Map of the Verse discussion

Quote:

---

Originally posted by citizen:

Quote:

---

Originally posted by jewelstaitefan:
Correct me if I'm wrong, but the orbital period of Persephone around Lux is only 4 days. Is that correct? Persephone has an orbital radius only about one tenth of our Mercury, and Lux has mass of 0.39 times our Sol, and the velocity must be so fast that it must complete an orbit around Lux in 4.16 days.

---

Actually it comes out for me at about 0.155 Days.

Using the equation derived from Kepler's 3rd Law:
T=2*PI*Sqr[r^3/GM]
Where:
r = Orbital Radius + Star Radius = 6,191,284,000 Metres
M = Gravitational Constant = 6.673x10^-11
G = 0.39xSol Mass = 7.756788x10^32 Kg

T=2 * PI * Sqr[2.373242832x10^29 / (6.673x10^-11 * 7.756788x10^32)]
T=2 * PI * Sqr[2.373242832x10^29 / 5.176104632x10^22]
T=2 * PI * Sqr[4,585,008.397]
T=2 * PI * 2,141.263271
T=13,453.95392 Seconds
T=13,453.95392 / 3600 = 3.73 Hours
T=13,453.95392 / 86,400 = 0.155717059 Days

I've run these numbers a few times with a few different methods and variations, so I'm fairly confident that that value is correct.

---

I'm not sure where your numbers come from.
I was using 5.9742 x 10^24 kg as the mass for Earth.
I was using 1.98892 x 10^30 kg as the mass of our Sol.
I think that 0.39 of Sol mass would be 7.4046 x 10^29 instead of 7.756 x 10^32

I don't know why you are adding together the orbital radius plus the radius of the Star - what formula uses that sum? All the equations I've been reading only use the radius from the center of each body, and always define r as being that distance.

White Paper defines radius of Persephone as 5.496 billion meters. Not sure where your figure came from.

NOTIFY: Y  | REPLY  | REPLY WITH QUOTE  | PERMALINK  | TOP  | HOME

I will jump ahead here now and post some data and resulting conclusions. I understand that there may be some errors in base calculations, but the conclusions end up being similar in the end. If it is determined that the figures are faulty, I can and will return to this post and add corrections. I do welcome any observed errors to be pointed out.

As mentioned previously, data specifically given in Map of the Verse or accompanying White Paper which do not conform to the laws of astrodynamics in the rest of the universe will be referred to as "Fiction" figures. The version of corresponding data derived from adherance to the laws of astrodynamics combined with the other given data in the Map or White Paper will be referred to as the "Science" figures.

Some abbreviation in the left column may be used to attempt column alignment.

T = orbital period (duration)
v = orbital velocity

Body ....T Fiction v ....T Science v
Earth 1 year 6.28Au/yr 1 year 6.28Au/y
Bernadet 23.7yr 2.19Au/yr 13.25yr 3.91Au/yr
Londiniu 27.0yr 2.09Au/yr 15.09yr 3.75Au/yr
PS Lux 164yr 1.15Au/yr 91.9yr 2.05Au/yr

Georgia 561yr 0.76Au/yr 270yr 1.58Au/yr
Red Sun 561yr 0.76Au/yr 276yr 1.55Au/yr
Kalidasa 1331yr 0.57Au/yr 628yr 1.21Au/yr
Blue Sun 2415yr 0.47Au/yr 1091yr 1.21Au/yr

PS Murph 64.0yr 1.57Au/yr 61.0yr 1.65Au/yr

Santo 143day 0.71Au/yr 6.0day 16.9Au/yr
Perseph 121day 0.70Au/yr 4.2day 20.4Au/yr
Pelorum 188day 0.70Au/yr 7.9day 16.4Au/yr
Hera 99.0day 0.69Au/yr 3.2day 21.8Au/yr
Shadow 196day 0.70Au/yr 8.9day 15.4Au/yr
Aesir 55day 0.71Au/yr 1.3day 29.7Au/yr
Anvil 205day 0.69Au/yr 9.1day 15.6Au/yr
Triumph 66day 0.69Au/yr 1.6day 28.1Au/yr
Silvrhld 198day 0.69Au/yr 8.5day 16.2Au/yr
Beylix 91day 0.71Au/yr 3.0day 21.2Au/yr
Oberon 198day 0.69Au/yr 9.5day 14.5Au/yr
Miranda 122day 0.70Au/yr 4.7day 17.9Au/yr

Moon Luna 27.3days to 27.3days
Avalon 27.3days to 32.5days
Rhilidore 27.3days to 24.8days
Summerhom 88.7days to 8.5days
Sweethome 410days to 84.2days
Urvasi 49.1days to 3.9days
7th Circle 546days to 24.6days

NOTIFY: Y  | REPLY  | REPLY WITH QUOTE  | PERMALINK  | TOP  | HOME

For traqveling around and navigating the verse, there is not going to be much difference between getting to a world orbiting in a system from one month to another, or even till the next year. The fastest directly orbiting body in the Core is Bernadette, and it completes an orbital cycle in 23 years (Fiction) or 13 years (Science). So your navigational adjustments are minimal. Teh body isn't moving all that much, when you're traveling AUs at a pretty good clip.
The greatest differential is going to be from one system to another, and even there most greatest from one world on the edge crossing over to another nearest world on the edge of the nearby system.
Let's consider the 2 greatest differences in distances to travel. They are from the Lux orbit (like Persephone) at the edge of the Core to the Murphy orbit (like Hera, Shadow) at the edge of the Georgia System, and also from Salisbury at the edge of the Kalidasa orbit to the Blue Sun system. Lux and Murphy are closest to each other in 2511 (specified in White Paper). This means that there is practically one line which passes through Georgia Sun, Murphy, Lux, White Sun, and Red Sun at this time.
Although Kalidasa is unlikely to be close to Blue Sun, we will pretend they are and use it as an extreme example. Lux, Georgia, Kalidasa are all in Prograde or Direct Grade orbital direction, and Blue Sun is in Retrograde.
While Lux and Georgia are both in Prograde orbital direction, having Murphy in Prograde orbit means that while it is nearest Lux it is in relative Retrograde - or orbiting away from the shared midpoint between Core and Georgia.

Fiction
Lux velocity is 1.15Au D/year. Goergia system velocity is 0.76Au D/year. Murphy orbital velocity is 1.57Au/year, but it is in relative Retrograde so it's relative verse velocity is 0.81Au R/year.
In a 6 year period, Lux travels 6.90Au through it's orbit. During that period, Murphy trvels away from Lux 4.68Au (opposite direction in the verse). In 2511 they were 22Au apart, and at the end of the 6 year period they are now 24.9Au apart. That is quite insignificant in terms of travel times.

Science
Same thing, with Lux traveling 12.3Au (D) in 6 years, and Murphy moving away .42Au (R) and their combined distance becoming 25.4Au - still minor.

Same thing for Salisbury to Blue Sun.
Fiction
Kalidasa System orbital velocity of .571Au (D)/year, and Salisbury with orbital velocity of 1.657Au (D)/year, adding together for 2.228Au (D)/year. Blue Sun orbits White Sun with velocity .468Au/year Retrograde.
During a 6 year period, Salisbury would distance itself farther from the shared (closest) point by 13.368Au, and Blue Sun would likewise move in the opposite direction 2.808Au in that same 6 year period. Total of 13.368 in sheering difference.
45Au at closest becomes 47.8Au after 6 years.

Science
Kalidasa has 1.21Au (D)/year and Salisbury has 1.88Au (D)/year, for a total of 3.09Au (D)/year. Blue Sun is 1.04Au (R)/year.
45Au at closest becomes 51.4Au after 6 years.
Again, not much difference.

NOTIFY: Y  | REPLY  | REPLY WITH QUOTE  | PERMALINK  | TOP  | HOME

Quote:

---

Originally posted by jewelstaitefan:
Did not forget, and clearly pointed this out immediately following:

---

I didn't really know what you referring to in the following, which is why I didn't pick up on it.

Quote:

---

Originally posted by jewelstaitefan:
As I understand the formulae, most circular orbits can be calculated using only the mass of the central (primary) body, because the satellite body is so much smaller as to render it's mass moot. But with these satellite Suns, their mass is sufficeint to require the full formula of the sum of the 2 masses in the calculations.
This means that IF the Georgia Sun and Red Sun were both at the same orbit, they would have different velocities. I think the simplest solution is that Red Sun is actually orbiting at slightly less orbital radius, thus it's velocity is matched to Georgia Sun's velocity at Georgia's orbital radius of 68Au.

---

Well, it's not quite that simple. The problem is that if the gravity of the other object is significant, it's not that it's mass needs to be taken account of for it's orbit, it's that it and the other body are now orbiting a common centre of gravity. Which means an apparent mass between the two bodies, which is the sum of their masses. This point is the barycentre.

The problem is that this means that the orbital radius for Georgia and Red Sun also has to be changed, since they're no longer orbiting White Sun, but White Sun, Georgia, and Red Sun are now orbiting a common centre of gravity.

That's very difficult math.

There's two fair approaches I think. You can either live with a level of simplification by treating the suns as a simple body, just orbiting White Sun (which seems to be how the verse by numbers intends it) or you can try and model the correct orbital mechanics. That last way is going to be incredibly difficult, and you're likely to find the system simply doesn't work.

Another approach might be to fudge the numbers a little, and see if you can't make the total mass of the Red Sun and Georgia systems to be equal, thereby cancelling each other out.

Quote:

---

I think that 0.39 of Sol mass would be 7.4046 x 10^29 instead of 7.756 x 10^32

---

You're right sorry. I did the math on the train home, I stupidly wrote up my initial figures that I realised were wrong right after doing them. Looking back at my notes the subsequent figures I used were the right ones, they also actually come out closer to yours. I'd run those a few times and they all came out the same.

Quote:

---

I don't know why you are adding together the orbital radius plus the radius of the Star - what formula uses that sum? All the equations I've been reading only use the radius from the center of each body, and always define r as being that distance.

---

Because the tendency is that people give orbital distances as the distance from the surface of the body, rather than the distance from the centre of gravity. In which case the orbital radius is the radius of the star plus the orbital radius. Do you believe that the Orbital distance given is the actual orbital radius? I can use those figures if you prefer:

T=2*PI*Sqrt[1.65989429×10^29/(7.4046x10^29 * 6.673x10^-11)]
T=2*PI*Sqrt[1.65989429x10^29/4.94108958x10^19]
T=2*PI*Sqrt[3359368.95]
T=2*PI*1832.85814
T=355,810.337 Seconds
T=98.8362046 Hours
T=4.11817519 Days

I have to admit I wondered why my figures were so different from yours (which is why I posted them) if I'd turned the page on my notebook I'd have found out. From the figures on my corrections in the notebook, it comes out as 4.92420009 Days, using my distance assumption. Hope that clears everything up.

It's up to you. The proper equation is more accurate, your method seems to get within an order of magnitude. As is obvious I don't have much time to spend on this stuff, if you want to use your method to get a baseline I can run the equation through as and when if you'd like?

Edited for clarity.

NOTIFY: Y  | REPLY  | REPLY WITH QUOTE  | PERMALINK  | TOP  | HOME

I had not heard of people using distance from the surface of a body as a substitute for radius, all references I have seen were for radius being equal to the distance from one center of mass to the other body's center of mass. Perhaps you work in some field which refers to geo-orbital satellites as being so many miles above the Earth?

My intention had been to point out the magnitude of difference in the White Paper's Fiction values versus the realistic astrodynamic values. We can already accept that the Fiction values could be utilized, and for comparison purposes we can show the values which adhere to laws of astrodynamics. It is possible that the White Paper may update their info with values more similar to "Science" values, so in discussions about these values it seems reasonable to include comparative values to understand the relative validity of conclusions - in many cases, the conclusions will remain virtually the same. Thus further agreement can occur on more issues.

I figured that showing the Fiction value for Persephone as 121 days compares to Science value of 4.2 Days offered adequate contrast. We don't need to detail the added decimal points for these purposes, I just wanted to ensure I wasn't off calculation by the magnitude you had indicated.

Regarding the mass and orbital velocity of the Suns, consider that if the mass of Georgia Sun was a small fraction of White Suns mass, we would use the same formula as the other bodies. I had wanted to use the mass sum figure to help approach what the value would be with so much more mass involved, making the orbital velocity greater than if Georgia was not so massive. The idea of Red and Georgia cancelling each other out is quite useful, but this adds even further the total amount of mass to factor in (adding the mass of Red plus White plus Georgia increased to total gravitational forces), and that would increase the velocity even more. I expect that a fair compomise for our rough guesstimations would be to use the sum of 2 masses to calculate the duration and velocity, and still assume that White is the central body, with all other Suns orbiting it. If we were to not consider it this way, using only one mass (that of White Sun), then the orbital velocity of Georgia will be much slower and the duration (period) will be much more.
Do you find this compromise reasonable? Is it a fair substitution for performing all the exacting mechanical formulae involved?

If you find an error where I indicate something like 4 days and you conjure something like 3 hours, I'd really like to know about vast errors I've created. If you don't, somebody eventually will, and it's best to catch major errors earlier than later.

I have also just filled in more data in my above post regarding travel/navigation changes with examples of Lux, Murphy, Salisbury, Blue Sun. It was rushed and incomplete yesterday, now it's more fleshed out, hope it makes sense.

I have also added more bodies to the table in the post before that. Now included are some of the bodies orbiting protostars and some orbiting Gas Giants. Some of these have a pretty fast clip, and complete full orbits in a day or so.
Clearly, hopping from one of these whizzers to another will have the greatest difference, requiring maybe a half hour one day, and then a full hour the next day. However, to travel TO these bodies from another system, the travel times and navigation are barely changing.

NOTIFY: Y  | REPLY  | REPLY WITH QUOTE  | PERMALINK  | TOP  | HOME

Quote:

---

Originally posted by jewelstaitefan:
I figured that showing the Fiction value for Persephone as 121 days compares to Science value of 4.2 Days offered adequate contrast. We don't need to detail the added decimal points for these purposes, I just wanted to ensure I wasn't off calculation by the magnitude you had indicated.

---

Seems completely reasonable to me.

Quote:

---

Regarding the mass and orbital velocity of the Suns, consider that if the mass of Georgia Sun was a small fraction of White Suns mass, we would use the same formula as the other bodies. I had wanted to use the mass sum figure to help approach what the value would be with so much more mass involved, making the orbital velocity greater than if Georgia was not so massive.

---

The point is that if Red Sun and Georgia are orbiting the same centre of gravity at the same distance they have to be orbiting at the same velocity. They're own mass is irrelevent, save to work out what the total mass of the centre of gravity is. The result is for accuracy if you want to include Georgia's mass in the barycentre, you have to include Red Sun's as well, because they're the same orbital system.

I think that might be what you're saying here, but I wasn't 100% sure:

Quote:

---

I expect that a fair compomise for our rough guesstimations would be to use the sum of 2 masses to calculate the duration and velocity, and still assume that White is the central body, with all other Suns orbiting it. If we were to not consider it this way, using only one mass (that of White Sun), then the orbital velocity of Georgia will be much slower and the duration (period) will be much more.
Do you find this compromise reasonable? Is it a fair substitution for performing all the exacting mechanical formulae involved?

---

Quote:

---

If you find an error where I indicate something like 4 days and you conjure something like 3 hours, I'd really like to know about vast errors I've created. If you don't, somebody eventually will, and it's best to catch major errors earlier than later.

---

It's always best, which is why I always try to show my working as feasible.

NOTIFY: Y  | REPLY  | REPLY WITH QUOTE  | PERMALINK  | TOP  | HOME

Quote:

---

Originally posted by citizen:

Quote:

---

Originally posted by jewelstaitefan:
Regarding the mass and orbital velocity of the Suns, consider that if the mass of Georgia Sun was a small fraction of White Suns mass, we would use the same formula as the other bodies. I had wanted to use the mass sum figure to help approach what the value would be with so much more mass involved, making the orbital velocity greater than if Georgia was not so massive.

---

The point is that if Red Sun and Georgia are orbiting the same centre of gravity at the same distance they have to be orbiting at the same velocity. They're own mass is irrelevent, save to work out what the total mass of the centre of gravity is. The result is for accuracy if you want to include Georgia's mass in the barycentre, you have to include Red Sun's as well, because they're the same orbital system.

---

I just italicized the term "velocity" in my above quote (I think), to emophasize my meaning. I agree that the Red and Georgia mass will cancel each other in terms of offsetting White's postition as the central body, but those masses must INCREASE the VELOCITY of Georgia and Red, or else their combined Grav force will pull them into a decaying orbit if they're only at the VELOCITY they would be at if 3 times the mass was not involved (Red would pull Georgia into White, and Georgia would pull Red into White).

Quote:

---

I think that might be what you're saying here, but I wasn't 100% sure:

Quote:

---

I expect that a fair compomise for our rough guesstimations would be to use the sum of 2 masses to calculate the duration and velocity, and still assume that White is the central body, with all other Suns orbiting it. If we were to not consider it this way, using only one mass (that of White Sun), then the orbital velocity of Georgia will be much slower and the duration (period) will be much more.
Do you find this compromise reasonable? Is it a fair substitution for performing all the exacting mechanical formulae involved?

---

Quote:

---

If you find an error where I indicate something like 4 days and you conjure something like 3 hours, I'd really like to know about vast errors I've created. If you don't, somebody eventually will, and it's best to catch major errors earlier than later.

---

It's always best, which is why I always try to show my working as feasible.

---

I'm trying to reduce the info overload here for many, already putting up enough tables and data sets and such. That's also why I listed some tbles, like acceleration of Serenity, so that calculations could be minimized for most readers here. But showing the work is good for finding the discrepancies.

NOTIFY: Y  | REPLY  | REPLY WITH QUOTE  | PERMALINK  | TOP  | HOME

Quote:

---

Originally posted by jewelstaitefan:
I just italicized the term "velocity" in my above quote (I think), to emophasize my meaning. I agree that the Red and Georgia mass will cancel each other in terms of offsetting White's postition as the central body, but those masses must INCREASE the VELOCITY of Georgia and Red, or else their combined Grav force will pull them into a decaying orbit if they're only at the VELOCITY they would be at if 3 times the mass was not involved (Red would pull Georgia into White, and Georgia would pull Red into White).

---

Actually they don't quite cancel out, but we can ignore that as an order of simplification.

I don't understand your objection though. The mass of the satelite isn't important to it's orbital speed, regardless of how massive it is. The Mass of the satelite, if large enough to make a difference, should be used to determine the apparrent mass of the barycentre. If both Georgia and Red Sun are orbiting the same barycentre at the same distance, they have to orbit at the same velocity as each other, that Georgia is more massive than Red Sun is entirely irrelevent to that. Sure they'll be orbiting at a greater velocity than the mass of White Sun would suggest on it's own, but Red Sun and Georgia will have the same velocity.

This is for the same reason that a cannonball and a feather dropped from the same height on the Moon land at the sametime. It's not to do with scale, relative or otherwise, two objects at the same distance from the same gravity centre will always orbit at the same speed, regardless of their own mass.

The apparrent mass of the barycentre, in simplified form ignoring other bodies, will be the sum of White Sun, Georgia and Red Sun. That is the orbital velocity will be a function of a bodies distance from an apparent gravitational centre with the mass of the whole system.

If we ignore the effect Red Sun and Georgia have on White Sun, we assume that there is a barycentre centred on White Sun that is the sum of White Sun's mass, Red Sun's mass and Georgia's mass. Since Georgia and Red Sun are the same distance from this barycentre, they have the same orbital velocity, given by:
v = Sqrt[G(mw+mg+mr)/r]

NOTIFY: Y  | REPLY  | REPLY WITH QUOTE  | PERMALINK  | TOP  | HOME