18 replies to this topic

[BobbyGo]

Spoiler for

If the fuel is used for guidance and anti-explosibility measures only, and not for propulsion; then all five spaceships could be flung from the moon towards Mars starting at the same time.  All the ships would be tethered in such a way that adjusting the course of one would alter the course of the fleet as a whole. For the first quarter of the trip, Spaceship #1 does all of the course correction.  For the second quarter, Spaceship #2; and so on until landing on Mars.  Once on Mars, Spaceship # 5 redistributes it's fuel equally between all of the spaceships to power their lasers and defeat the Martians.

[bushindo]

Dear Bushindo....you should notice that I have concidered the moon as our base station(!) and not the earth.So you should  think a little bit (laterally),and try to reduce the number to 5 ships only!...note : all of them will reach mars

 

So I guess the lateral solution of this puzzle is contingent upon the properties of this 'fuel'. My previous solution assumes that "the fuel spent is proportional to distance travelled". Since that doesn't seem to be the case, I'd like some clarification about the conditions of the puzzle.

1) My impression is that the fuel is used to make constant minor course corrections during the trip (per OP: "without fuel the spaceship will miss its direction") and to maintain the life-support and ship computer (per OP: "… and may explode"). Is this correct? If that is not correct, what is the fuel being used for?

2) Consider the following two scenarios
    * A single ship flies from base (x=0) to the one-fourth point (x=1/4)
    * A ship flies from the halfway point (x=1/2) to the three-fourth point (x=3/4)
    Does the ship use the same amount of fuel (1 tank) in both scenarios?

3) Are the ships supposed to land on the surface of Mars?

[wolfgang]

Yes...thats right...Thanks

Spoiler for

If the fuel is used for guidance and anti-explosibility measures only, and not for propulsion; then all five spaceships could be flung from the moon towards Mars starting at the same time.  All the ships would be tethered in such a way that adjusting the course of one would alter the course of the fleet as a whole. For the first quarter of the trip, Spaceship #1 does all of the course correction.  For the second quarter, Spaceship #2; and so on until landing on Mars.  Once on Mars, Spaceship # 5 redistributes it's fuel equally between all of the spaceships to power their lasers and defeat the Martians.

[bushindo]

Yes...thats right...Thanks

Spoiler for

If the fuel is used for guidance and anti-explosibility measures only, and not for propulsion; then all five spaceships could be flung from the moon towards Mars starting at the same time.  All the ships would be tethered in such a way that adjusting the course of one would alter the course of the fleet as a whole. For the first quarter of the trip, Spaceship #1 does all of the course correction.  For the second quarter, Spaceship #2; and so on until landing on Mars.  Once on Mars, Spaceship # 5 redistributes it's fuel equally between all of the spaceships to power their lasers and defeat the Martians.

 

 

Dear wolfgang, the solution that you consider correct suffers from two problems: 1) It violates common understanding of thermodynamics and 2) even if we allow such violation, it does not satisfy the conditions in your original post. Here is why

Spoiler for

From your original post, each ship needs to make constant trajectory corrections since "without fuel the spaceship will miss its direction". The solution that you accept states that 4 space-ships can "piggy-back" on the course correction ability of 1 ships. That is, the ships would be tethered in such a way that adjusting the course of 1 ship would alter the course of the whole.

Of course, a simple understanding of physics would indicate that we don't really save any fuel if we allow 1 ship to change the course for all 5. If a single ships needs to make a minor course correction, it would need to provide enough thrust (energy) to move its mass however much required. If a single ship is tethered to 4 other ships, Newton's equation (F=ma) implies that the navigating ship would need 5 times the energy to alter the current course. So, in reality, tethering 5 ships together would make the single navigating ship burn fuel 5 times as fast as it changes course.

That said, even if we allow such violation, how do you suppose to get the ships home. From your OP, "each spaceship has a fuel capacity to allow it to fly exactly 1/4 way  to Mars" and "Each spaceship must have enough fuel to return safe to the base space station". Even allowing for the thermodynamics violation, all your 5 ships would end up on Mars with 1 tank left, which is only good enough for 1/4 of the way back to the moon base.

While I understand that lateral and out-of-box thinking are valued around here, in general such solutions have to be internally consistent (and avoid violating explicit conditions set forth in the original post). Also, in this forum, we obey the law of thermodynamics.

[phaze]

Spoiler for Query

Do we need to account for the fact that both the moon and Mars are in motion? I.e If it is a new moon (moon between earth and sun) the trip to mars is further than if it is a full moon (moon between Earth and Mars)

[wolfgang]

I take it in such a way that 4 ships are connected to a 5th ship from 4 sides to give it the energy all the trip ,i.e. only the central ship will be functioning and the others adhering to it are as energy suppliers only.

 

Yes...thats right...Thanks

Spoiler for

If the fuel is used for guidance and anti-explosibility measures only, and not for propulsion; then all five spaceships could be flung from the moon towards Mars starting at the same time.  All the ships would be tethered in such a way that adjusting the course of one would alter the course of the fleet as a whole. For the first quarter of the trip, Spaceship #1 does all of the course correction.  For the second quarter, Spaceship #2; and so on until landing on Mars.  Once on Mars, Spaceship # 5 redistributes it's fuel equally between all of the spaceships to power their lasers and defeat the Martians.

 

 

Dear wolfgang, the solution that you consider correct suffers from two problems: 1) It violates common understanding of thermodynamics and 2) even if we allow such violation, it does not satisfy the conditions in your original post. Here is why

Spoiler for

From your original post, each ship needs to make constant trajectory corrections since "without fuel the spaceship will miss its direction". The solution that you accept states that 4 space-ships can "piggy-back" on the course correction ability of 1 ships. That is, the ships would be tethered in such a way that adjusting the course of 1 ship would alter the course of the whole.

Of course, a simple understanding of physics would indicate that we don't really save any fuel if we allow 1 ship to change the course for all 5. If a single ships needs to make a minor course correction, it would need to provide enough thrust (energy) to move its mass however much required. If a single ship is tethered to 4 other ships, Newton's equation (F=ma) implies that the navigating ship would need 5 times the energy to alter the current course. So, in reality, tethering 5 ships together would make the single navigating ship burn fuel 5 times as fast as it changes course.

That said, even if we allow such violation, how do you suppose to get the ships home. From your OP, "each spaceship has a fuel capacity to allow it to fly exactly 1/4 way  to Mars" and "Each spaceship must have enough fuel to return safe to the base space station". Even allowing for the thermodynamics violation, all your 5 ships would end up on Mars with 1 tank left, which is only good enough for 1/4 of the way back to the moon base.

While I understand that lateral and out-of-box thinking are valued around here, in general such solutions have to be internally consistent (and avoid violating explicit conditions set forth in the original post). Also, in this forum, we obey the law of thermodynamics.

[Morningstar]

I take it in such a way that 4 ships are connected to a 5th ship from 4 sides to give it the energy all the trip ,i.e. only the central ship will be functioning and the others adhering to it are as energy suppliers only.

 

 

Yes...thats right...Thanks

Spoiler for

If the fuel is used for guidance and anti-explosibility measures only, and not for propulsion; then all five spaceships could be flung from the moon towards Mars starting at the same time.  All the ships would be tethered in such a way that adjusting the course of one would alter the course of the fleet as a whole. For the first quarter of the trip, Spaceship #1 does all of the course correction.  For the second quarter, Spaceship #2; and so on until landing on Mars.  Once on Mars, Spaceship # 5 redistributes it's fuel equally between all of the spaceships to power their lasers and defeat the Martians.

 

 

Dear wolfgang, the solution that you consider correct suffers from two problems: 1) It violates common understanding of thermodynamics and 2) even if we allow such violation, it does not satisfy the conditions in your original post. Here is why

Spoiler for

From your original post, each ship needs to make constant trajectory corrections since "without fuel the spaceship will miss its direction". The solution that you accept states that 4 space-ships can "piggy-back" on the course correction ability of 1 ships. That is, the ships would be tethered in such a way that adjusting the course of 1 ship would alter the course of the whole.

Of course, a simple understanding of physics would indicate that we don't really save any fuel if we allow 1 ship to change the course for all 5. If a single ships needs to make a minor course correction, it would need to provide enough thrust (energy) to move its mass however much required. If a single ship is tethered to 4 other ships, Newton's equation (F=ma) implies that the navigating ship would need 5 times the energy to alter the current course. So, in reality, tethering 5 ships together would make the single navigating ship burn fuel 5 times as fast as it changes course.

That said, even if we allow such violation, how do you suppose to get the ships home. From your OP, "each spaceship has a fuel capacity to allow it to fly exactly 1/4 way  to Mars" and "Each spaceship must have enough fuel to return safe to the base space station". Even allowing for the thermodynamics violation, all your 5 ships would end up on Mars with 1 tank left, which is only good enough for 1/4 of the way back to the moon base.

While I understand that lateral and out-of-box thinking are valued around here, in general such solutions have to be internally consistent (and avoid violating explicit conditions set forth in the original post). Also, in this forum, we obey the law of thermodynamics.

I don't see how that helps. Since the controlling ship still needs 5x the amount of fuel to go the same distance, it would only get 1/8 of the way before having to turn back.

[bushindo]

I take it in such a way that 4 ships are connected to a 5th ship from 4 sides to give it the energy all the trip ,i.e. only the central ship will be functioning and the others adhering to it are as energy suppliers only.

 

 

 

Your proposal (tethering 4 ships to the 5th) is akin to increasing the mass of the 5th ship by five times while also increasing the fuel tank five times. Your solution assumes that fuel usage  for the navigating ship is the same whether it is alone or whether it has 5 times the mass. In physics, as in life, there is no such thing as a free lunch. You can't carry 5 times the mass to Mars without expending extra energy.

 

Perhaps you are thinking that the navigating ship only has to set a course for the entire fleet, so the energy usage is independent of the mass. Recall that in space, if you need to change the course, you will need to change the momentum vector of the entire fleet. That means if you want to move 1 degree to the left, for example, the navigating ship will need to provide enough thrust (energy) to move its entire mass to the left that much. 

 

Even if we allow the conservation-of-energy violation, the 5 ships still can not make it to Mars and back. From your OP, "each spaceship has a fuel capacity to allow it to fly exactly 1/4 way  to Mars" and "Each spaceship must have enough fuel to return safe to the base space station". Since each tank will take you 1/4 of the way to Mars, 5 tanks are enough for 1.25 of the distance to Mars. How are your 5 ships supposed to get to Mars and get home on 5 tanks?

[Prime]

I take it in such a way that 4 ships are connected to a 5th ship from 4 sides to give it the energy all the trip ,i.e. only the central ship will be functioning and the others adhering to it are as energy suppliers only.

 

 

 

Your proposal (tethering 4 ships to the 5th) is akin to increasing the mass of the 5th ship by five times while also increasing the fuel tank five times. Your solution assumes that fuel usage  for the navigating ship is the same whether it is alone or whether it has 5 times the mass. In physics, as in life, there is no such thing as a free lunch. You can't carry 5 times the mass to Mars without expending extra energy.

 

Perhaps you are thinking that the navigating ship only has to set a course for the entire fleet, so the energy usage is independent of the mass. Recall that in space, if you need to change the course, you will need to change the momentum vector of the entire fleet. That means if you want to move 1 degree to the left, for example, the navigating ship will need to provide enough thrust (energy) to move its entire mass to the left that much. 

 

Even if we allow the conservation-of-energy violation, the 5 ships still can not make it to Mars and back. From your OP, "each spaceship has a fuel capacity to allow it to fly exactly 1/4 way  to Mars" and "Each spaceship must have enough fuel to return safe to the base space station". Since each tank will take you 1/4 of the way to Mars, 5 tanks are enough for 1.25 of the distance to Mars. How are your 5 ships supposed to get to Mars and get home on 5 tanks?

 

The fuel feeds a small generator on board producing enough electricity to send a signal to Mars' Sub-Ether Tractor Beam station. The signal relays precise position, velocity, and mass of the ships. The Tractor Beam on Mars supplies all required energy and does all the work in pulling and guiding the ships towards their destination.

Once arrived, the ships must bomb the Tractor Beam station, because such is their mission.

You might ask, why Marsians are playing along. Because they know the ship has enough fuel only for a fraction of the distance to send the signal. It's simple.

Edited by Prime, 16 March 2013 - 12:48 AM.