 Goku's iconic "Spirit Bomb" has aided the hero in difficult situations in the world of Dragon Ball. With the aid of a photon sphere model, we obtain a glimpse into the necessary requisites. By creating a hypothetical sun-sized SB, we find that a photon sphere would require 5x1042 humans and would span 1x108 episodes.

Harrison, Zoe

Holesinsky, Tomas

Mandhai, Soheb

Swithenbank-Harris, Benjamin George

English

University of Leicester Open Journals

Journal of Physics Special TopicsAn undergraduate physics journalP2 2 Understanding Goku’s Spirit BombS. Mandhai, Z. Harrison, T. Holesinsky, B. G. S. HarrisDepartment of Physics and Astronomy, University of Leicester, Leicester, LE1 7RHNovember 11, 2016AbstractGoku’s iconic ”Spirit Bomb” has aided the hero in difficult situations in the world of Dragon Ball. Withthe aid of a spherical photon gas model, we obtain a glimpse into the necessary requisites. By creatinga hypothetical sun-sized SB, we find the model would require 1.5x1075 humans and would take about1.4x1026 s to form.IntroductionDragon Ball (DB) is a popular Japanese an-imated series with a main protagonist named“Goku”. In order for Goku to overcome the vil-lains he encounters, he calls upon the power ofSpirit Bomb (SB). The SB is fueled by “pure”energy referred to as “ki” which stems from anyform of life. We model these Spirit Bombs asphoton gas spheres in order to approximate theirphysical parameters as dictated by our universe.It is possible to obtain an approximation for theenergy contribution required; assuming only hu-man contributions.TheoryWe model the SBs as spherical distributions thatare composed entirely of photons; the behaviourof which can be assumed to be similar to a pho-ton gas. Furthermore, we assume the photondensity for the distribution is sufficient enough toexhibit self-gravity. In order to maintain the sim-plicity of the structure, further relativistic andNewtonian effects, besides those relating to theaforementioned, are negated.In order to calculate the total energy require-ment for each SB, the number of collective pho-tons, N , from Equation 2, is required. To ap-proximate the temperature for a SB from Equa-tion 1 we assume that all SBs are of the sametemperature. In the DB series [2], a SB is de-picted to “vaporise” a target object; this is inter-preted as the ability to break bonds. By assum-ing the target is composed primarily of carbonatoms, we are able to estimate the temperaturebased on the common bond dissociation energyof a carbon bond (approximately 415.5 kJ mol−1- based on methane C-H bonds [3]):T =23EtR(1)Where T is the Temperature of the SB, R isthe ideal gas constant and Et is the thermal en-ergy. In this investigation, Et is set to the men-tioned bond dissociation energy for one mole ofcarbon bonds (Note: We assume gravitationalcompression produces additional heat). By keep-ing a constant T , we are able to find the numberof photons:N =(16pik3ζ(3)c3h3)V T 3 (2)P2 2 Understanding Goku’s Spirit Bomb, November 11, 2016Spirit Bomb Type Radius (m) PhotonNumberTotal Energy(J)Humans FormationTime (s)Large 8.99 7.98e+69 3.18e+51 5.51e+46 300Universal 5.93 2.29e+69 9.09e+50 1.58e+46 85.9Android 13 14.2 3.16e+70 1.26e+52 2.18e+47 119Fusion 0.762 4.86e+66 1.93e+48 3.36e+43 0.183Solar 6.98e+08 3.73e+93 1.48e+75 2.57e+70 1.4e+26Table 1: Various different SBs that have been included in the investigation for this paper. Note:Exponents are denoted by ”e+”. Shaded cells indicate values for a hypothetical photon sphere.Note: The names correspond to different depicted SBs [1].Here, ζ (3) is the Ape´ry’s constant, V is thevolume of the spherical distribution (granted by4piR3/3) and the remaining terms are constantswith their associated definitions [4] (Note: Theradius is obtained by scaling the known heightsof characters with a frame in which a SB is com-parable). The product of N with the energyof each individual photon, with wavelength, λ,yields the total energy of the SB (Etot), where:Etot = N(hcλ) (3)We may also calculate the time required togather sufficient energy (tsb); assuming a lineartimescale and a constant supply of energy.E˙ =Etottsb(4)DiscussionWe used a photon wavelength of 500 nm due tothe blue tone of the SB [2]. From Equation 2and 3 we estimated the total energy of the SBwith additional calculations uncovering the num-ber of humans required to form various observedSBs. As average adults have a metabolic rate80 W [5], over 30 minutes (active digestion) [6]this would produce 1.44x105 J of energy. A SBonly accepts 50% of the remaining ”ki” per in-dividual [2]. Hence the average human supplies5.8x104 J; assuming a one time donation and a20% brain energy reserve. The ratio of SB energyover the energy per human yields the number ofhumans required to donate sufficient energy.Furthermore, using the energy accumulationduration for the “Large” SB (which is quotedto be about 5 minutes [2]), the energy expan-sion rate is found to be 1x1042 W . Thus thecorresponding formation times can be found bysolving Equation 4 for tsb (refer to Table 1).ConclusionDuring our investigation we were able to approx-imate various parameters for four SBs that aredepicted within the DB series. We were alsoable to consider the possible parameters for asun-sized SB; see Table 1. It is apparent thatGoku would require an astronomical number ofhumans to obtain the energy required to form theSBs depicted (more so than the Earth is capableof supplying).References[1] Spirit bomb, https://goo.gl/f14lpg, Accessedon 23/10/2016.[2] Toriyama, A., Dragon ball, 1984.[3] Bond enthalpy, https://goo.gl/hHe3sr, Ac-cessed on 23/10/2016.[4] University of California, Photons and Black-body Radiation.[5] Cross, R;Spencer, R., Sustainable gardens,CSIRO Publishing, 2008.[6] https://goo.gl/kXFAER, Accessed on10/10/16.

P2_2 Understanding Goku's Spirit Bomb

https://journals.le.ac.uk/ojs1/index.php/pst/article/download/873/805

P2_2 Understanding Goku's Spirit Bomb

Abstract

Similar works

Full text

Available Versions

University of Leicester Open Journals