I noticed a few days ago I was requested to do this calc in a thread. I apologize for not getting to it then, I've been catching up on my reading and haven't been as active as I once was. Regardless, here's a calc of the feat.
The feat[]
Everyone probably knows the feat by now, it's one of the more iconic scenes in Dragon Ball. To quell the rampage of a berserk Oozaru Gohan, Piccolo does the sensible thing and blows up the moon. However, in conjunction to its fame, the feat is also quite controversial. As such, there are several calcs of the eat around the internet, usually varying from Moon level to Large Planet level. We personally settled on the Small Planet level end quite some tie ago, but it was noted by multiple users, including myself, that the calc was unreliable given the assumed timeframe. Since it's a manga and not anime, the timeframe is ambiguous, but not impossible to gauge.
The issue with using the anime timeframe is it betrays the few visual queues we do get. The manga implies it takes place over the course of several seconds given the rocks falling fro the air, while the anime portrays it happening within seconds. Fair enough, do you want to watch 30 seconds of a moon crumbling? Neither do I. So this calc will attempt to find a timeframe based around the falling rocks in the sky. This is far from a perfect method, but it should give us a minimal timeframe to use without the use of assumptions.
The calculation[]
Part #1: Tails and rocks[]
So Kid Gohan lays at 112 pixels and his tail is 74 pixels.
According to this post on Neoseeker, Kid Gohan is around 126 cm tall. This is their source, but the images are down (damn you, Photobucket!), but 126 cm seems like a reasonable number so I'm comfortable with using it.
112 / 74 = 1.51351351351
126 / 1.51351351351 = 83.2500000002 cm
I'm scaling off of his tail because the angle doesn't show Gohan's body in the full length, given his scrunched up neck. Anywho, his tail is 64 pixels in this shot and the rock is 81 pixels
81 / 64 = 1.265625
83.2500000002 * 1.265625 = 105.36328125 cm. Seems reasonable given its size in comparison to Gohan's body. Off to the third scan.
No, it's very likely Akira Toriyama didn't make sure the rocks were consistent, and fair enough it's a small detail only us nerds would notice, but these rocks both appear to share the same characteristics of one another and appear to be roughly the same shape. Thus, using this should be fine.
The rock has a diameter of 27 pixels while the screenheight is 1156 pixels.
2atan(tan(70/2)*(object size in pixels/screen height in pixels))
2atan(tan(70/2)*(27/1156)) = 0.0221323101 Radians
0.0221323101×180°/π = 1.2680879596° Degrees
Now to the Angsizer.
Angsizing yields: 47.604 meters in the air.
Scratch that. According to the other calcs, this was sent 390 meters in the air. I guess that makes sense given Piccolo wasn't at ground level at this. Using 47 meters inflates results pretty badly.
Now for mass.
The rock is of an vague shape, hard to tell due to Piccolo's leg. Seems vaguely rectangular however. We don't see its full width, so the 12 pixels shall serve as a low end for what little width we can make out. The low end height is 13 pixels, based on its smaller side. This should give us an overall low end mass.
64 / 12 = 5.33333333333
83.2500000002 / 5.33333333333 = 15.609375 cm
64 / 13 = 4.92307692308
83.2500000002 / 4.92307692308 = 16.91015625 cm
V = LWH
105.36328125 * 15.609375 * 16.91015625 = 27,811.3724906 cm^3, or 0.027811372490600002 m^3
I'm not sure what type of rock it is, I believe we typically use Granite for unknown rock types, right? Density of Granite is 2,650 kg/m^3
0.027811372490600002 * 2,650 = 73.7001371001 kg
Part #2: Timeframe and Kinetic Energy[]
Off to the Splat Calculator. Using the parameters we calculated, we find a timeframe of 8.92s. Using a rough projectile motion calculator, I get a timeframe of 17.8368s. Almost exactly Derp's value, just slightly less.
Moon diameter is 153 pixels, or 3,474 km
The minimal distance it was scattered is 35 pixels
153 / 35 = 4.37142857143
3,474 / 4.37142857143 = 794.705882353 km
794.705882353 km / 8.92s = 89,092.5877 m/s
794.705882353 km / 17.8368s = 44,554.2857 m/s
The moon has a mass of 7.3476731e+22 kg
7.3476731e+22 * 0.5 * 89,092.5877^2 = 2.9161038e+32 J
69.69 Zettatons (lol)
Low end Planet level
7.3476731e+22 * 0.5 * 44,554.2857^2 = 7.2928755e+31 J
17.43 Zettatons
Mid-End Small Planet level
I prefer the high end since I don't really know how to do with projectile motion yet. Any pointers would be appreciated.
Note[]
I really don't follow DBZ so if I messed up anything regarding context, please let me know. If I made any mistakes point them out and I shall correct them. Thank you.
On an amusing note, I've been calcing for two years and this is my first DBZ calc yet (unless you count this old Dragon Ball Evolution calc I did. That's gotta be a record.