The Bradbury Revisited

[plutherus]

Some 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:

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

Comments

A few calculations

[(Anonymous)]

Hi, Dave Goldberg here, and I enjoyed your post. I just wanted to address a couple of things. First, I hope you do enjoy the "User's Guide," but you won't find detailed calculations in there. I did, as you note, do a later post where I showed the math behind the energy calculation. If there is interest, I might also do a technical post on the relations between acceleration, travel time as seen by the earth, and travel time as experienced by the astronauts.

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.