Power generation

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(Star Trek Power Generation)
(Star Trek Power Generation: formatted as an article rather than a discussion)
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At the other extreme, [[Data|Commander Data]] once said the ship's reactor was generating "12.75 billion gigawatts per (second)"<ref>TNG "True Q"</ref>.  This is a nonsensical statement, since watts per second is not a unit of power.  The word "second" was actually cut off by an alarm in the episode, but it does appear in the script, so we have a reasonable idea of what Data's next word would have been.  To add to the inaccuracy, Data was responding to a statement about the amount of ''energy'' in the warp core, which should be in either joules or watts ''multiplied by time'', not watts divided by anything.
 
At the other extreme, [[Data|Commander Data]] once said the ship's reactor was generating "12.75 billion gigawatts per (second)"<ref>TNG "True Q"</ref>.  This is a nonsensical statement, since watts per second is not a unit of power.  The word "second" was actually cut off by an alarm in the episode, but it does appear in the script, so we have a reasonable idea of what Data's next word would have been.  To add to the inaccuracy, Data was responding to a statement about the amount of ''energy'' in the warp core, which should be in either joules or watts ''multiplied by time'', not watts divided by anything.
  
Despite the officers' statements, a plan to use the ship to stabilize the orbit of a small moon suggests considerably more than one terawatt of power generation, but far less than 12.75 million terawatts.  Although it was never successfully completed (and the need to do so was eventually removed by [[Q]]), the proposed plan would require approximately 21,000 TW<ref>TNG "Deja Q" -- changing the velocity of a 6E13 kg mass by 4 km/s within 7 hours</ref> of power to work.  Attempting to move this moon pushed the ''Enterprise'' to its limits, but it would have been a trivial task if the ship could have applied even a small fraction of 12.75 billion gigawatts to the task.
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Despite the officers' statements, a plan to use the ship to stabilize the orbit of a small moon suggests considerably more than one terawatt of power generation, but far less than 12.75 million terawatts.  Although it was never successfully completed (and the need to do so was eventually removed by [[Q]]), the proposed plan -- which would change the velocity of a 6E13 kg mass by 4 km/s within 7 hours<ref>TNG "Deja Q"</ref> -- would require approximately 21,000 TW of power to work.  Attempting to move this moon pushed the ''Enterprise'' to its limits, but it would have been a trivial task if the ship could have applied even a small fraction of 12.75 billion gigawatts to the task.
  
That would be true, if the Bre'el IV moon was only 2.5 kilometers wide and massed out at 6E13 kg. However alternative scalings, using screen shots of the E-D in very close proximity to the asteroidal moon, shows it to be considerably larger. Also the moon had noticeable effects on it's primary Bre'el IV, raising the tides up to 10 meters while at orbital perigee.  
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===Trekkie Counter=-arguments Regarding "Deja Q"===
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Trekkies argue that the Bre'el moon in "Deja Q" was much more massive than 6E13 kg, based on screen shots of the [[Enterprise-D]] in very close proximity to the asteroidal moon. The also attempt to estimate the mass of the moon from tidal effects on the planet Bre'el IV.  
  
Tidal force is the difference in gravitational force between the edges and center of mass of an object, so we're trying to match the difference Gm/R^2-Gm/(R+/-r)^2.  
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According to the tidal argument, tidal force is the difference in gravitational force between the edges and center of mass of an large mass, which can be found using the formula Gm/R^2-Gm/(R+/-r)^2.  
  
Thus the E16 kg range (~4E16 kg) on a first-order estimate, which is more reasonable, bearing in mind for assumptions and typical variables with 10^(16.5+/-1.5) kg based on the tidal effects alone for a lower-end estimate. This would place the Bre'el moon in the same mass and size catagory as Mars' asteroidal moons Phobos and Deimos (20-30 km).  
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Using this argument, they generate a mass for the moon in the E16 kg range (~4E16 kg) as a first-order estimate, bearing in mind for assumptions and typical variables with 10^(16.5+/-1.5) kg based on the tidal effects alone for a lower-end estimate. This would place the Bre'el moon in the same mass and size catagory as Mars' asteroidal moons Phobos and Deimos (20-30 km).  
 
   
 
   
To make a moon weighing 1E16 KG move by 92 m/sec requires 4.23E19 J. Since took ten seconds during the first attempt to apply that delta-V, approximately 4.2E18 watts. Comparable to, though substantially lower than Data's 12.75 billion gigawatt quote from "True Q".
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To make a moon weighing 1E16 KG move by 92 m/sec requires 4.23E19 J. Since it took ten seconds during the first attempt to apply that delta-V, approximately 4.2E18 watts. Comparable to, though substantially lower than Data's 12.75 billion gigawatt quote from "True Q".
  
 
==References==
 
==References==

Revision as of 13:41, 8 March 2009

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