Forum:Runabout warp speed question

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In the DS9 Episode Battle Lines (episode), Opaka implores Sisko to investigate a signal they discover while taking her on a tour through the worm hole, and Kira says the signal is about 0.35 light years away -- yet the Runabout is due back at the station at "14:00 hours" suggesting (perhaps) that same day. They run into trouble at their destination that would naturally delay their return, but my thoughts were, can a Runabout (listed at max of warp 5, or 125x the speed of light) travel 0.35 light years and be back to DS9 in less than 24 hours? If not, what warp speed would the Runabout need to break in order to do so? Ablestmage (talk) 01:46, November 2, 2012 (UTC)

For a Runabout, warp 5 is, not $5^3 = 125c$ (TOS), but $5^{10/3} \approx 213.7c$ (DS9). The round trip of $.7 ly \approx 255.7$ light days would therefore require only a slightly faster speed of warp 5.28, or $5.28^{10/3} \approx 256.3c,$ to handle a 24-hour round trip, rather than warp 6.35 (TOS).--Glenn L (talk) 23:34, November 12, 2012 (UTC)