Packing Enough Fuel for Geosynchronous Orbit

So you've managed to get into orbit, but you were shooting a little higher. Here are some tips and tricks on how you can use conservation of energy to calculate how much extra fuel you will need to bring in order to get into kerbin geo-synchronous orbit.

Firstly, if you've never played Kerbal Space Program, or have but haven't become addicted to video game physics, we will need to cover some of the in game facts; When doing orbital mathematics many formulas use a gravitational parameter unique to the major body of mass in the system.

Kerbin (the in game equivalent of Earth) is about 1/10 th the radius of earth however, it has the same gravitation acceleration at the surface as Earth (9.8 m/s^2). This fun fact leaves many game theorists to presume the planet is made entirely out of lead as only a material as dense as lead would be be able to produce that much gravitational force in such a small radius.

Due to the Length of this blog it has been broken up into 3 Parts:

PART I: Calculating Geosynchronous Orbit Radius

PART II: Calculating Change in Energy

PART III: Finally Getting The Fuel Bill

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