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*To*: starship-design@lists.uoregon.edu*Subject*: starship-design: Momentum*From*: wharton@physics.ucla.edu (Ken Wharton)*Date*: Thu, 24 Jul 1997 15:32:40 -0700*Reply-To*: wharton@physics.ucla.edu (Ken Wharton)*Sender*: owner-starship-design

>Why do you people keep saying this? Photons are the _best_ way to turn >energy into momentum. What's the momentum of 1 kg of mass converted >into photons vs. the momentum of 1 kg of mass converted to energy and >used to accelerate another 1 kg of mass? Steve, I'll restate the formula I just derived: P = [(E^2 / c^2) + 2 E M]^0.5 If you disagree with the way I derived this, let me know. Keep in mind that E is kinetic energy, not total energy (total energy includes rest mass). If you don't like the looks of it, check it out in the limits of M->0 and M>>E/c^2; you'll see you get the momentum/energy relationship of zero-mass and sub-relativistic objects respectively. If you take 1kg of mass and convert it to energy you get (1kg x c^2) = 10^17 Joules. The momentum of E = 10^17 Joules of photons is simply E/c, or P = 3 10^8 kg m/s. However, if you accelerate a 1kg object with the 10^17 Joules instead, you can use the above equation to find that P = [(10^17)^2 / c^2 + 2 10^17 1kg]^0.5 P = [3 10^17]^0.5 kg m/s P = 5.5 10^8 kg m/s (I've rounded here, but the answer should be exactly the square root of three greater than the photon case.) In this case the ratio between Mc^2 and E was 1; as this ratio gets bigger (either the mass is larger or the energy drops) the difference from the photon case gets even larger. I suggested a ratio of 4:1 as a way to get three times the momentum as the incident beamed energy. Another way to think about this would be to think about this would be to put a 100 watt bulb in a mirrored box on wheels, with a hole cut in one side. The box wouldn't go anywhere, despite the fact that 100Joules per second was streaming out in photons. The momentum per second would only be 100Joules/(3 10^8 m/s) = 3 10^-7 kg m/s. But if instead you put 100 Joules into a 2kg weight every second, they'll be flying out at 10m/s, one a second, with a very sizable momentum indeed (namely 20 kg m/s per second). The huge mass/energy ratio causes quite a difference in momentum. Ken

**Follow-Ups**:**starship-design: Momentum***From:*Steve VanDevender <stevev@efn.org>

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