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Specifically talking about the Spirit of Fire, but not restricted to that if there's other examples. Can they travel fast enough that time dilation would be noticeable, or would Serina's life be over before they even leave the Shield World's star system? Sure, I know that even if they were going at 50% the speed of light they wouldn't exactly be saying "we're nearly there!" any time soon, but could they even get to that speed in the first place or would they be lucky to get 10%? Or is even 1% out of their reach?

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I've been unable to find a canonical top speed for any "fast-mover" in the Halo universe. There's a very brief mention of a railgun (the MAC) that can accelerate objects

"up to 40% of light speed"

in the Halo Encyclopedia as well as a slightly fuller explanation of how the sub-light drive systems actually function, through the use of artificially controlled gravity. This strongly suggests that the upper barrier to sublight is the speed of light itself.

On the assumption that the Spirit is capable of a continual thrust of 1g, per this excellent answer, their speed would top out at just below c after around a year of acceleration, after which they'd simply need to wait until they were a light year from their destination before starting to decelerate. Even if the ship was capable of drastically faster acceleration, the most time they could theoretically shave from their journey is two years.

The unlockable in Halo Wars states that the return journey of the Spirit will take a considerable amount of time. There's no mention of relativity effects but I think we can assume those would take place:

Thanks to Sergeant Forge's sacrifice, the Spirit of Fire escapes from the Forerunner Shield World. Spirit of Fire sets a course for home as the majority of the crew prepare to enter cryo sleep for a journey that will take years, if not decades.

  • I thought I'd responded to this but apparently I was drunk. Since they're in cryo, relativity isn't important to the crew but is for Serina's short life span. Perusing Halopedia only gave me that interplanetary distances can be crossed in "less than an hour." Vague. There was no mention of artificially controlled gravity. Did it specify if that tech was across all factions? Cos it sounds rather Covenant-y. Lastly, is there a reason we should assume 1g of acceleration? My physics is weak, math formulas aren't my thing. – Judy Jan 11 '15 at 6:16
  • @Judy - There's absolutely no reason to assume 1g of thrust. I chose it solely for illustration purposes. On the other hand, if it's actually 100000g or 10000000g, the most they can save is two years of travel time since they'll just reach the speed limit faster. – Valorum Jan 11 '15 at 8:53
  • I thought that IRL there were problems with the amount of fuel required being impossible to do that indefinitely. Obviously, it's a pretty soft sci-fi shooter game series, so disbelief suspended, but would a more "realistic" scenario not be that they carefully chart a course, use as much of their fuel/power/whatever as they can spare to accelerate as much as possible and then just drift the rest of the way at whatever speed they reached, which may well not be c? Or is this getting too speculation-y? – Judy Jan 12 '15 at 6:54
  • @Judy - Within that universe, gravity control seems to be a normal "thing". There's no good reason to assume that they can't achieve a continual thrust all the way up to 99.99% of c. – Valorum Jan 12 '15 at 9:49
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It's established that the Shaw-Fujikawa slip drive can accomplish about 2.625 light-years per day.

As for sublight speeds, the ships depend on power output.
Going off of Halo 4 - Midnight, the Chief had managed to catch up to the Didact's ship despite it having a head start, and at one point Cortana noted the Didact's ship was 300 kilometres away. Several seconds later the Chief had caught up to the Didact's ship and hid under its shields to accompany it in slipspace. Do note that this requires rather extreme accelerations and requires a great amount of force in order to perform this feat. They'd be going at least 216,000 kilometers per hour or over 134,000 miles per hour.

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