In order to examine the feat we have to take a closer look at the 8th page of the 483th chapter of the Dragonball manga.
- http://www.mangavolume.com/index.php?serie=dragon-ball&chapter=dragon-ball-483&page_nr=8
At the third panel we can see that Gotenkusu gets serious (accelerate) before he flies around the world.
To this calculation I will make two estimations. That Dragonball earth is equal in size to our own and that the laws of the universe is the same as ours.
Now lets take a closer look at the orbits Gotenkusu formed when he flew around the earth.
The earth is scaled down to 4.4 cm in diameter. This will be used as the main-frame for the calculation of the diameter of the orbits.
The largest orbit is 9.0 +/- 0.5 cm (the ring is partially off-panel)
Orbit 2: is 8.6 cm
Orbit 3: 6.75 +/- 0.25 cm (also partially off-panel)
Orbit 4: 6.5 cm
Orbit 5: 4.5 +/- 0.5 (off-panel in both ends)
Since the circumference linearly increases with the diameter [c = πØ — > 2c = 2πØ] we can directly translate these into earth circumferences.
The earth is 4.007*10^7 around the equator, and 3.994*10^7 around the poles. Which gives an average of:
(4.007 + 3.994)*10^7 / 2 = 4.001 * 10^7
Note*: The exact values are used in the calculation, not the approximated values used in this post.
So, 4.4 cm = 4.001 * 10^7m, meaning that each centimeter would equal.
4.001*10^7 / 4.4 = 9.1*10^6 m
We now add the orbits together and get: 35.35 +/- 1.25 cm
Multiplying with the factor of increase calculated above (1cm = 9.1*10^6 m) we get that Gotenkusu flew:
3.2*10^8 m +/- 1.1*10^7 m
So Gotenkusu flew at maximum: 3.3*10^8 m, and at minimum 3.1*10^8 m.
Seeing how one of the most vital units in this calculation is missing, namely time, it’s difficult.
Gotenkusu mentioned that he was, after the flight, able to take a nap before Pikkoro caught up to him. Pikkoro further stated that he had only one minute left.
So the time he flew around the earth can be anything in-between 0 - 29 minutes. Or anything in-between
3.1*10^8 / (29 * 60) = 178 km/s
3.3*10^8 / 0 — > ∞
So anywhere in-between 178 km/s to infinite speed (hypothetical).
As you see, the time for this feat is vital.
If we base the time on the plasma tail behind Gotenkusu as base for the feat we’ll end up with a fraction of a second or about >32*10^8 m/s (that’s 11 times the speed of light) - > is used because the plasma tail doesn’t disappear in the manga.
However the solution could also be found in the anime, as it’s the second canon of Dragonball.
In the anime Gotenkusu flies 9 times around the world — It should also be noted that we don’t know how many times Gotenkusu flew around the earth, we only know it’s more than five times. This however has no affect on the calculations at hand, since we’re only looking for the time-interval for when he flew around the earth — this was accomplished in 9 seconds.
Meaning that one lap took 0.78 seconds. The average lap in Dragonball (manga) was 7.1 +/- 0.5 cm or 7.1 cm.
The multiplying factor makes the distance 6.5 * 10^7 m. Which is translated into 8.3 * 10^7 m/s or 27.8% of the speed of light.
Conclusion:
Gotenkusu’s speed based on the manga scan is hypothetically in-between 178,000 m/s and ∞ m/s.
Based on the physics of the plasma state in outer atmosphere, Gotenkusu traveled at approximately 11.0 times the speed of light.
Based on the time from the anime Gotenkusu flew at 27.8% of the speed of light.
