Introduction[]
This is a calc of Vegeta destroying Planet Arlia from episode 11 of Dragon Ball Z.
Version 1: Earth-sized Planet[]
Explosion size[]
In this end, I'll be treating Planet Arlia as an Earth sized planet with two moons the size of Earth's Moon.
Arlia: 31 px
Explosion: 1062 px
The Polar diameter of Earth is 12,713.6 km or 12,713,600 m.
Explosion Diameter: 12713600 / 31 * 1062
Explosion Diameter: 435,543,329.03225803 m
Explosion Radius: 217,771,664.51612902 m
Timeframe[]
The explosion starts at frame 400 and ends at frame 457, giving a timeframe of 2.28 seconds.
Velocity[]
217771664.51612902 / 2.28 = 95513887.9 m/s
Mass[]
Since we see the moon close in on and explode with the planet, I'll use the Earth's mass + the mass of two moons.
2*7.3e22 + 5.972e24 = 6.118e24 kg
Kinetic Energy[]
Relativistic KE Calculator: 3.023e40 Joules
Version 2: Super Dragon Ball-sized Planet[]
The planetary parameters and the justification for this end is on this blog.
Moon mass[]
Arlia: 295 px = 37196.2204 km
Moon: 76 px = 9582.755 km
The moon's gravity is about 0.166 G, using the Planetary Parameter Calculator:
Diameter: 9582.755 km Gravity: 0.166 G
Mass: 5.6e23 kg
Velocity[]
1062 / 31 = 34.2580645x
34.2580645 * 37196.2204 = 1274270.52 km
1274270.52 * 500 = 637135260 m (explosion radius)
637135260 / 2.28 = 279445289 m/s
Total Mass[]
2*5.6e23 + 5.083e25 = 5.195e25 kg
Kinetic Energy[]
Since the velocity is over 93% the speed of light, we have to use 4x the value of the Newtonian KE, as per the Kinetic Energy page.
0.5*5.195e25*279445289^2 = 2.02837917e42 Joules 2.02837917e42*4 = 8.113517e42 Joules
Results[]
Version 1: 7.225 Quettatons of TNT (Dwarf Star level+)
Version 2: 1.94 KiloQuettatons of TNT (Large Star level)