformed by tidal forces. The roche limit for rigid, solid bodies is within this fluid limit, so the fluid limit can be considered to be a valid outer limit at which a body would be broken up by tidal forces. It is important to note that the Roche Limit of satellites with different compositions would be different around a given planet, since it depends on the density of the satellite material.
The fluid Roche Limit formula is as follows: Roche limit ={(2.44)*((Planet Density/Satellite Density)^(1/3))}
The constant of 2.44 is assumed to be correct for this purpose, but it should be noted that some sources give other values between 2.4 and 2.5 (depending on the specific derivation used). The density of the planet and satellite are in kg/m³, the Planet radius and Roche Limit are in metres. The density of the planet can be calculated using the values in the journal.log files - we know the planet mass in Earth masses (1 Earth mass = 5.9742e24 kg) and we know the radius is metres (so we can calculate the volume using V = 4/3*pi*(radius^3), and the density is mass divided by the volume. The calculated Roche limit is expressed in units of the planet's radius - multiplying this by the radius of the planet in metres will give the Roche Limit distance from the centre of the planet in metres.
The satellite density is determined by associating a density value with the RingClass given in the journal.logs. The densities below assume a solid body with no spaces or voids - realistically, many asteroid-sized objects could have voids in them and may be as low as half the stated density.
Icy: 1000 kg/m³.
Rocky: 3500 kg/m³
Metal-Rich: 5500 kg/m³
Metallic: 8000 kg/m³
Plugging these numbers into the Roche Limit formula, we can see that satellites made of less dense material will be torn apart further away from the planet than those made of denser material - i.e. the Roche Limit is further from the planet for low density materials than for high density materials.
From this, we can arrive at two more definitions:
Ring System: A Ring System is a collection of material orbiting a body within its Roche Limit. Massive objects cannot form within a ring system because they would be disrupted by tidal forces.
Accretion Disk: An Accretion Disk is a collection of material orbiting a body beyond its Roche Limit from which massive objects (satellites) can form.
The key difference between a ring system and an accretion disk is the Roche Limit. Within the Roche Limit, tidal forces would disrupt satellites of a given density and would break them up into fragments that form ring systems. These are generally long-lived features since they are usually maintained by impacts within the ring system.
Beyond the Roche Limit, tidal forces would not disrupt satellites of a given density - any debris beyond this distance is free to coalesce (accrete) into larger bodies. This is how planets form in protostellar disks, and how moons form in protoplanetary disks. If an satellite was somehow broken up (e.g. by a giant impact) then at least some of the debris could become an accretion disk around the central body that could then reform into new satellites. Since planet/satellite formation and giant impacts by their very nature occur in very young systems, these are the most likely places to find accretion disks - after a relatively brief span of time, all of the material in the disks forms into satellites or is dispersed.
Hill Spheres: For added complication, there is a potential outer limit for the extent of Accretion Disks - the Hill Sphere. This is the volume where the planet's gravity dominates over that of the star that it orbits.
Hill Sphere = a(1-e) * {(planet mass/3*star mass)^(1/3)}
where a=semi-major axis of planet orbit, e=eccentricity, and the masses are in kg.
This can be calculated using the data known for each planet and its primary star. The actual zone of stability is within about 1/3 of the Hill Sphere - beyond this distance other influences reduce the stability of orbits (though retrograde orbits between 33% and 100% of the Hill Sphere may be stable). In practical terms, it would be best to assume that the maximum size of an Accretion Disk would be 33% of the calculated Hill Sphere distance for that planet. Also, the hill sphere of a planet is usually larger in extent the further the planet is from the star - thus, planets orbiting very close to a star (within 1 AU) would not have huge accretion disks that were millions of km in radius. This must be determined on a case by case basis.
It is important to note a few specific cases to clarify these definitions:
1) While most of Saturn's rings are within its Roche Limit, it does have rings beyond the Roche Limit - the E Ring, and the Phoebe Ring. However, these rings are actively maintained by geyser eruptions on Enceladus (in the case of the E Ring) and micrometeorite impacts from Phoebe for the ring there. They are also composed of much smaller particles than the main rings (dust to pebble-sized). If the processed that maintained them were to cease, these rings would disappear rapidly.
2) The so-called "Super Saturn" J1407b (http://earthsky.org/space/huge-distant-planet-has-rings-200-times-bigger-than-saturns) has often been touted as a "giant ring system" and therefore used as justification for over-sized rings in Elite Dangerous. However, looking at the details it should be obvious that this is actually an Accretion Disk and not a true "ring system" - the disk is around a brown dwarf star that is only 16 million years old, and satellites are forming in the disk.
Now that these have been defined, we can determine the Roche Limits for the worlds in Elite Dangerous. The source data can be extracted from the journal.logs saved by ED.
---------------------------------
Data: I have scanned 227 ringed objects - terrestrial objects, gas giants, and brown dwarfs. I calculated the Roche Limits using the planet density and the assumed RingClass density (listed above) and compared that with the Outer Limit distance of each ring system of those bodies.
The half-density values (due to spaces and voids reducing the density of the satellite) were used to simulate an extreme outer limit for the ring system size.
One system was under 100 million years old and had four ringed planets. These rings were beyond the Roche Limit of those planets, but that was acceptable since they could be considered to be Accretion Disks.
Using the solid density values, I found that 194 out of the remaining 221 ringed objects (88%!) had rings that extended beyond their Roche Limits. Using the half-density values (assuming satellites that were not solid and contained gaps and voids in them) I found that 179 out of the 221 ringed objects (81%) had rings that extended beyond their Roche Limits.
In practical terms, the Roche Limits of most terrestrial bodies and gas giants were between 2 and 5 planetary radii for Icy Rings, and 1 to 4 planetary radii for Metallic Rings. Brown Dwarfs are significantly denser objects and their rings can extend out to between about 5 and 8 BD radii as a result (though they would not be icy due to the heat from the brown dwarf).
In some cases (for solid metallic rings) he Roche Limit is within 1 planetary radius - this means that satellites with that density would not be torn apart before they hit the planetary surface, and so rings made of that material would not be able to exist around that planet.
---------------------------------
Solutions: I think the simplest solution would be as follows:
Regardless of system age, if any planets or satellites orbit within the Roche Limit (or have orbits that enter the Roche Limit) then they should either be removed or replaced by rings.
If the age of the system is over 100 million years old:
1) If the inner radius of a ring is beyond the Roche Limit, then remove that ring completely.
2) if the ring has not been removed in (1): if the outer radius of a ring is greater than the Roche Limit for the Ring Material then reduce the Outer Radius to the same distance (or just within) the Roche Limit.
If the age of the system is less than 1 million years old
1) if the ring system is larger than the Roche Limit then it can remain as an Accretion Disk. If the outer radius of the Accretion Disk is beyond 1/3 of the planet's Hill Sphere then reduce the outer radius to this distance. This is the only circumstance in which huge disks that have radii of millions of km are possible.
2) Ring systems with an outer radius smaller than the Roche Limit remain unchanged as Ring Systems.
---------------------------------
Discussion: Given the radii of even the largest planetary object (around 70000 to 80000 km) and the fact that the Roche Limit of most planets is within 5 planetary radii, it should be apparent that ring systems should not be found anywhere near 1 million km from the planet, let alone beyond it. While Brown Dwarfs are denser objects, they are also usually smaller than this maximum radius so their more extensive rings systems wouldn't extended much further in terms of absolute distance from the BD (also, Icy rings would be extremely unlikely around BDs given the heat that they emit - though they could possibly be found around the coldest Y dwarfs if they were created long after the BD formed).
While this precludes extensive ring systems for older systems, the "over-sized ring systems" that we currently see in the game would be totally acceptable around bodies in young systems that are less than 100 million years old. These would be identified as Accretion Disks and their greater rarity would make them much more impressive when encountered.
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