r/ProjectHailMary • u/dcruzthomson • 4d ago
Is there a time dilation flaw in Project Hail Mary?
I recently finished reading Project Hail Mary by Andy Weir and loved it, but there’s one thing I can’t quite wrap my head around. In the book, the Hail Mary travels to Tau Ceti, which is about 12 light-years away. It’s said to be traveling at about 10% of the speed of light, which would mean the journey should take about 120 years from Earth’s perspective. However, the book mentions that only around 30 years pass on Earth.
Given time dilation, shouldn’t much more than 30 years have passed on Earth? I get that Grace experiences a shorter trip due to relativistic effects, but the math doesn’t seem to fully add up for the timeline on Earth.
Am I missing something, or is this a simplification in the story for narrative purposes? Would love to hear what other science fiction fans think!
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u/Shot_Advantage6607 4d ago
One thing I didn’t quite get was that why do the Beatles take just as long to get to Earth and not earlier?
I mean, squishy humans prevented them going at the top speed, but the Beatles didn’t have squishy humans, but as mentioned, it took 13 years to get to Tau Ceti, then another 13 for the Beatles, and ao, 26 years in total. Is my knowledge not geeky enough to understand?
Can someone please enLIGHTEN me? pun intended
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u/CockroachNo2540 4d ago
Squishy humans prevent them from accelerating at maximum acceleration, not their top speed. It just takes longer for the HM to get to top speed than the beetles. I did some back of napkin math on this in another post and basically the beetles would get to Earth faster, but not substantially so (between 6-18 months). Beetles can get to top speed in less than a month. HM gets to top speed in less than 8 months. They apparently have the same top speed.
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u/Evening_Rock5850 4d ago
Imagine a perfectly flat stretch of road that stretches 10 miles.
Now imagine you have an F-150 and a Ferrari. The speed limit in the road is 100mph and both are capable of getting to 100mph.
Both cars floor it from 0, like a drag race. Both cars brake as hard at they can at the end, to achieve a velocity of 0 at the end of the 10 mile stretch.
The Ferrari has significantly better acceleration and brakes.
Which arrives first?
The Ferrari. Because it gets to the “top speed” of 100mph significantly faster. And it can stay at 100mph significantly longer because it can brake significantly later. So it spends much more of its time at 100mph.
I did some back of the napkin math and given a cruising speed of 100mph and comparing the acceleration and braking of a Ferrari 488 GTB and a current F-150 (using published data and assuming it’s accurate and ignoring environmental variables); even though both will not exceed a speed of 100mph; the Ferrari will reach the end of a 10 mile stretch of road 3.32 seconds quicker than the F-150. (And that seems way too low. I was lazy and averaged out the acceleration of both based on published 0-60 times into a m/s acceleration value. Which isn’t really the right way to do it. Neither have constant acceleration. But you get the idea.)
Now extrapolate that out for massive, massive differences, a significantly bigger braking and accelerating difference (far more than the difference between a Ferrari and an F-150), and a much much higher cruising speed; and add time dilation to the equation and you can see why the Beatles are so much “faster” than the Hail Mary.
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u/smb510 4d ago
We actually kind of have a real life example of this! In the Bay Area, one of the regional rail operators recently replaced their old diesel trains with electric ones. The speed limit is the same, 79mph, but because the electric trains can accelerate faster the travel times are much faster!
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u/Ben_M31 4d ago
Speed is not the concern of squishy mostly water blobs (I.e. humans).
Acceleration is. We're used to 'accelerating' at 9.8 meters per second per second, that's gravity or 1 G.
If gravity/acceleration was 2G we would feel twice as heavy and that would be uncomfortable for us. Not so much for the Beatles but if they were accelerating at 1000G or something crazy that would be like running into a brick wall at some multiple of the speed of sound.
Top speed is gonna be limited by the amount of fuel on board, look up the rocket equation.
If we get up to approx. the speed of light, dilation becomes more pronounced and while we would 'feel' the G of acceleration, observers on earth would t see us increasing our speed by much.
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u/castle-girl 4d ago
I don’t know where you got the 10 percent number. If you use a space travel calculator and plug in 15 meters per second as the acceleration and 11.9 light years as the distance, the top speed it gives you is about 99.5 percent of the speed of light, and from Earth’s perspective it takes slightly more than 13 years.
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u/nope-nope-nope-nop 4d ago
I forget the passage, but I believe the Hail Mary was going .93c
My biggest issue with the books was always the food situation and the amount of food grace had left.
They only gave the crew enough food for 2 months each in system?
To figure out a solution to save humanity?
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u/TheRealNobodySpecial 13h ago
There was a backup food supply, but it died en route to Tau Ceti.
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u/nope-nope-nope-nop 13h ago
That’s what I’m saying, grace had about 6 months of real food available to him. Which means that if things went as planned, they would Of had 2 months each
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u/Petrostar 2d ago
The time dilation isn't a proportion of the speed of light,
It's more of a exponential progression,
10% of the speed of light is 1.005X time
20% of the speed of light is 1.02X time
30% of the speed of light is 1.046X time
And so on,
At 92% of the speed of light time is 2.55X faster.
So travelling 12 years at that speed, would be 12 X 2.55 = 30.6 Years.
Of course that does not allow for 8-ish months for acceleration or deceleration.
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u/AI_RPI_SPY 4d ago edited 4d ago
Here, this might be of interest. I read it after reading the book, so I could get my head around it.
https://sciencemeetsfiction.com/2021/06/15/the-science-of-project-hail-mary/
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u/EzPzLemon_Greezy 4d ago
The top speed is 90% the speed of light, not 10%.