Calc The Dark Forest calcs, part 1

Earth's Remembrance continues to be a captivating, fantastic and more than often insane series. It also has quite a few impressive feats, some of which are given to us directly!

1. First Stellar Hydrogen Bomb test

The test was carried out at dawn. Sunrise on Mercury was a process that took over ten hours, and a faint light had just appeared on the horizon. When the detonation countdown reached zero, rings of ripples centered on ground zero spread outward, and the ground on Mercury seemed momentarily to become soft as satin. Then, at the blast site, a mountain slowly rose like the back of a waking giant. When the peak had risen to around three thousand meters, the entire mountain exploded, sending billions of tons of mud and rock flying into the air in a towering display of rage by the ground toward the sky. And alongside the surging ground came the radiant light of the underground nuclear fireball, which shone on the rock and earth flying through the air to cause a grand spectacle of fireworks in the black Mercury sky. The fireball lasted for five minutes, as chunks of rock fell to the ground amid a nuclear glow, before it went out.
Ten hours after the conclusion of the blast, observers noticed that a ring had appeared around Mercury. This was due to the considerable amount of rock that had achieved cosmic velocity in the violent explosion and had turned into myriad satellites of various sizes. They spread out evenly in orbit, making Mercury the first ringed terrestrial planet. The ring was thin, and as it sparkled in the harsh light of the sun, it looked almost like someone had taken a highlighter to the planet.
Another proportion of the rocks achieved escape velocity and left Mercury behind entirely, becoming satellites of the sun in their own right and forming an extremely sparse asteroid belt in Mercury’s orbit.

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This bomb creates a mass of land like a mountain to rise 3000m (3km) up and explode billions of tons of mud and rock flying, some of which even goes into space having exceeded escape velocity. The fireball lasts for 5 minutes. This is a colossal explosion and thankfully...we have an exact yield for it!

The giant breakthrough in computing technology meant that computers were at last capable of handling the theoretical stellar model ofa nuclear explosion developed over the past decade, and the manufacture of large-yield stellar hydrogen bombs could begin forthwith. The projected yield of the first bomb was the equivalent of 350 megatons of TNT, or seven times more powerful than the largest hydrogen bomb ever manufactured by humanity.

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“Sure,” Rey Diaz said with a nod, “but the real reason you invested so heavily in my plan is because you wanted to get your hands on the stellar hydrogen bombs.”
“Ridiculous! What would we do with them?” The US representative shot back. “They’re incredibly inefficient weapons in a space battle, and on the Earth, there’s no practical significance even for those old twenty megaton hydrogen bombs, much less a three-hundred-megaton monster.”

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Rey Diaz's first stellar hydrogen bomb has a yield of 350 megatons (and is also stated to be a '300 megaton monster'), as stated before and after it's tested on Mercury.

2. Spacesuits thrusters speed

As people became used to the environment of space, they gradually adopted the habit of crossing solo. Using space suits as a sort of space bicycle with thrusters that could push them to speeds of up to five hundred kilometers per hour was the easiest means of travel within a few hundred kilometers of the space elevator. By this point, people were flying between the space elevator and the surrounding stations all the time.

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With the thrusters on a spacesuit, one can accelerate themselves of speeds of up to 500km/h, or 138.888889m/s.

3. Type 2010 pistol muzzle velocity

Now the thirty meteorites were speeding toward their targets. The Type 2010 pistol had a muzzle velocity of five hundred meters per second, so they would take around ten seconds to cross the distance, during which Zhang Beihai could only pray that his targets did not change position.

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The Type 2010 pistol has a muzzle velocity of 500m/s.

T = 500/340.29
= Mach 1.46933498

4. Space Elevator's height

On the screen, the cylindrical cabin was rising from the base. It ascended quickly and accelerated rapidly, then disappeared into the evening sky. Because the guide rail was invisible, it looked like it wasascending on its own. The cabin could reach a maximum speed of five hundred kilometers per hour, but even at that speed it would take sixty eight hours to reach the space elevator’s terminus in geostationary orbit

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The cabin of the space elevator of Verne Island can reach speeds of up to 500km an hour, but would still take 68 hours to reach the top.

L = 500km X 68
= 34000km

Final Results
First stellar hydrogen bomb yield = 350 megatons
Maximum speed of space suits via thrusters = 138.889m/s
Type 2010 pistol muzzle velocity = Mach 1.468
Space Elevator's height = 34000km