With ISp defined as ${v_e}\over{g_0}$, the naive approach would tell me, the maximum possible specific impulse, with propellant moving at speed of light relative to the craft, is $c\over{g_0}$ or 30,570,322s.

Of course, with relativistic physics naive approach is often wrong and I feel like I'm making some oversimplification here... so, if I am, could someone straighten it out? What happens with Specific Impulse when extreme energies are put into the propulsion, accelerating the propellant to relativistic speeds?

  • $\begingroup$ Great question! Would the limiting case be a photon rocket? $\endgroup$ – Organic Marble Jul 10 '16 at 21:14

A photon rocket should have a Ve of c, hence ~30 megasecond Isp. The rocket equation would be tricky to apply, of course -- if you have a magic matter-energy reaction that perfectly converts "fuel" into linear-directed photon exhaust, it works fine, but if energy is going elsewhere, the effective exhaust velocity will be different. You'd account for relativistic effects in applying the ∆v using everyone's favorite sigmoid function, the hyperbolic tangent.

what, you don't have a favorite sigmoid function?

  • 2
    $\begingroup$ So - I "naively" plug the speed into ISp, but need to go relativistic when using that ISp for anything else? - on a different note: Considering how weird a unit 'megasecond' is, I checked... that's almost a year. ...And I just got a good line for a sci-fi novel. "...and her ISp is measured in weeks." $\endgroup$ – SF. Jul 11 '16 at 1:27

No. The number you gave is for a photon drive. However, if you throw particles out the back at relativistic velocity they weigh more than the fuel you drew from the tank. Since there's no limit on how much relativistic mass you can pile on the particle there's no limit on the ISP. Note, however, that there's no way you can boost particles like that using onboard energy.

  • $\begingroup$ Wouldn't that just increase the mass flow? Their mass increase comes from equivalent decrease of mass of on-board power supply.due to its energy loss (RTG battery acting as a fuel tank). $\endgroup$ – SF. Jul 12 '16 at 4:48
  • $\begingroup$ @SF. Note that I said it would not be possible from onboard energy. If you have to supply the boosting energy you're going to lose more mass than this gains you. The only way to actually pull it off is to obtain the energy from some outside source. $\endgroup$ – Loren Pechtel Jul 12 '16 at 15:33

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