Electron-positron annihilation as a propellant

[Jarvitä]

Well, that's true... but in terms of Physics alone... if you pump a certain amount of power, you can get lots of low energy photons with little bit of momentum each, or one photon with a lot of momentum.

Yes, but in terms of positron-electron annihilation, you're stuck with two 511 keV photons.

 

[RisingFury]

EDIT: RisingFury, thanks, I see the P-c relation now. But I still don't understand how the momentum itself can be independent from wavelength, when it's clearly defined as [math]\frac{h}{\lambda}[/math]?

Imagine having 1 mJ of energy. You can either create one photon with the energy 1 mJ or you can create two, with the energy 0.5 mJ.

Indeed, their wavelengths would be different, but if you add the momentum of both photons and compare them to the photon of higher energy, you'll see they supply the same momentum.

 

[tori]

But that's wrong. The momentum and energy of photons clearly depend on the wavelength/frequency.

Yes, but momentum != thrust. With a given amount of energy, you can either make a whole bunch of low-momentum photons, or one high-momentum one. The relationship is linear on both sides, so it cancels out. It is clear from the pythonesque math dump in my previous post.

Edit: RisingFury was faster.

 

[xlns]

So, an electron and a positron colliding at low energies (ie, relatively slow, not ... for a 100 ton spacecraft, from a single kilogram of propellant, no reaction mass required.

Is there anything obvious I'm missing, other than the fact that we just don't have a way of producing this much antimatter yet?

If it may interest anyone, having an *ideal* antimatter-driven propulsion would take almost 900kg of antimatter per payload kilogram to get to Vega, circa 30ly away - non-stop thrust assumed, minimum travel time. A great review of relativistic rocket is on Baez's http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html (generally great site). Reading some of those numbers, space distance really starts you thinking; as Stanislaw Lem put it, enormous, void wall placed by the Lord between us and Others.

 

[xx_mortekai_xx]

I thought the photons' momentum itself acts as a reaction force?

ie, in a perfect vacuum and absence of any other forces, lighting a flashlight / laser pointer will eventually propel you in the opposite direction of the beam? Imagine that, with high energy gamma rays instead of visible light.



The amount of energy needed to produce m antimatter is [math]E\ =\ m\ \frac{c^{2}}{\eta{}}[/math], eta representing the efficiency of the factory as a number between 0 and 1. In the best case, you only need as much energy as you're going to get out of it. And even at lower efficiencies, it's probably still more effective to use this energy on an AM factory on Earth than to bring means to produce it along with the spacecraft.

The only issue I see with that is that you wouldnt necessarily have gamma rays only emanating from one direction. The unidirectional spread would cancel most, if not all, of the total velocity change, leaving you with a very inefficient means of propulsion.