The development and construction of the Death Star had begun long before the first debate ever took place about the Doctrine of Fear. He believed that after the total annihilation of a planet, fear would spread throughout the galaxy and maintain order. Tarkin intended to make an example of a rebellious system as soon as the Death Star was capable. Tarkin's answer to any potential dissonance was the Death Star. Opponents to the Doctrine of Fear (and there were many in the Empire) claimed that this new policy would rip the Empire apart and that planets would revolt without direct representation in the Senate.
Little is actually known about the details of the highly classified reactor design, but we do know that it is a massive fusion reactor fed by stellar fuel bottles that line the periphery of the main reactor chamber. The Death Star's hypermatter core is based largely on early Sienar Systems hypermatter implosion core that was the power source of the Confederacy of Independent Systems' Great Weapon (the early inspiration for the Death Star - more on this later). The hypermatter reactor is the heart of the Death Star. The answer to both of these problems was solved with the invention of the hypermatter reactor. The greatest challenge was always powering a cannon big enough to fire a beam that could destroy a planet and moving a battle station the size of a small moon. The greatest challenge in designing the Death Star was not creating a cannon big enough to fire a beam that could destroy a planet, nor was it creating a battle station the size of a small moon. Photo courtesy NASA/JPL/Space Science Institute A main beam then blasts from the nexus to the intended target. The main cannon and eight tributary lasers fire beams that converge at the outer perimeter of the Superlaser dish in an amplification nexus. This allows the Death Star to aim the Superlaser within a certain field of fire without having to turn the entire station. All of the tributary lasers can be angled for targeting.
There are also four back up lasers in case any of the main eight tributaries fail. The lens is known as "the Eye" and is surrounded by eight tributary lasers. The Superlaser has a massive lens built around a huge synthetic focusing crystal. The sun is the source of power and the lens is the focus. These rays intersect under the lens and at the point of intersection a beam of heat is created that burns the leaf. When a magnifying glass is held at the correct angle between the sun and a leaf, the sunrays are focused through the lens. If you've ever burned a leaf with a magnifying glass you understand the basic principle behind the Superlaser. This is off by a factor of 3/4, but suffices to show that while the gravitational pull is significant, it wouldn't hold the Death Star together it has to be held together structurally.Photo courtesy © Lucasfilm Ltd. The Death Star would have an acceleration of $G M_ N$. Then the bottom hemisphere is 270 km above Earth and the top hemisphere is 330 km above Earth. Let us suppose the Death Star is orbiting 300 km above Earth and has a radius of $r$ of 80 km. The center of mass of a hemisphere is $\frac38$ the way from the center of the sphere to the edge. Consider the Death Star as two hemispheres, one closer to Earth and one further.
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