If an explosion were to occur at any point on earth, how powerful would that explosion have to be for it to be audible or otherwise detectable by every person on the planet? Detection could mean either seeing or hearing the blast or feeling the tremors created by the shock wave.
Bonus question: is any such explosion possible without it destroying the planet, the atmosphere or wiping out all life on earth?
A rough estimate puts the average distance between most antipodes on land at just shy of 20 000 kilometres.
The largest nuclear bomb ever detonated, Tsar Bomba, had a yield of 50-58 megatons of TNT and was detectable almost a 1000 km away, according to Wikipedia:
The heat from the explosion could have caused third-degree burns 100 km (62 mi) away from ground zero. A shock wave was observed in the air at Dikson settlement 700 kilometres (430 mi) away; windowpanes were partially broken to distances of 900 kilometres (560 mi). Atmospheric focusing caused blast damage at even greater distances, breaking windows in Norway and Finland. The seismic shock created by the detonation was measurable even on its third passage around the Earth.
The most powerful volcanic eruption known was that of Mount Tambora in 1815. Classified as Volcanic Explosivity Index 7 (note that it goes up to 8) with an estimated yield of 800 Mt, it was heard about 2 600 km away.
On 5 April 1815, a moderate-sized eruption occurred, followed by thunderous detonation sounds, heard in Makassar on Sulawesi 380 km (240 mi) away, Batavia (now Jakarta) on Java 1,260 km (780 mi) away, and Ternate on the Maluku Islands 1,400 km (870 mi) away. On the morning of 6 April, volcanic ash began to fall in East Java with faint detonation sounds lasting until 10 April. What was first thought to be the sound of firing guns was heard on 10 April on Sumatra island more than 2,600 km (1,600 mi) away.
The Wikipedia page on TNT equivalents list some interesting events but branches off into seismic and cosmic events after the entry for the Tsar Bomba.
So, is it possible to go bigger?
Answer
You can use this website to calculate the effects of impacts. If you take the distance to be 20,000 km, projectile diameter to be 10 km, the density to be 3000 kg/m^3, impact velocity 30 km/s, impact angle 45 degrees and target type sedimenatary rock, then you get this result, the only big effect is the airblast:
The air blast will arrive approximately 16.8 hours after impact. Peak Overpressure: 1670 Pa = 0.0167 bars = 0.237 psi Max wind velocity: 3.91 m/s = 8.75 mph Sound Intensity: 64 dB (Loud as heavy traffic)
This means that you could reduce the 1.69 x 10^8 MegaTons TNT somewhat and still have an audible result on the other side of the planet.
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