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Time and Space

Michael Morris
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Joined: Jan 30, 2002
Posts: 3451
Commander Gorlock of the Interstellar Engineers Group has been assigned the task to deliver an explosive device to a small planet some 0.13 parsecs from the space station that he is located on. The planet is experiencing severe tektonic events that threaten its existance. Scientists have estimated that the planet may not be salvageable in only 187 sidereal days. The purpose of the explosive device is to realign the two tektonic plates that are causing the problem. Once the explosive device arrives, a minimum of 2 sidereal days will be required to set the charge and realign the plates. The only material that can produce the explosive power necessary is extremely volatile. It must be assembled by experts and thus may not be assembled in flight. The volatility of the bomb's components causes the bomb to be ineffective 77 sidereal days after assembly. Considering these parameters what is the minimum velocity that Commander Gorlock must maintain to reach the planet in time to save it?
You may use these constants:
Parsec - 3.086E16 meters
C (velocity of light) - 3.0E8 meters/second
Sidereal Day - 86164 seconds
Your velocity may be stated as a percentage of the velocity of light and need not be more than three digits of accuracy for example: V = .578C or 57.8% C.
No warp speeds. 100% light speed is impossible, any value below that is acceptable.


Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius - and a lot of courage - to move in the opposite direction. - Ernst F. Schumacher
Anupam Sinha
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Joined: Apr 13, 2003
Posts: 1088
Very high speed.
Anupam Sinha
Ranch Hand

Joined: Apr 13, 2003
Posts: 1088
On a more serious note aren't they late.
Michael Morris
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Joined: Jan 30, 2002
Posts: 3451
Originally posted by Anupam Sinha:
Very high speed.

DUH! Care to take a shot at it Anupam?
Michael Morris
Ranch Hand

Joined: Jan 30, 2002
Posts: 3451
Originally posted by Anupam Sinha:
On a more serious note aren't they late.

Not sure what you mean here. Are you suggesting that within the constraints of velocity, that our good Commander can't get there in time?
Anupam Sinha
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Joined: Apr 13, 2003
Posts: 1088
Sorry for the previous post. Didn't really get the question. I think that I still don't understand the question really but anyways my answer is 0.843C. I hope this is correct but think that this would be wrong.
Michael Morris
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Joined: Jan 30, 2002
Posts: 3451
Originally posted by Anupam Sinha:
Sorry for the previous post. Didn't really get the question. I think that I still don't understand the question really but anyways my answer is 0.843C. I hope this is correct but think that this would be wrong.

Well, that's not the answer I got. So could you explain how you came up with that?
Joel McNary
Bartender

Joined: Aug 20, 2001
Posts: 1817

I got V = .838C Here's my figures:
187 Days till planet dissolves
2 days to prepare the device once it arrives
---
185 days travel time. (We can ignore the 77 days 'till the bomb is ineffective because we hope that the bomb is not ineffective).
185 days travel time * 86164 seconds = 15940340 seconds travel time
.13 parsecs = 4.0079 * 10^15 metres
Commander Gorlock must travel 4.0079 * 10^15 meters in 15940340 seconds, or he must travel at 251,431,274 meters/second.
C = 300, 000, 000
251,431,274 / 300,000,000 = .838104246667
So, Commander Gorlock arrives on site only to discover the planet is gone. He only took 185 days to travel, but (due to relativity), he took much longer than that to the outsiders. Or were you discounting relativity?


Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.
Anupam Sinha
Ranch Hand

Joined: Apr 13, 2003
Posts: 1088
I wasn't counting the 187th day. So I had :
distance=.13*3.086E16
time=184*86164
speed = distance/time
speed/3.0E8 = 0.843
[ July 01, 2003: Message edited by: Anupam Sinha ]
Michael Morris
Ranch Hand

Joined: Jan 30, 2002
Posts: 3451
Originally posted by Anupam Sinha:
I wasn't counting the 187th day. So I had :
distance=.13*3.086E16
time=184*86164
speed = distance/time
speed/3.0E8 = 0.843
[ July 01, 2003: Message edited by: Anupam Sinha ]

What about the volatility problem with the bomb?
Anupam Sinha
Ranch Hand

Joined: Apr 13, 2003
Posts: 1088
What about the volatility problem with the bomb?

The bomb will be ineffective only after 77 days. So the captain has 184 or 185 days to reach and set up the bomb then leave. I guess that the volatility problem will not come into play as the bomb is being left for less than 77 days.
Michael Morris
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Joined: Jan 30, 2002
Posts: 3451
So, Commander Gorlock arrives on site only to discover the planet is gone. He only took 185 days to travel, but (due to relativity), he took much longer than that to the outsiders. Or were you discounting relativity?
Maybe I'm seeing it wrong? Relativity does count. I arrived at a solution. Let's let some others weigh in and see if I'm full of bovine excrement.
Jim Yingst
Wanderer
Sheriff

Joined: Jan 30, 2000
Posts: 18671
What about the volatility problem with the bomb?
What about it?
The volatility of the bomb's components causes the bomb to be ineffective 77 sidereal days after assembly.
If Gorlock doesn't start assembling the bomb until day 185, it doesn't really matter if the thing becomes inert 77 days later (or 79?) does it? It's done its job long before that.
Were you perhaps suggesting that the bomb components will become inert prior to assembly, if more than 77 days have elapsed since they were taken from whatever safe storage they were in on Earth?
[ July 01, 2003: Message edited by: Jim Yingst ]

"I'm not back." - Bill Harding, Twister
Michael Morris
Ranch Hand

Joined: Jan 30, 2002
Posts: 3451
If Gorlock doesn't start assembling the bomb until day 185, it doesn't really matter if the thing becomes inert 77 days later (or 79?) does it? It's done its job long before that.
I must not have been clear on that point. The bomb is assembled by experts on the space station before Gorlock takes off. The constraints are he must make the journey to the planet within 185 days of the planets time frame and within 75 days of his time frame.
Jim Yingst
Wanderer
Sheriff

Joined: Jan 30, 2000
Posts: 18671
All right then, to make the trip in a subjective time of 75 days, a speed of .900 c is necessary. Round up a bit since a safety margin would be a good thing here, really. And it should be fun trying to accelerate to that speed in the first place (and decelerate later of course). I sure hope the ship has some of Star Trek's "inertial dampeners" (if not the warp drive) or the crew may end up as jello by the end of the trip.
Jim Yingst
Wanderer
Sheriff

Joined: Jan 30, 2000
Posts: 18671
[Joel]: So, Commander Gorlock arrives on site only to discover the planet is gone. He only took 185 days to travel, but (due to relativity), he took much longer than that to the outsiders. Or were you discounting relativity?
Relativity does indeed turn out to be important, but it's the other way around. The trip looks like it takes 185 days according to outside observers (the same guys who measure the distance to the planet as .13 parsecs) however the proper time on the ship is less. Proper time means the time as measured in a frame of reference that moves with the ship. In that frame, the ship isn't moving; everything else is. And the proper time tp is given by:
tp = t * sqrt( 1 - (v/c)^2 )
Using your values of t = 185 days and v = .8381 c we have
tp = 100.9 days
which means that unfortunately the bomb has gone inert. The means that a solution which meets the 185-day deadline is too slow - instead, forget that time and speed, and figure out how fast you need to go to get an elapsed proper time for the bomb of 75 days.
Michael Morris
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Joined: Jan 30, 2002
Posts: 3451
Originally posted by Jim Yingst:
All right then, to make the trip in a subjective time of 75 days, a speed of .900 c is necessary. Round up a bit since a safety margin would be a good thing here, really. And it should be fun trying to accelerate to that speed in the first place (and decelerate later of course). I sure hope the ship has some of Star Trek's "inertial dampeners" (if not the warp drive) or the crew may end up as jello by the end of the trip.

Yup, I actually got .9004 c. Inertial dampers would be a plus, without 'em how do you drink your coffee on the commute?
Jim Yingst
Wanderer
Sheriff

Joined: Jan 30, 2000
Posts: 18671
Yup, I actually got .9004 c
Me too, but you said 3 digits were acceptable. And the value of c you gave was only good for 2 digits anyway.
 
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