The Bradbury Revisited
Oct. 7th, 2010 08:09 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
plutherusSome time ago, I asked for some help on some calculations (http://plutherus.livejournal.com/255206.html). I was trying to figure out how interstellar travel times, assuming a constant acceleration of 9.8m/s^2 (i.e., 1G, i.e., all those aboard the space ship will experience Earth-normal gravity throughout the trip.)
I recently revisited this calculation, after the discovery of Gliese 581g, 20 light-years away. I had no better luck doing the calculation this time. (It has occurred to me that in the intervening 7 years, I could have learned enough calculus to make the calculation easy.)
Fortunately, someone else had the same question - physicist Dave Goldberg. Apparently, he did the calculations for Alpha Centauri in his book, A User's Guide to the Universe, and has recently re-done them for Gliese 581.
More details are at his blog. He still doesn't show his work, there, though. I've added his book to my Amazon queue, so I'll eventually see if it's in there. His conclusions, though, are similar to my own:
To get to Gliese 581, while accelerating at a nice comfortable 9.8m/s^2, would take roughly 6.1 years from the traveler's perspective, or 22.4 years from Earth's. (That is, they will get the signal saying the travelers have arrived safely about 42.4 years after they leave.)
A couple of assumptions he makes, though, that I disagree with:
First, he writes:
Right, but why would you lug all that fuel around? Leave it here, and use it to power, say, a giant laser, which could push an interstellar craft along using a solar sail. Also, Goldberg writes that:
But, of course, there's no reason to collect the energy on Earth. By the time we've gotten to the point where we're seriously considering an interstellar manned flight, we should be able to build a giant particle accelerator and anti-matter factory orbiting the Sun, somewhere inside the orbit of Mercury, perhaps, where solar cells, plus the gravity of the Sun itself, should make things much more efficient.
EDIT: Turns out he did show the actual math used, in a later post: http://usersguidetotheuniverse.com/?p=1249
I recently revisited this calculation, after the discovery of Gliese 581g, 20 light-years away. I had no better luck doing the calculation this time. (It has occurred to me that in the intervening 7 years, I could have learned enough calculus to make the calculation easy.)
Fortunately, someone else had the same question - physicist Dave Goldberg. Apparently, he did the calculations for Alpha Centauri in his book, A User's Guide to the Universe, and has recently re-done them for Gliese 581.
More details are at his blog. He still doesn't show his work, there, though. I've added his book to my Amazon queue, so I'll eventually see if it's in there. His conclusions, though, are similar to my own:
To get to Gliese 581, while accelerating at a nice comfortable 9.8m/s^2, would take roughly 6.1 years from the traveler's perspective, or 22.4 years from Earth's. (That is, they will get the signal saying the travelers have arrived safely about 42.4 years after they leave.)
A couple of assumptions he makes, though, that I disagree with:
First, he writes:
Even if you have [an anti-matter drive system], you still need to lug all of that fuel around. It turns out that:
* To do the trip above requires (at least) 530 times as much mass in fuel as in the ship and cargo itself.
Right, but why would you lug all that fuel around? Leave it here, and use it to power, say, a giant laser, which could push an interstellar craft along using a solar sail. Also, Goldberg writes that:
The whole trip would require something like:
* E=1.8\times 10^{25}Joules
Or approximately 5% of the sun’s energy output in a second. That sounds reasonable, until you realize that that tiny amount would take approximately:
* 3 million years to collect on earth if the entire surface were covered with solar panels
But, of course, there's no reason to collect the energy on Earth. By the time we've gotten to the point where we're seriously considering an interstellar manned flight, we should be able to build a giant particle accelerator and anti-matter factory orbiting the Sun, somewhere inside the orbit of Mercury, perhaps, where solar cells, plus the gravity of the Sun itself, should make things much more efficient.
EDIT: Turns out he did show the actual math used, in a later post: http://usersguidetotheuniverse.com/?p=1249
A few calculations
Date: 2010-10-07 11:52 pm (UTC)You're right, of course, that we might not be limited to the energy available on earth by the time we make such a trip. I just wanted to put the energy requirements in perspective. And I agree that a light sail powered by an earth-based laser would, indeed, get around some of the energy requirement issues. It does creates others, however.
For instance, you'd need to be able to collimate and aim the laser with ridiculous precision, which would require doing so above the atmosphere.
There's also the fact that as the ship approaches the speed of light, the beam would appear more and more redshifted from the ship perspective, meaning that it would pack less of a wallop than it should. I'd have to do the calculations in detail, but in essence, it would mean that the laser would have to increase in power tremendously in mid-flight.
Re: A few calculations
Date: 2010-10-08 06:36 pm (UTC)I didn't think about the red shift problem. I suppose a tunable laser (would a free electron laser work in space?) could solve the problem of material becoming less reflective at different frequencies, but not the problem of the energy transfer itself.
So either we have a laser that steadily increases in power, or a spaceship that steadily decreases in acceleration. (What is the derivative of acceleration anyway?) That'll be fun to compute. I couldn't even do the first part, so I'm not even going to try here :)
Or s ship that carries its own reaction mass with it. 530 times could conceivably be doable. If I recall correctly, most of the mass of the space shuttle is fuel, though probably not 99.8% of it. (That would be a hell of a lot of anti-matter to make, though, compared to the thousands of atoms that CERN has made to date. :)
Of course, I'm not sure how they'd slow down using this method, either, unless they sent robots ahead to build another giant perfectly collimated and aimed laser there.
Anyway, thanks for the posts. I look forward to reading the book.
Re: A few calculations
Date: 2010-10-08 07:50 pm (UTC)m_i/m_f ~ e^(2*tanh^-1(v/c)), by only needing the fuel to slow down, you go from needing ~450 times as much fuel, to sqrt(450)~21 times as much fuel as cargo. The bigger issue, though, is still the whole question of how you'd possibly focus and aim a laser over those sorts of distances.
BTW, you might also enjoy today's (rather mathematical) post on how to compute the time dilation of an accelerating ship:
http://usersguidetotheuniverse.com/?p=1273
Dave