Inspired by the Project Hail Mary thread. Tau Ceti is about 12 light years away. I have questions:
If you accelerated at 1 g all the way there (not worrying about having to go into some kind of Tau Ceti orbit), how long would it take for the spacecraft to make it there, from the perspective of Earth and from the perspective of the ship?
If you had to actually do something at Tau Ceti, I guess you would accelerate at 1 g to the midpoint and then decelerate at 1 g for the rest of the way. How long would that take, from the ship and from Earth’s reference frame?
How fast would you be zipping by TC in scenario 1?
I think that accelerating at 1 g for any significant length of time gets into lots of relativity questions, which are now well beyond my capabilities. Thanks!
I was just going to update this thread! Anyway, if the g force is a simple input once someone figures out the formulas, I wouldn’t mind answers at both 1 and 1.5 g.
Disclosure: I used this calculator for the answers.
Tau Ceti is about 12ly away - if you want to accelerate at 1g all the way there, you will zip past it at 99.7% of the speed of light in about 3 years, 2 months ship time, or just under 13 years Earth time.
If you want to accelerate half way, then decelerate the other half (all at 1g), it takes a little over 5 years ship time, still about 13 years earth time (weirdly).
The calculator I used did include the fuel mass (basically about 25 times the weight of the ship, for a ship between 100 and 1000 tonnes), but I am not certain it included the fuel required to accelerate the fuel mass, and the mass of that fuel and the fuel required etc.
Either way, most of the trip is at very close to the speed of light. It’s only the time spent accelerating up to (and down from) that speed that makes it a bit more than the light travel time. So there’s little difference in Earth-time for either scenario.
No. It’s an acceleration, not a speed. If you want it in more familiar terms, 1 g means 0 to 60 MPH in about 2.7 seconds (or 1 to 120 in 5.4 seconds, or 0 to 180 in 8.2 seconds). For low speeds like that, it’s linear. But of course, if you keep it up for long enough, you end up dealing with relativity, and so it’s not linear any more, and you have to be careful to define just what you mean.
Yes, longer and shorter than 11 years. From the perspective of Earth, it took a bit longer, because everything takes longer to get anywhere than light does. From his perspective, it took much less, because of time dilation.
That’s relevant for a constant-thrust engine, but that’s not very practical for a manned mission, since it would result in much higher accelerations once the tank is almost empty. Here, we’re describing a constant acceleration, which would require the engines to decrease their thrust as the ship’s total mass decreases. If we’re controlling the engines to keep a constant acceleration, we don’t need to know anything about the amount of fuel in order to calculate the times.
Something something deflector array, yadda yadda force field, Cochran shields at maximum.
For fans of this sort of thing, the unfortunately named Epstein Drive from the Expanse series is a reality-grounded Fusion engine designed to produce constant thrust for reasonable transit times within the solar system.
Robert L. Forward’s “Starwisp” technology, as modified by Geoff Landis, could theoretically achieve and was designed to have an acceleration of 24 m/sec^2.
Mind you, you can’t put people on it, or any kind of payload that doesn’t require specialized handling. And it requires that people on earth devote a LOT of effort into beaming microwave or possibly laser power at it to keep it accelerating. That’s how it keeps accelerating - the effective rocket “motor” stays behind, and the reaction mass is photons. It’d get up to 10% of the speed of light, and have a payload of 80 grams.
Conveniently (and coincidentally), c divided by 1 year is just about exactly 1 g. This doesn’t, of course, mean that accelerating at 1 g for 1 year will get you to c, because relativity, but it does mean that accelerating at 1 g for any appreciable fraction of a year will get you to an appreciable fraction of lightspeed, and that relativity is therefore relevant. It also means that accelerating at 1 g for 1 year will get you to a proper velocity of 1, which you can use to calculate the travel time as experienced by the travelers.