Calc Keys To The Kingdom - Sunsprites chase the Helios

Calculations
An impressive speed feat.
Grim Tuesday said:
‘So they’re all copies of real ships in real places?’ Now that Arthur looked closely at the bottles, he could see that the ships were moving, the sea splashing, the sun – sometimes more than one sun – shifting in the sky.

‘All but one bottle,’ answered Tom. ‘There’s one that holds a real place, not a copy. One where time flows like it should, not round and round for a few copied hours.’

‘What do you mean?’ asked Arthur. ‘What’s in that one bottle?’

Tom smiled. ‘I’m as pleased as punch you asked that question, for it’s the one I’ve been wanting to tell you. That single bottle holds a sun, and several worlds, and a sunship, the finest ever built. Sail into the sun, she can, right to its blazing core – with the crew none the hotter for it.’

‘Why would you sail to the centre of that sun?’ asked Arthur.
Tom takes Arthur and Suzy to the core of a Sun on a sunship through a star system. On the way back, they're chased by sunsprites.
Grim Tuesday said:
Tom didn’t answer. He was intent on a gauge that was slowly filling with a red dye. As it got to two-thirds full, he spun the wheel and held it fast, straining against some unseen pressure. The gauge almost immediately became totally suffused with the red dye and stayed full.

‘A good wind and both sails taut,’ shouted Tom. ‘They’re trying to hold us back, but they’ll fall away. Aye, there they go!’

Arthur couldn’t see anything in the portholes, or at least he couldn’t be sure what he was seeing. But the hammering lessened, and the indistinct shapes in the brightness were no longer all over the place but bunched up in the bottom corners of the portholes. From there, they slowly disappeared.

After five minutes, there was no more hammering. Tom relaxed a little at the wheel, though he didn’t lash it or let go.
The ship is moored near a Saturn-like planet.
Grim Tuesday said:
His eyes slid away from the ship, drawn to a planet with many feathery rings, like Saturn but much brighter.
It takes them 20 minutes to 30 minutes to return to the mooring spot.
Grim Tuesday said:
‘This one’s come unstuck too,’ said Arthur. He scratched his head. ‘We’ve got an hour or so sailing back, haven’t we, Captain?’

‘Half that, or maybe a third,’ replied Tom. ‘The solar wind is with us now.’
The most impressive thing is though, the sunsprites where able to keep up with them for a time.

A gas giant needs to be beyond the frostline in order to form. For an Sun-like, star, that's 5 astronomical units (748000000km).
http://www.astronoo.com/en/articles/frost-line.html
Frost line or ice line defines the boundary where simple molecules condense (dihydrogen H2, dinitrogen N2, dichlorine Cl2, water H2O, ammonia NH3, hydrogen sulfide H2S, carbon dioxide CO2, methane CH4, ethane C2H6). This line is a little less than 5 au (≈ 700 million km) from the Sun, well beyond the asteroid belt and just before the orbit of Jupiter. It marks the clear separation between the terrestrial planets and the gas planets.

T = 748000000km/35min
= 356190476m/s
= 1.18812353845C

Now the high end.

T = 748000000km/25min
= 498666667m/s
= 1.66337295583C

Final Results
Sunsprites chase the Helios (low end) = 1.188C
Sunsprites chase the Helios (high end) = 1.663C


Not only would this scale to the Architect, the Old One, the Trustees and the Architects Children, but possibly also the Dawns, Noons & Dusks.

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Stocking Anarchy
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