I think this other one is more accurate as it takes in account the fact that the Solar Disc has completely covered the planet from the star, causing its temperature to massively drop. It won't use any pixel scaling here, outside to get the thickness of the disc.
Thanks to
this, we know that (assuming Moon = Disc):
- Radius of Umbra = RadiusMoon - ((Distance Moon-Earth - RadiusEarth)/(Distance Sun-Earth - Distance Moon-Earth))*(RadiusSun - RadiusMoon)
If you don't know, the Umbra is the part that's completely covered in darkness during an eclypse, and what gets their temperature to decrease.
The distance between Sun and Planet is the easiest to take here. Minimal AU to be habitable is
0.9 (and I'll use it as the ice trapping these aliens was melting super fast), which will be
149597870700 m * 0.9 = 134638083630 m, or 134638083.63 km.
The 2nd thing that's unknown here is the distance between Disc and Planet, which will be using the formula from
here. The density for the Disc will be stainless steel, which is (
7500 + 8000)/2 or 7750 kg/m3.
The rest will be taken care off in the 3 ends, which are the same of the 1st method: Our Earth, Viltrum (
again, as VBW currently accepts it) and, as a generous high end, the
densest planet ever according to Wikipedia.
For the Thickness, instead...
- Sun Disc: 79 px
- Petal: 7.21 px
- Ratio: 10.95700416
- Petal: 87.05 px
- Thickness: 9.9 px
- Ratio: 8.792929293
Meaning that the diameter of the Disc is 96.34416284 times higher than its thickness.
Earth end
To find the distance between planet and disc (Earth's density is
5513 kg/m3):
- 2.4 * 6371 * ((5513/7750)^(1/3)) = 13649.4225 km
To find the Radius of the Disc, we know that, assuming that X is the radius of the Disc:
- 6371 = X - ((13649.4225 - 6371)/(134638083.63 - 13649.4225))*(696340 - X)
- Putting it in Microsoft Calculator gives me 6408.300913699 km
- Thickness = 6408.300913699 / 96.34416284 = 66.51467743 km
Now time to get the AP:
- Sun Disc's volume = pi * (6408.300913699^2) * 66.51467743 = 8.58130139e9 km^3 = 8.58130139e24 cm^3
- Sun Disc's mass = 8.58130139e24 * 7.75 = 6.650508577e25 g = 6.650508577e22 kg
- Fragmentation = 208 * 8.58130139e24 = 1.784910689e27 Joules or 426.6 Petatons (Multi-Continent)
- Pulverization = 1000 * 8.58130139e24 = 8.58130139e27 Joules or 2.05 Exatons (Multi-Continent)
- Assuming KE under 1 second because it's fun = 0.5 * 6.650508577e22 * (6408300.913699)^2 = 1.365559589e36 Joules or 326.38 Yottatons (Large Planet)
Viltrum end
To find the distance between planet and disc (Viltrum's density is
5513 * 1.25 = 6891.25 kg/m^3):
- 2.4 * 6371 * ((6891.25/7750)^(1/3)) = 14703.3947 km
To find the Radius of the Disc, we know that, assuming that X is the radius of the Disc:
- 6371 = X - ((14703.3947 - 6371)/(134638083.63 - 14703.3947))*(696340 - X)
- Putting it in Microsoft Calculator gives me 6413.702376182 km
- Thickness = 6413.702376182 / 96.34416284 = 66.57074167 km
Now time to get the AP:
- Sun Disc's volume = pi * (6413.702376182^2) * 66.57074167 = 8.60301884e9 km^3 = 8.60301884e24 cm^3
- Sun Disc's mass = 8.60301884e24 * 7.75 = 6.667339601e25 g = 6.667339601e22 kg
- Fragmentation = 208 * 8.60301884e24 = 1.789427919e27 Joules or 427.68 Petatons (Multi-Continent)
- Pulverization = 1000 * 8.60301884e24 = 8.60301884e27 Joules or 2.06 Exatons (Multi-Continent)
- Assuming KE under 1 second because it's fun = 0.5 * 6.650508577e22 * (6408300.913699)^2 = 1.36555959e36 Joules or 326.38 Yottatons (Large Planet) (lol)
Densest Planet end
To find the distance between planet and disc (density is
23 g/cm3, or 23000 Kg/cm3):
- The radius is 0.4 Jupiter's, which means that the radius 0.4 * 71492 = 28596.8 km
- 2.4 * 28596.8 * ((23000/7750)^(1/3)) = 98628.87 km
To find the Radius of the Disc, we know that, assuming that X is the radius of the Disc:
- 28596.8 = X - ((98628.87 - 28596.8)/(134638083.63 - 98628.87))*(696340 - X)
- Putting it in Microsoft Calculator gives me 28944.200763688
- Thickness = 28944.200763688 / 96.34416284 = 300.4250586 km
Now time to get the AP:
- Sun Disc's volume = pi * (28944.200763688^2) * 300.4250586 = 7.90695289e11 km^3 = 7.90695289e26 cm^3
- Sun Disc's mass = 7.90695289e26 * 7.75 = 6.12788849e27 g = 6.12788849e24 kg
- Fragmentation = 208 * 7.90695289e26 = 1.644646201e29 Joules or 39.31 Exatons (Moon)
- Pulverization = 1000 * 7.90695289e26 = 7.90695289e29 Joules or 188.98 Exatons (Moon)
- Assuming KE under 1 second because it's fun = 0.5 * 6.12788849e24 * (28944200.763688)^2 = 2.56687064e39 Joules or 613.5 Ronnatons (Brown Dwarf)