Ion propulsion maximum speed (c)?

Factual Questions
1

IANA rocket scientist, but I have a simple theory, and am wondering why it wouldn’t work.

Given recent advances in ion propulsion and the current testing with DS1, would it be possible to send up a small spacecraft–unmanned, very minimalist–with an ion propulsion engine, and enough fuel to accelerate to the speed of light, point it in a direction and let it go?

http://nmp.jpl.nasa.gov/ds1/tech/ionpropfaq.html

and in particular, question 6, could be used to arrive at the amount of fuel necessary.

This seems to me a pure science experiment, but wouldn’t the gain be worth the cost? Why won’t it work?

2

The speed of a spacecraft that uses reaction mass is limited by the amount of mass it has. Reaction mass is the matter that a rocket engine ejects in order to obtain thrust. Once you run out of reaction mass, you can no longer accelerate. So the more xenon that DS1 carries, the higher the ultimate speed it can reach.

Of course, we all know that objects with rest mass cannot reach Einstein’s constant (c). But, a spacecraft could reach arbitrarily close to c, if you are willing to give it an arbitrarily large amount of reaction mass. For the DS1 experiment, the larger the mass of the spacecraft, the more expensive it will be to get it into orbit. I imagine that the DS1 engineers have chosen the largest size practical for their budget.

A spacecraft can get around the reaction mass limit by either collecting reaction mass from the space it travels through (e.g., a Bussard scoop). Or, the spacecraft can use photons as reaction “mass”. These options have even lower thrusts than an ion engine, but may be more efficient for very long missions (think interstellar).

3

We really don’t need an(other) experiment to determine the amount of reaction mass necessary.

The non-relativistic rocket equation is:

dV = V[sub]e[/sub]ln(m[sub]0[/sub]/m)

That is say, the total change in velocity (dV) is equal to the exhaust velocity (V[sub]e[/sub]) times the natural logarithm of the mass ratio (the ratio of the fueled rocket to the unfueled rocket, m[sub]0[/sub]/m).

Note that the velocity V is a vector; i.e., it has a direction (which is why I underline it).

Now, off the top of my head, I don’t know what the exhaust velocity of an ion drive is. Let us suppose, however, that it is 100 km/s (kilometers per second; about 62.5 miles per second). If the unfueled rocket (payload, drive, structural members, etc.) weighs 100 kg (kilograms; about 221 lb.), then we need e (appprox. 2.72) times as much propellant to accelerate it to the exhaust velocity of the propellant.

Now, light speed is about 3x10[sup]5[/sup] km/s (to the usual approximations used for government work :slight_smile: ). SSR tells us that nothing can be accelerated to light speed, and I don’t remember the relavistic rocket equation, anyway. Let us accelerate our 100 kg. rocket to a mere 5% of light speed, about 15,000 km/s. Given that 100 km/s exhaust velocity, we need e[sup]150[/sup], or about 1.39x10[sup]62[/sup] tonnes of propellant, more xenon, I am reasonably sure, than exists in this universe.

Ion propulsion sounds cool, and it certainly beats hydrogen/oxygen chemical rockets. But we’re not going to build a star drive out of it.

4

I am constantly amazed at the wealth of knowledge on the SDMB. When I read that sentence I cracked up - where else can you see a threads about rocket science and farting a mere two clicks apart?

I had a great link about the different velocities of ion propulsion engines but can’t seem to find it. Here are a few that may lead some additional info.

http://sec353.jpl.nasa.gov/apc/Electric/09.html
http://sec353.jpl.nasa.gov/apc/Electric/07.html
or the whole ball of wax at http://sec353.jpl.nasa.gov/apc/index.html
and http://www.hughespace.com/factsheets/xips/xips.html

NP: YES - Big Generator

5

Hmm…
Nah.

6

In this link provided by Opengrave (thanx!), I see that the NSTAR ion propulsion engine to be used on DS1 is said to have a specific impulse (I[sub]sp[/sub]) of about 3300 (specific impulse is exhaust velocity divided by the nominal acceleration of gravity at Earth’s surface). I was pretty far off, as I was guessing a I[sub]sp[/sub] of a bit over 10,000. My mass ratio estimates, therefore, should be multiplied by about e[sup]3[/sup]. or about 20. For the case of accelerating to 100 km/s, this makes a big difference, and is probably a show-stopper. For the case of accelerating to 5% of light speed, I think we can say that it doesn’t make any practical difference :slight_smile: