Somtaaw wrote:In another post in 2017, we got off-topic (like usual) about Eridani violations and were discussing Hermes buoys, and I again brought up the observed timers about Mobius, acceleration and the Hermes buoy being deployed at the exact moment the GR drones were decelerating to Mobius.
In ~2.5 hours a Hermess Buoy zipped ahead of Terekhov's makeshift squadron and made a close approach to the Solly destroyers in orbit of Mobius also undetected. But I don't think we have nearly enough information to figure their possible accel curve.
Here's what I can determine if you wanna take a pass:
-Terekhov's distance was again 215.9 million km, starting velocity was 913 KPS, and acceleration of 5.7 KPS squared.
-9 minutes later they're upwards of 4000 kps (not very exact I know), Sollies specifically mention
three hours and fourteen minutes to a zero/zero intercept with the planet…and us, of course. Turnover in about an hour and a half. Velocity at turnover will be right on thirty-five thousand KPS.
More datums for (trying to) calculate Hermes Buoy acceleration & stealth profile:
Quentin Saint-James had reentered normal-space twenty-six minutes earlier. During that time, she’d increased her n-space velocity to just over ninety-four hundred kilometers per second and traveled just under 7.8 million kilometers towards the planet officially designated Mobius Beta.
The Ghost Rider drones had to close from 96 light-seconds to 92 to detect the Solly ships, and Helen made her suggestion involving Hermes Buoys within approximately 5 minutes of that happening.
Terekhov regarded her thoughtfully for a moment, then nodded. “Works for me,” he said, and smiled at Pope. “And now that Ensign Zilwicki has so masterfully summarized her proposed approach, let’s give some thought to making it work most effectively.”
We don't know how long it took him to flesh out her summary and launch the Buoy, but it wasn't likely to be longer than approximately 15 minutes after the Ghost Riders hit that 92 light-second distance.
so our final datum is Terekhov was in-system approximately 26-30 minutes (how long would the Ghost Riders take to decelerate 4 light-seconds?), and then an unknown amount of time for Terekhov to quiz Helen, then plan and only Himself or Bu9 know how long it takes to actually kick a Hermes over the side and accelerating on its own drive. But let's assume he kept it brief, and overall he had the Hermes activating it's own drive after being in system for exactly 45 minutes?
Then for it to actually transmit
The (Manties)'d been in-system for almost two and a half hours now. In fact, they’d made their turnover and begun decelerating forty-eight minutes ago. The range was down to thirty-one million kilometers—under two light-minutes—and he’d started sweating the moment it dropped to forty million.
At some point prior to this, the Hermes buoy was already on station 40,000 km away from the Sollies and the ONLY reason they knew that was because it started broadcasting to them at that time. So it made the trip over I don't have the calculations for how many km's, in an absolute maximum of 105 minutes and stayed completely covert, although it probably made it faster.
Well let's see what I can do.
tl;dr version: It seems it could have an accel around 825 gees.
Okay, first step is verifying the numbers on Terekhov are consistent and make sense. And they initially seem close enough; allowing for some rounding.
Time 0
* Initial velocity 913 KPS
* Acceleration 5.7 KPS squared (581.63 gees)
* Range 215.9 million km
Time 9 minutes (540s)
* up to ""just under four thousand KPS" -- from 913 KPS, 540s @ 581.63g = 3,991 KPS
Time 99 minute (5940s) [projected]
* Turnover at 90 min from T=9m, at "right on thirty-five thousand KPS" -- 5940s @ 581.63g = 34,771 KPS and 105,981,480 km
Time "almost two and a half hours"; 48 minutes (2880s) after turnover [if turnover was as projected this is 2h 27m (8820s) from emergence]
* "range was down to thirty-one million kilometers" -- from 34,771 KPS, 2880s @ -581.63g = 18,355 KPS and 182,482,920 km. 215,900,000 km total distance - 182,482,920 km = 33,417,080 km.
Not perfect but probably within a rounding error.
Time 3 hours 23 minutes (12180s) [projected]; 1h 44m (6240s) after turnover
* Zero/zero in 3h 14m from the same 9 minute mark -- from 34,771 KPS, 6240s @ -581.63g = -797 KPS and 211,980,360 km.
Not quite perfectly 0 KPS and 215,900,000 km; but presumably still within a rounding margin of error. (Actual zero velocity would be more like 6100s, 1h 41m 20s and that'd actually put them 55,720 km closer to the planet; as they wouldn't yet have started accelerating away again)
Problem is this bit in the middle
Shadow of Victory wrote:Quentin Saint-James had reentered normal-space twenty-six minutes earlier. During that time, she’d increased her n-space velocity to just over ninety-four hundred kilometers per second and traveled just under 7.8 million kilometers
Because, from 913 KPS, 26m (1560s) @ 581.63g gives you 9,805 KPS and 8,360,040 km.
Not 9,400 KPS and 7,800,000 km.
Still that's within the range of possibilities. He'd need to adjust acceleration at least twice within the 17 minutes between those observations; as there's no fixed accel that would hit both velocity and range given his known values at the 9 minute mark. And even going to no accel for a while and back to 581.63g won't so it. However one example that would is from the 9 to 10 minute mark drop to 0g accel, then from 10-26 minutes come up to 575 gees -- which would end up at said 26 minute mark with a velocity of 9,401 KPS and a distance of 7,752,048 km.
However if he's varying things up that much then we might as well throw the rest of the flight profile out; he could have turned over at a different time, increased acceleration to above 5.7 KPS^2, or anything else.
And we seemed to be doing so well. Ugh.
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Still, that 26 minute fix is in the same scene as the Hermes buoy appears to be launched -- so let's take the dangerous approach of ignoring the inconsistencies and using its data for velocity and range at buoy launch.
We know he transmitted with the buoy at "less than forty thousand kilometers out!" from the SLN ships, and that at that point he's been in the system for "almost two and a half hours" and make "turnover [...] forty-eight minutes ago"; which we previously estimated was actually 2h 27m (8820s) from emergence.
So if we take those paragraphs both as true,
and assume that the buoy decelerated to zero at that 40,000 km,
and that it did so only just before the Manties transmitted then we'd have the following data points.
* Launch of Buoy T=0s
velocity 9,400 KPS, range 138,000,000 km from planet.
(215.9 million km upon emergence - 7.79 million km [just under 7.8] at launch)
* Arrived Buoy T=7,260s
velocity 0 KPS, range 40,000 km
And some fiddly trial and error later I've got a usable set of numbers. (Mind you, the precision is way beyond what I should use given how comparatively large the uncertainties in the starting numbers are).
If the buoy has an acceleration of 825.25g then it fits the above numbers.
From 9,400 KPS, 3048.853s @ 825.25g give us 34,057 KPS and 66,247,683 km downrange; and we turnover and accelerate for 4211.147s @ -825.25g which brings up down to 0.0054 KPS at 137,958,150 km downrange (or 41,850 km short of the planet where the SLN ships are)
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But if he launched later, or the buoy arrived earlier, then all those numbers are off and we're back to having to guess how long he waited to launch
(and what accelerations he adopted during that time; in order to get the new base velocity) and/or how much sooner it arrived. Either of those would produced a higher acceleration number.
Or if the buoy was flying by with a non-trivial remaining velocity then it could have had a lower acceleration.
Or hell, if for some reason
it flew a variable acceleration path and/or didn't follow the least time route then all these numbers are totally out the window.
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(Now, why did I just spend around 2 hours working on all this?
)