I watch kids shows, too many, I fully admit it.
On the show Phineas and Ferb, there is an episode, "Escape from Phineas Tower" (Episode 315a) where the titular characters create a machine that within less than a day is able to enclose the entire galaxy. This opens up an interesting question, how powerful of a civilization are Phineas and Ferb according to the Kardashev scale? (I don't know who asks these questions really, but it is a good chance to do some math) A quick explanation of the Kardashev scale, it serves as a means of scientists to roughly gauge how advanced a civilization is according to how much energy they can manipulate. The scale is named after a soviet astronomer by the name of Nikolai Kardashev. According to the current scale there are 3 types, a Type 1 can manipulate the total energy of a planet roughly the size of planet Earth (10^16 to 10^17 watts), a Type 2 civilization the power output of a local star (4*10^26 watts), and finally Type 3 where the civilization can capture the power output of their entire galaxy (4*10^37 watts), basically a boat load of power.
These values get us to a starting point of how to calculate how powerful Phineas and Ferb are, we know how much energy a given civilization type produces, and we know Phineas and Ferb's creation creates a barrier that encompasses the galaxy. What we don't know exactly how quickly the barrier encompasses the galaxy and how thick the barrier is. Both of these values are incredibly significant to our calculations, the thicker the more total energy required, the faster the more power production.
For me the first thing I want to calculate is the overall surface area of the barrier, for sake of convenience I am assuming a completely smooth surface and that the barrier is spherical, this makes the calculations a tad easier. Much like the edge of the atmosphere the edge of our galaxy is not an instant transition from something to nothing, the density of stars tapers off, for convenience I will say this edge is at 50,000 lightyears from the center of the galaxy.
For the kind of math I would like to do, it is necessary to convert from light years to meters.
Now that we know how many meters are in a single light year, we can multiply by 50,000 to get the number of meters for the radius of the galaxy.
From the above calculations we find our answer spells out to four hundred seventy three quintillion meters (4.73037E+20 m). Honestly I am having a hard time properly coming up with a reference for how big that number is.
We now know our radius, with that knowledge calculating the surface area of our sphere is a pretty easy equation from high-school geometry, seen below.
The initial estimation will assume that the barrier is a massive sheet of graphene, The choice of graphene is relatively arbitrary, but has the advantage of being a known material with an estimated surface area for a given mass (specific area), 2630 square meters per gram. It is a relatively easy process of dividing the area of the sphere by the specific area to get the mass of the barrier.*
After this plug and chug we find that the graphene barrier has a mass of 1.069E+39 grams, to put that in perspective the Earth, has a mass of "only" 5.972E+27 grams.
Great, we know a lot of numbers, but how do we calculate the Kardashev civilization class of Phineas and Ferb. We use one of the most famous equations in physics e=mc^2, using this equation we can calculate how much energy it would take to create the mass of the barrier**
The final answer is getting tantalizingly close, we now know the energy required to produce the mass of the barrier is 9.61E+55 Joules, a boat load of energy. All that is left is to estimate the wattage of the system and from there we can guesstimate what Kardeshev civilizaiton class we have going on. Calculating wattage is generally relatively straightforward, you divide the number of joules by the number of seconds it takes to release that energy. First I will calculate how long it would take a Type 3 civilization to build this barrier. This simply requires we divide the energy of the barrier by the power output of a Type 3 civilization
(9.61E+55 J)/(4E+37 W)=2.4E+18 seconds
That is the equivalent of 76 billion years, that means a civilization capable of capturing all of the energy of their galaxy would take over6 5*** times longer than the universe has been in existence, to create that barrier.
On the show this takes less than a minute, but making life easier, it will be assumed that the barrier was built in 100 seconds.
(9.61E+55 J)/(100 s) = 9.61E+53 Watts according to the wikipedia entry on the Kardashev scale, the entire visible universe only has around 10^45 Watts of power available, this would lead us to assume that Phineas and Ferb are the avatars of godlike beings whose rule encompasses a range of universes.
*For the general case we would arbitrarily designate a thickness for the barrier and the material the barrier is comprised of. So long as the assumed thickness of the barrier is less than 500 light years there is no real need to do a complicated volume calculation, as the second radius is less than 1% greater than the original radius. If you are so inclined to make your calculations overly accurate or make the barrier incredibly thick, calculate the volume of the larger sphere, and subtract the volume of a 50,000 light year sphere. With the barrier's volume calculated, divide the volume of the barrier by a selected material's density. Now you can rejoin the math above.
** I am making the assumption that all of the barriers mass was created through some kind of matter synthesizer, this is because the episode doesn't show the barrier requiring any mass feed-stocks, that and it makes my life easier. If some one wants to go crazier on details, please feel free. Also I acknowledge this calculation ignores the chemical energy of the bonds in the graphene, if memory serves that additional potential energy should be negligible to the system's overall value, please correct me if I am wrong.
*** edited 12/14/2015 I forgot that the universe is currently estimated to be 13.82 billion years old, for some reason I was thinking 12 billion years, amateur hour malarkey I know
On the show Phineas and Ferb, there is an episode, "Escape from Phineas Tower" (Episode 315a) where the titular characters create a machine that within less than a day is able to enclose the entire galaxy. This opens up an interesting question, how powerful of a civilization are Phineas and Ferb according to the Kardashev scale? (I don't know who asks these questions really, but it is a good chance to do some math) A quick explanation of the Kardashev scale, it serves as a means of scientists to roughly gauge how advanced a civilization is according to how much energy they can manipulate. The scale is named after a soviet astronomer by the name of Nikolai Kardashev. According to the current scale there are 3 types, a Type 1 can manipulate the total energy of a planet roughly the size of planet Earth (10^16 to 10^17 watts), a Type 2 civilization the power output of a local star (4*10^26 watts), and finally Type 3 where the civilization can capture the power output of their entire galaxy (4*10^37 watts), basically a boat load of power.
These values get us to a starting point of how to calculate how powerful Phineas and Ferb are, we know how much energy a given civilization type produces, and we know Phineas and Ferb's creation creates a barrier that encompasses the galaxy. What we don't know exactly how quickly the barrier encompasses the galaxy and how thick the barrier is. Both of these values are incredibly significant to our calculations, the thicker the more total energy required, the faster the more power production.
For me the first thing I want to calculate is the overall surface area of the barrier, for sake of convenience I am assuming a completely smooth surface and that the barrier is spherical, this makes the calculations a tad easier. Much like the edge of the atmosphere the edge of our galaxy is not an instant transition from something to nothing, the density of stars tapers off, for convenience I will say this edge is at 50,000 lightyears from the center of the galaxy.For the kind of math I would like to do, it is necessary to convert from light years to meters.
Now that we know how many meters are in a single light year, we can multiply by 50,000 to get the number of meters for the radius of the galaxy.
From the above calculations we find our answer spells out to four hundred seventy three quintillion meters (4.73037E+20 m). Honestly I am having a hard time properly coming up with a reference for how big that number is.
We now know our radius, with that knowledge calculating the surface area of our sphere is a pretty easy equation from high-school geometry, seen below.
The initial estimation will assume that the barrier is a massive sheet of graphene, The choice of graphene is relatively arbitrary, but has the advantage of being a known material with an estimated surface area for a given mass (specific area), 2630 square meters per gram. It is a relatively easy process of dividing the area of the sphere by the specific area to get the mass of the barrier.*
After this plug and chug we find that the graphene barrier has a mass of 1.069E+39 grams, to put that in perspective the Earth, has a mass of "only" 5.972E+27 grams.
Great, we know a lot of numbers, but how do we calculate the Kardashev civilization class of Phineas and Ferb. We use one of the most famous equations in physics e=mc^2, using this equation we can calculate how much energy it would take to create the mass of the barrier**
The final answer is getting tantalizingly close, we now know the energy required to produce the mass of the barrier is 9.61E+55 Joules, a boat load of energy. All that is left is to estimate the wattage of the system and from there we can guesstimate what Kardeshev civilizaiton class we have going on. Calculating wattage is generally relatively straightforward, you divide the number of joules by the number of seconds it takes to release that energy. First I will calculate how long it would take a Type 3 civilization to build this barrier. This simply requires we divide the energy of the barrier by the power output of a Type 3 civilization
(9.61E+55 J)/(4E+37 W)=2.4E+18 seconds
That is the equivalent of 76 billion years, that means a civilization capable of capturing all of the energy of their galaxy would take over
On the show this takes less than a minute, but making life easier, it will be assumed that the barrier was built in 100 seconds.
(9.61E+55 J)/(100 s) = 9.61E+53 Watts according to the wikipedia entry on the Kardashev scale, the entire visible universe only has around 10^45 Watts of power available, this would lead us to assume that Phineas and Ferb are the avatars of godlike beings whose rule encompasses a range of universes.
** I am making the assumption that all of the barriers mass was created through some kind of matter synthesizer, this is because the episode doesn't show the barrier requiring any mass feed-stocks, that and it makes my life easier. If some one wants to go crazier on details, please feel free. Also I acknowledge this calculation ignores the chemical energy of the bonds in the graphene, if memory serves that additional potential energy should be negligible to the system's overall value, please correct me if I am wrong.
*** edited 12/14/2015 I forgot that the universe is currently estimated to be 13.82 billion years old, for some reason I was thinking 12 billion years, amateur hour malarkey I know
I have a question . Why did you assume that the radius of the galaxy is 50000 ly ? Can you explain me that please ? I didn't understand this point .
ReplyDeleteThank you .