September 29, 20XX
Due to many Earth's domestic meta-human clashes that often also result in wars, and invasions by alien despotic empires; the United Federation of Planets was firmly established after the recent alien invasion that the Doctor and Clara Oswald stopped. The Federation eventually became a vast interstellar alliance composed of numerous member worlds, each with its own form of government, culture, and species. However, the heart of the Federation's government is located on Earth, where the Federation Council, a legislative body, and Starfleet Command, the evolved exploration arm of the Federation with its expansive military companies, are based.
The Federation is characterized by its principles of diplomacy, cooperation, and a commitment to peace and exploration. Its government promotes the values of diversity, equality, and the betterment of all sentient life in the galaxy. The Federation Charter, often referred to as its constitution, outlines these fundamental principles and serves as a guiding document for its member worlds.
Captain James T. Kirk is one of the most iconic figures that are often ranked with Earth's air pioneers and astronauts. He is best known as the charismatic and adventurous captain of the starship USS Enterprise that was in the subject of defending against many alien invasions and wars alongside even had a hand in this planet's colonization. Kirk is known for his leadership, courage, and strong sense of morality. He embodies the ideals of the Federation, including a commitment to diplomacy, exploration, and the defense of freedom and justice.
Kirk is known for his hands-on approach to problem-solving and his willingness to bend the rules when necessary to achieve the greater good. He often relied on his intuition and the loyalty of his diverse crew to navigate the challenges of deep space.
Many years later, Captain Jean-Luc Picard was too also well known. He is most prominently known as the recent captain of the USS Enterprise. Picard is known for his intellectual prowess, diplomacy, and unwavering commitment to Starfleet's principles.
Unlike Kirk, Picard is often characterized by his calm, measured demeanor and preference for diplomacy over force. He is a skilled negotiator and a staunch defender of individual rights and ethical conduct. Picard's leadership style emphasizes collaboration and the pursuit of knowledge through exploration.
Earth's Federation and Starfleet with its numerous allied defenders (both Earth or alien) often clash with other alien invaders, and their main common foe was the Galactic Empire.
With the Rebel Alliance, they fight against the forces of this Empire that is lead by a tyrannical yet cunningly manipulative emperor with dark telekinesis abilities who is known as a Sith lord, who recently lead the near-extinction of his foes known as the Jedi.
The origins of the Jedi and Sith can be traced back to alien ancient times. The Jedi, were a group of Force-sensitive individuals who sought balance and harmony within themselves and the Force. However, over time, a faction within them began to embrace the dark side of the Force, giving birth to the Sith Order. This schism laid the groundwork for countless conflicts to come with many involving belligerents including those on Earth, Cybertron, and this evolved colonized planet.
The most infamous Sith Lord, Darth Bane, initiated the "Rule of Two," which mandated that there could only be two Sith at any given time—a master and an apprentice. This rule was established to prevent the infighting that had weakened previous Sith empires. Despite this, the Sith and Jedi continued to clash in a series of wars, often with galaxy-altering consequences.
Eventually, this large alien civilized galaxy's system would establish the Galactic Republic, in which after a near-millennia centuries (with the Jedi and Sith conflicts in the shadows, whereas the Jedi established themselves a cooperative governmental branch known as the Jedi Order), would be plagued by a new conflict known as the Clones Wars.
The Galactic Republic have sent its representatives, adventurers, observers, and ambassadors to Earth (which was during the aftermath of World War Two) before. They have extensive history with Earth's governmental figures and meta-humans.
The Clone Wars was a pivotal conflict in this galaxy's system, while for Earth it was during the Cold War years. It was orchestrated by Darth Sidious (also known as Emperor Palpatine) to bring about the downfall of the Galactic Republic and the Jedi Order by taking advantage of the political factions' in-fighting's and conflicts between the Republic and the Confederacy's Separatist Movement.
The Clone Wars began with the creation of the Grand Army of the Republic, composed of clone troopers cloned from the Mandalorian bounty hunter Jango Fett. The Republic's Jedi Knights, led by Jedi Grandmaster Yoda and others, served as generals in the war against the Separatists, who were led by Count Dooku (Darth Tyranus).
Throughout the Clone Wars, various battles, campaigns, and intrigues unfolded across the galaxy. Key events included the Battle of Geonosis, the rise of the Sith, the introduction of iconic figures like Jedi Generals Anakin Skywalker and Ahsoka Tano, and the growing influence of Chancellor Palpatine.
Ultimately, the Clone Wars resulted in the Jedi's downfall. The execution of Order 66 compelled the clone troopers to turn against their Jedi leaders, leading to the near-annihilation of the Jedi Order. Anakin Skywalker, seduced by the dark side and becoming Darth Vader, played a central role in this tragedy.
Earth (which its Federation lend and allied its armies with the meta-humans, the United Nations, the main planet, and colonized Moon and Mars) quickly drew back its forces with many alien refugees and any possible Jedi survivors with many numerous causalities.
After the fall of the Republic and the rise of the Galactic Empire under Emperor Palpatine's rule, oppression and tyranny gripped the galaxy. Sheev Palpatine established a totalitarian regime, ruled with an iron fist, and wiped out nearly all Jedi. The galaxy yearned for liberation under this galactic Cold War.
The Rebel Alliance emerged as a beacon of hope and resistance against the oppressive Galactic Empire. Comprised of various factions, species, and freedom fighters, the Rebel Alliance included iconic figures such as Princess Leia Organa, Han Solo, and Luke Skywalker.
The Rebel Alliance embarked on a series of daring missions and engagements against the Empire, aiming to undermine its control and ultimately bring about its downfall. Key moments included the theft of the Death Star plans and the Battle of Yavin with the belligerents from Earth's Federation, Cybertron's Autobots, and this colonized planet.
Chem Notes: (filled with academic musings)
Calculating Equilibrium Constants from Measured Equilibrium Concentrations
STEP 1: Prepare the Initial-Change-Equilibrium (ICE) table.
STEP 2: Decide in which direction the reaction will proceed.
STEP 3: Define the changes of all substances in terms of x.
– Use the coefficient from the chemical equation as the coefficient of x.
– The x change is − for materials on the side the reaction is proceeding away from, + for substances on the side the reaction is proceeding toward.
STEP 4: Solve for x.
– For second-order equations, take square roots of both sides or use the quadratic formula.
– Simplify and approximate the answer for very large or small equilibrium constants, if possible.
Using Approximations to Simplify the Math: 5% Rule × 100 5% approximate x initial concentration
• For relatively large initial concentrations of reactants, the reactant concentration will not change significantly when it reaches equilibrium.
• Assuming the reaction is proceeding forward, then
[X]equilibrium = ([X]initial – ax) ≈ [X]initial
• Meaning the equilibrium concentration of reactants will be the same as the initial concentration
• If the approximate value of x is less than 5% of the initial concentration, the approximation is valid.
Step 1: Prepare the Initial-Change-Equilibrium (ICE) table.
This table helps you keep track of the initial concentrations, the changes that occur as the reaction proceeds, and the equilibrium concentrations.
Step 2: Decide in which direction the reaction will proceed.
This is typically based on the reaction conditions and the reaction's equilibrium constant (K). If Q (the reaction quotient) is greater than K, the reaction will proceed in the reverse direction. If Q is less than K, the reaction will proceed in the forward direction. If Q equals K, the system is at equilibrium.
Step 3: Define the changes of all substances in terms of x.
You're right, you use the coefficients from the balanced chemical equation to determine how much each substance changes. For reactants, it's -x because they are being consumed, and for products, it's +x because they are being formed.
Step 4: Solve for x.
Depending on the complexity of the equilibrium expression, you may need to use algebraic methods to solve for x. For simple equilibrium expressions, it may involve square roots or basic algebra. For more complex ones, you might need to use the quadratic formula.
Using Approximations to Simplify the Math: 5% Rule
The 5% rule is a useful guideline when solving for x because it simplifies the math. If the value of x you calculate is less than 5% of the initial concentration of reactants, you can make the approximation that the equilibrium concentration of reactants is essentially the same as the initial concentration. This simplifies the calculation considerably.
To summarize, these steps and the 5% rule are helpful tools for calculating equilibrium constants when you have measured equilibrium concentrations, especially when dealing with reactions with relatively large initial concentrations of reactants. However, for highly accurate or precise calculations, it's important to remember that the 5% rule is an approximation and may not always be suitable. In such cases, you would need to solve the equilibrium expression more rigorously.