To preface this:
You may notice I have 1 post. That post is this post. I have no history with this site, and freshly joined. I was called in by a good friend of mine who frequents this site and loves Flight Rising. She was quick to show me the exploits of such members as @
catgame21234, @
violalore, and @
Recko, just to name a (very small) fraction of the brilliant minds on this site. She encouraged me to join Lightning, said I'd love it. This site is great and the aspects of it are well designed, however I'm nothing more than a newbie and I feel it rude to try and develop some kind of assessment without the usual two to three month "introductory period" you usually find on forumboards. When the question was given, however, I simply couldn't help myself. I had to do the work. It was my mission to do the math.
With that, I offer some generic number crunching as Lightning Flight's intern lab tech.
An Assessment of Energy Exertion from Earthshaker in Relation to Sorneith
As Defined by a Flight of Scientists
In order to properly assess the energy exerted upon the planet of Sorneith, we'll need to break down physical properties of Sorneith to determine exactly how much energy might be required to change properties at a planetary scale. We'll also need to define exactly what properties are being changed, and in what manner. With that said, let us define the properties being changed.
catgame21234 wrote on 2017-08-14:
...how strong would you guys think eartshaker needed to be to tilt the planet?
how about make the planet stop moving?
what needs to be done in order for this to happen with raw power alone?...
Question A relates directly to the first stated question: how much energy (derived from "power", above) will it require to tilt the planet? We'll still need to determine exactly what that means, however, as there is no direct reference to obliquity and we'll need to establish what a "regular" tilt is in order to effectively determine an "irregular" tilt. After defining an irregular tilt, this is a simple difference between regular and irregular tilts (with oscillations of obliquity, this requires us to use mean obliquity). After determining the difference in tilts by degree, we have to assess the amount of energy required to turn a planet by this many degrees.
Because obliquity relates directly to the rotational axis (and, in turn, its relationship to the orbital axis), we will measure this as an amount energy required to move the rotational axis of Sorneith by X degrees.
Question B relates directly to the second stated question: how much energy (again, derived from "power", above) will it require to stop the planet from moving. This is requires an assessment of the angular momentum of Sorneith and the energy in order to stop the planet's movement (the "brick wall" approach).
Let's start with Question A.
We have some information already concerning the nature of Sorneith in a planetary sense.
Erra as quantified by catgame21234 wrote on 2017-07-03:
Sornieth Volume: 3.656*10^21 m^3
Sornieth Mass: 2.01*10^25 kg
Sornieth Density: 5.498*10^3 kg/m^3
Sornieth Radius: 9,556,500 m
Link to thread and page.
There are also moons that may affect the obliquity of the planet, but we have little to no understanding of these moons, both in a canon sense and in a community derivation sense. The Arcanist's decision to hide information concerning orbiting bodies around Sorneith, while unfortunate, thankfully has a minimal impact on calculations. It's expected that these moons may have a stabilizing effect on the planet, but this remains to be seen.
With that in mind, let's define obliquity for Sorneith
as we currently understand it (see, above).
Milankovitch cycles (described here by
Indiana University Bloomington or
Wikipedia) theorize that changes in the Earth's planetary movements will have an effect on climate (or rather, climatic patterns over long periods of time).
It's notable that this theory describes effects that changes in obliquity might have. A change in axial tilt will change the distribution of solar radiation on the planet's surface, which is
hypothesized, not proven to have an effect on climate. We might see more closely equalized temperatures across the planet at a lessened tilt (as the effects of radiation are distributed equally throughout an orbital period), whereas we might infer that temperatures are more extreme at an increased tilt, but the physical consequences of this are not within my knowledge to be determined.
It's important that we establish this, as we are forced to determine obliquity in both regular and irregular cases. The regular case might see us arbitrarily assign Earth's obliquity to Sorneith, as we've established that the planets are very similar and it wouldn't be much of a stretch to say that life can develop under these circumstances.
There's no source that I could easily find (emphasis: easily), but according to R. Nave assessing a point by Ward and Brownlee on
this HyperPhysics page, the development of advanced life might well include axial tilt. The energy absorbed by the poles due to their position appears to have a profound impact on the climate. It appears as though while the overall energy radiating to the planet may not change, the extremes in its distribution may have climatic changes that in turn have profound consequences on the development of advanced life.
Let's now assess based on what we know.
Regular Tilt refers to the obliquity of Sorneith prior to Earthshaker's impact as measured in degrees. It is represented as ?.
Irregular Tilt refers to the obliquity of Sorneith after Earthshaker's impact as measured in degrees. It is represented as ?.
Regular Tilt is approximately equal to the axial tilt of the Earth. As we want a clean number, we'll use the mean obliquity. Earth's mean obliquity is 23.44° (in opposition to its true obliquity: 23.26°). We'll assume that
? = 23.44°. (All information derived from the
Earth Fact Sheet,
this astronoo page, and
the Wikipedia page for Axial Tilt)
Irregular Tilt is not synonymous with Regular Tilt, we can confidently say that the two are different as according to the
lore.
? ≠ ?. It's not immediately obvious exactly how drastically changes in obliquity and climate can affect the planet, however we can work based on some assumptions. Assumption 1: there is weather on Sorneith, defined as changes in the state of atmosphere. I haven't found anything to back this up directly, so we'll have to simply assume that there are atmospheric changes that are induced by the forces of nature acting upon a planetary body, rather than the deities acting on the planet. Assumption 2: an increase in axial tilt will result in more extreme atmospheric changes, especially after 54° (in which the poles receive more energy than the equator). Assumption 3: it is harder for advanced life to exist in the presence of temperature extremes and/or atmospheric extremes (natural distasters). Advanced life developed on the planet of Sorneith while at Regular Tilt, which allows us to draw similarities with Earth. Advanced life continues to exist on the planet at Irregular Tilt, with creatures like salamanders and rabbits existing in seemingly stable ecosystems.
Again, we have to refer to Assumption 3 in that extreme atmospheric changes will damage ecosystems and render them unstable.
Our decisions here are arbitrary. There's no real way to determine how extreme Sorneith is in its weather patterns, even when compared to Earth. There's no lore I can find that definitely tells us whether Sorneith was more extreme at Regular Tilt or Irregular Tilt (thereby preventing us from making a claim by inequality). That said, there is speculation that Sorneith might be massive tropical planet, which might have the extremes we may need to differentiate the weather enough. This has been downplayed, however.
catgame21234 wrote on 2017-07-03:
Conclusion?: Sornieth can most deffently be a water world without the supercontinent being flooded by huricains and tropical storms that generate on a tropical planet.
Link to quote.
Seeing as @
catgame21234 is a reverent, brilliant figure, I have absolutely no intention to dispute what they've concluded.
Which, thankfully, allows us to make a conclusion of our own!
We'll assume that the extremes in weather have been
reduced. Again, there is no real point where we can determine an effective "stopping point" for degrees, so we will arbitrarily assume that mean obliquity is changed by an easy 10 degrees (easy for me, anyway, as it makes the calculations nicer).
So:
? = 23.44°
? = 13.44°
Now that we have both the Regular Tilt and Irregular Tilt, we can push forward and determine the amount of energy required to change this.
This is
angular momentum. Yeah, I know. It's not very nice to look at.
This is
Viktor Toth's computation of a change in angular momentum for rotating the Earth's rotational axis by 90 degrees. He did everything we were essentially asking, and he's saved me a ton of work. Thanks, my guy!
Now we just plug numbers in.
It was determined that Sorneith's orbital period was 365 days.
catgame21234 wrote on 2017-07-03:
Sornieth's specs (known to me)
- Gravitational force: ???
- Mass: ??? Will assume that Sornieth is made the same way earth is.
- Radius: 5,939 mi
- Diameter: 11878 mi
- Density: ??? Will assume that Sornieth is made the same way earth is.
- Orbital period: 365 days
- Moon(s): 1 or 2 "(Sornieth) does boast one to two modestly-sized moons" I shall asume two earth sized moons
I'm sure you can probably guess what thread this came from.
We'll assume Sorneith has the same distance from its star as Earth does. We can make this assumption because it's assumed that Sorneith gets the same overall energy from the sun that the Earth does. (Even if it didn't, the very presence of complex life would put us in a very close possible area. Also, I'm aware that I'm
also assuming that the size and class of Sorneith's star is the same as the Sun. Please forgive me.)
Our angular velocity is the same, at 2π/86400 s^−1. The mass of the planet is 2.01*10^25 kg. The radius of the planet is 9,556,500 m.
To quote Viktor, our new best friend,
"The amount of change is the vector difference between the two".
Let's calculate the vector difference.
23.44° - 13.44° = 10°
We know from Viktor that the vector difference of two perpendicular vectors of equal magnitude is sqrt(2). We have a formula available
here.
We have vectors of equal magnitude at an angle of 10 degrees. Magnitude equals 1.
A for x = A*cos(10 deg) = 1*0.9848 = 0.9848
B for x = B*cos(0 deg) = 1*1 = 1
A for y = A*sin(10 deg) = 1*0.1736 = 0.1736
B for y = B*cos(0 deg) = 1*0 = 0
R for x = 0.9848-1 = -0.0152
R for y = 0.1736-0 = 0.1736
R = sqrt((-0.0152)^2 + (0.1736)^2) = sqrt(0.303) = 0.1740
So now we can multiply.
L = 2/5ωM(r^2)
L = 2/5(2π/86400 s^−1)(2.01*10^25 kg)(9,556,500 m)^2 = 398,609,264,023,836,619,651,466,903,004,483,927,359,427,579 m^2(kg)/s
L*0.1740 = 69,358,011,940,147,571,819,355,241,122,780,203,360,540,398 m^2(kg)/s
(I don't really understand what the 2/5 is, but I assume that it is the time derivative. That said, I'm relying on Viktor's easy method to save me time. If I've messed this up,
please correct me. I have no intention of willfully doing the wrong thing, simply lacking the effective knowledge here.)
Now to convert that into energy...
E = 1/2(2/5)(M)(r^2)(ω^2) = 0.2(M)(r^2)(ω^2)
E = 0.2(2.01*10^25 kg)((9,556,500 m)^2)((2π/86400 s^−1)^2) = 1,941,583,323,444,725,408,155,100,150,671 J
That's 1.94*10^30 joules of energy. Viktor converted into megatons, so why don't we?
4.63*10^16 Mt
Well now we have our answer for Question A.
Earthshaker, with his front leg, potentially delivered 46 quadrillion Megatons of force onto Sorneith, changing the axis of rotation for the planet.
The
Chicxulub crater is one of the largest impact strutures on the planet Earth. There are larger ones, but there are impact specifics, which makes this one interesting. The energy of the impact is thought to be 2.10*10^17 joules of energy. At 1.94*10^30 joules, we can assume that somewhere on Sorneith (likely buried deep beneath the oceans) is a massive impact structure and crater multiple hundreds of kilometers in diameter.
Now, Question B.
We'll have the planet hit a brick wall in space, coming to a stop in 1 meter.
Converting angular momentum to linear momentum (described in relation
here) requires much simpler math than that above.
v = Rω
v = distance of Sorneith to its star * 2π/86400 s^−1
Again, we can assume Sorneith is an equal distance to its star that Earth is to the Sun. Again^2, we're also assuming the star Sorneith orbits is near-identical to the Sun, for the purpose of simplicity.
R ≅ 149,597,870,700 m
v = 149,597,870,700 m*2π/86400 s^−1 = 10,879,064 m/s
Our linear momentum has been calculated. We can use a kinematic equation to figure out how to stop it.
final velocity = initial velocity+2accelerationΔdisplacement
0 = (10,879,064 m/s)^2+2a(1 m)
a = -((10,879,064 m/s)^2) / 2(1) = -59,177,016,758,048 m/s/s
0 = (10,879,064 m/s)^2+2(-59,177,016,758,048 m/s/s)(1 m) = 0
F = ma
F = (2.01*10^25 kg)(-59,177,016,758,048 m/s/s) = -1.18*10^39 N
It seems unwise to convert newtons into joules. I want to make this easy for myself, so I'll change the criteria a little.
The lab tech messed up our system wrote:
Question B relates directly to the second stated question: how much energy (again, derived from "power", above) will it require to stop the planet from moving. This is requires an assessment of the angular momentum of Sorneith and the energy in order to stop the planet's movement (the "brick wall" approach).
Let's reword as:
Question B relates directly to the second stated question: how much
force will it require to stop the planet from moving. This is requires an assessment of the angular momentum of Sorneith and the
force in order to stop the planet's movement (the "brick wall" approach).
Well, we have an answer:
1.18*10^39 N
To compare that conventionally, the jet engine of a F100 fighter jet produces a thrust of about 130,000 N. That's 9 decillion fighter jet engines working together to stop the planet in 1 meter.
So, there we go! My job as newbie lab tech has been fulfilled. I'm not exactly sure how this might help Bossman, but I'm sure there's some value to it.
Do not take anything I've written at face value. Break it apart. Analyze every detail I've written. Tell me I'm wrong, because it makes me better to know where and what my mistakes were! If I say I've done anything, it's put some numbers into a number machine.
PS:
I just want to say - this was immensely fun. I had never in my life heard of a Milankovitch cycle before. I've never had to calculate vector difference. I had never used a kinematic equation prior to this post. My desire to solve the problem went far beyond what I know, but it was a hell of an adventure. Many thanks to the FR buds for giving me something cool to do.
EDIT + PPS:
It looks like the forum doesn't like unicode Cyrllic script. I'll try and find another symbol for the representations of Regular and Irregular Tilt, but I think it's alright. We didn't lose the Greek letters, so we're okay for the most part.
