## Why Phi? Sylvia & Sons Swing Serenely by Shining Stars

Posted: January 26, 2016 by tallbloke in Astronomy, Astrophysics, Phi, solar system dynamics

Out at the unfashionable end of the Asteroid Belt, lies a seldom seen squashed spud of rock known as Sylvia. NASA has this:

Composite image showing the two moons at several locations along their orbits (shown by red dots). Image Credit: NASA

Discovered in 1866, main belt asteroid 87 Sylvia lies 3.5 AU from the Sun, between the orbits of Mars and Jupiter. Also shown in recent years to be one in a growing list of double asteroids, new observations during August and October 2004 made at the Paranal Observatory convincingly demonstrate that 87 Sylvia in fact has two moonlets – the first known triple asteroid system. At the center of this composite of the image data, potato-shaped 87 Sylvia itself is about 380 kilometers wide. The data show inner moon, Remus, orbiting Sylvia at a distance of about 710 kilometers once every 33 hours, while outer moon Romulus orbits at 1360 kilometers in 87.6 hours. Tiny Remus and Romulus are 7 and 18 kilometers across respectively. Because 87 Sylvia was named after Rhea Silvia, the mythical mother of the founders of Rome, the discoverers proposed Romulus and Remus as fitting names for the two moonlets. The triple system is thought to be the not uncommon result of collisions producing low density, rubble pile asteroids that are loose aggregations of debris.

Ah, yes, it’s ‘collisions’ again. But wait, there’s some order in the chaos here, discerned by Stuart ‘Oldbrew’, who says:

Romulus and Remus are 3:8 in orbits = 5 conjunctions
Re:Ro mass ratio is 1:1.274 using Wiki = ~root phi

The orbital ratio 3:8 is of course two Fibonacci numbers, separated by a third, 5. The conjunctions Stuart refers to, occur every 33 * 87.6 / (87.6 – 33) = 52.945 hours. So 5 conjunctions occur every 284.725 hours. During that period, Romulus orbits 284.725/87.6 = 3.02 times and Remus orbits 8.02 times. This tells us that the precession of the conjunction cycle is rapid, completing every 50 conjunction cycles.

I wouldn’t have noticed Sylvia if She hadn’t turned up in a table of orbital distances (from the Sun) generated when I worked out an equation to improve Bodes Law. That’s  a heuristic which quite accurately predicts the orbital distances of celestial bodies out as far as Uranus, whereafter the equation goes rapidly of the rails, missing Neptune by a loooong way. My new equation pinpoints Neptune well, skips the Neptune orbit-crossing dwarf planet Pluto and goes on to nail Makemake, and comes close to hitting Eris. The discoverer of those two, Mike ‘Plutokiller’ Brown is in the news currently with his conjecture for ‘Planet 9’.

As you’d expect, my equation uses phi and associated number terms, and with a nod to gravity, a power-law progression based on powers of 2. I’ll write a post about that soon.

1. tallbloke says:

That blurry image looks like it’s showing that Sylvia has oblate spheroidal proportions of somewhere between 2:3 and 3:5…

2. oldbrew says:

‘at the unfashionable end of the Asteroid Belt’

Where’s the fashionable end? 😉

‘So 5 conjunctions occur every 284.725 hours’

55 Sylvia rotations = 285.1 hours [difference = 0.375 hours = 22.5 minutes]
http://en.wikipedia.org/wiki/87_Sylvia

That’s 11 Sylvia rotations per conjunction of the satellites.
3 + 8 = 11. Hmmm…
‘Romulus and Remus are 3:8 in orbits = 5 conjunctions’

3. oldbrew says:

‘Tiny Remus and Romulus are 7 and 18 kilometers across respectively.’

7 and 18 are Lucas numbers, which tells us their diameter ratio must be close to a Fibonacci equivalent – for example 5:13 (98.9% match based on these ‘ball-park’ stats.).
18/7 = 2.5714285
13/5 = 2.6

4. tallbloke says:

From the wiki page:
Sylvia is 385×265×230 ± 10 km
377 and 233 are adjacent Fibonacci numbers, very close to phi ratio.
Mass of Sylvia is 1.478±0.006×10^19kg
Romulus 9.3×10^14kg
Remus 7.3×10^14kg

Sylvia has around 9000 times the combined mass of her sons. She a big mama.

5. tallbloke says:

OB: That’s 11 Sylvia rotations per conjunction of the satellites.
3 + 8 = 11. Hmmm…

Axial period: 33 * 87.6 / (33 + 87.6) = 23.97 hours

6. oldbrew says:

Axial period is just over 24 hours using Wikipedia. Other numbers may change slightly too.
http://en.wikipedia.org/wiki/87_Sylvia#Satellite_system

Sylvia’s semi-major axis is about 3:2 with Jupiter (99.38% true).

On the Wiki numbers the Rom:Rem orbit ratio is 17:45 = 28 conjunctions – in which case it’s back to the drawing board 😐

The axial period would be very close to 1 day. The difference between a Rom-Rem synod and a Sylvia rotation would be 2 days (2.216~ minus 0.216).

7. tallbloke says:

I wonder if we can apply what we know to help work out which figures are correct?

In general, I think NASA are more of an authority on orbital parameters than wikipedia, but as these are recent discoveries, it’s possible wiki is more up to date.

8. Curious George says:

Our friend Gavin Schmidt works for NASA.

9. tallbloke says:

Yes, but not for the Jet Propulsion Laboratory (NASA-JPL) which looks after the rocket science and has to get things right. Gav works for the Goddelpus Institute for Screwy Statistics (NASA-GISS).

10. oldbrew says:

Sylvia orbit:
Wiki: 2381.697 d
JPL: 2370.617 d

rotation period:
Wiki: 5.183642 h
JPL: 5.184 h

No JPL data found for Sylvia’s mini-moons.
http://ssd.jpl.nasa.gov/sbdb.cgi

NB there’s an asteroid called Romulus but that’s not the Sylvia moon…
‘Romulus is the outer and larger moon of the main-belt asteroid 87 Sylvia, not to be confused with the directly Sun-orbiting asteroid 10386 Romulus.’ – Wiki

11. oldbrew says:

‘An artist’s impression of 87 Sylvia and its twin companions, Romulus and Remus (Credit: Danielle Futselaar/Seti institute)’

12. oldbrew says:

Paper abstract: ‘Orbits, masses, and evolution of main belt triple (87) Sylvia’ (2012)
http://arxiv.org/abs/1206.5755

13. Wayne Job says:

Hi Rog, It would seem that we are nearing the end of our experiment, may be a doco on TV not sure yet. Give you some info soon Wayne

14. tallbloke says:

Wayne, I want the scoop, so keep me informed. 🙂