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The History of Kerbal Space Program
Kerbal Space Program is the brainchild of Felipe Falanghe, a programmer working at Squad, a multimedia advertising and marketing company operating out of Mexico City, Mexico. In 2011, he met with his superiors at Squad to discuss the possibility of making a game; he was surprised when they encouraged him and requested a design document and business plan. Leveraging the resources available at Squad, Falanghe released the initial version of Kerbal Space Program on June 24, 2011.
The game places the player in charge of a space program run by a race of small green humanoids known as Kerbals. The player is responsible for planning, designing, and controlling space ships and vehicles of all sorts to accomplish various goals, either game-provided or personally decided. In the original version, only rockets were available to be designed and launched; subsequent version updates have introduced unmanned satellites, rovers, orbital stations, and even space planes. A later version also introduced Career Mode, where the player must manage budgeting their vehicle parts against completing objectives which reward them with money and scientific research, which allows them to develop more sophisticated parts and take on more advanced tasks.
Since its original release in 2011, the game has exploded in popularity, due in no small part to many video series' on YouTube (known as "Let's Play") featuring footage of the game being played. In 2013, the game was introduced on Steam's Early Access program, and quickly became one of the highest selling games participating in the program.
Physics Concepts in Kerbal Space Program
Due to software and hardware limitations, physics concepts are implemented in simplified fashion.
Gravity
Rather than simulate every gravitational interaction between dozens of celestial bodies and possibly thousands of vehicle parts, gravity is only calculated between actively controllable ships and the celestial body exerting the highest gravitational force. In other words, a celestial body only exerts gravitational force on objects within its sphere of influence. This means a ship can be placed into a desired orbit and remain there indefinitely, irrespective of gravitational perturbations that would occur in real world situations. Additionally, celestial bodies in-game have far reduced sizes compared to their real-life counterparts: Both Kerbin and Mun have radii at about a tenth of the Earth and Moon respectively, but the force of gravity is roughly the same between analogues.
Atmosphere
Atmosphere in Kerbal Space Program is also similar to real atmosphere, with some simplifications. Like real-life, atmospheric pressure decreases exponentially with altitude; unlike real-life however, which has weather patterns that can change pressure, pressure on Kerbin remains constant for a given altitude anywhere on the planet. While in the atmosphere, vehicles will experience air resistance and may slow motion through it (this makes aerobraking possible; more on that in Advanced Maneuvers). In order to prevent rounding issues with the pressure calculation, pressure stops being calculated after it reaches 0.001% of surface value; on Kerbin, this occurs at an altitude of approximately 69km. In addition to Kerbin, four other celestial bodies have atmospheres: Eve (analogue for Venus), Duna (Mars), Jool (Jupiter), and a moon of Jool, Laythe (closest analogue being Titan).
A Light Course in Orbital Mechanics
An orbit is an elliptical path traced around a celestial body by an object. In Kerbal Space Program, this is always between a planet, moon, or sun, and the player's craft. Two important points lie on this ellipse: the apoapsis, which is the point of highest altitude the orbit attains; and the periapsis, which is the point of lowest altitude. Because orbital velocity scales inversely with altitude, this also means the apoapsis is the point at which the craft is orbiting slowest, and the periapsis is the point at which the craft is orbiting the fastest; this is a very important fact for performing any orbit change maneuver (or "burn") as it can tell you which point along the craft's orbit will be most efficient to perform a burn at.
In addition to knowing the apoapsis and periapsis of the orbit (also known as the apsides), it is also useful to know its inclination, or the angle between the plane of the orbit and either the celestial body's equatorial plane or the ecliptic plane the body makes with reference to its star. A perfectly equatorial orbit has an inclination of 0 degrees; a polar orbit has either an inclination of 90 degrees or 180 degrees. The line formed at the cross-section of the orbit and equatorial plane defines two other useful points: the ascending node, where the orbit crosses north (or normal) of the equatorial plane; and the descending node, where it crosses south (or antinormal).
The Tsiolkovsky Rocket Equation
To fully understand what one can accomplish with a given vehicle, it is necessary to understand the concept of Δv. In general terms, Δv acts as a sort of budget for the craft, and each task you want to accomplish costs a certain amount of Δv. More specifically, Δv is a measure of how much the craft is able to change its velocity before exhausting its fuel supply and winding up adrift. To prevent this, it is important to know how to calculate the Δv of a given ship design, for which the Tsiolkovsky Rocket Equation is used.
Given the total mass of the vehicle, the mass of the vehicle with no fuel (known as dry mass), and the specific impulse of the engines used (a measurement at how efficient the engine is at producing thrust per unit of fuel mass), the Δv is calculated as follows:
The result of this calculation is Δv as it would be applied in the vacuum of space; travelling through atmosphere is more difficult, and therefore requires significantly more Δv. From launch at sea level on Kerbin to achieving a stable orbit at 100km takes approximately 4700 m/s of Δv. By comparison, the maximum theoretical Δv on a single ship is just under 8200 m/s.
Advanced Rocketry Maneuvers in KSP
Orbital Transfers
The first transfer technique players are likely to attempt is a Hohmann transfer. This is characterized as a transfer from one orbit to a higher orbit by first burning prograde (towards the direction of movement) at periapsis until the apoapsis is at the desired altitude, waiting until the craft reaches the apoapsis, and then burning prograde again to circularize the new orbit; the burn can be performed retrograde to instead transfer to a lower orbit. The benefit to burning at periapsis is due to the Oberth effect: that a rocket engine produces more useful energy when travelling at higher speeds.
Another transfer that players might wish to employ is the bi-elliptic transfer. This involves transferring to an extremely elliptical orbit, waiting until the craft reaches apoapsis, burning again to bring periapsis up to the desired final altitude, waiting until the craft reaches the new periapsis, then burning retrograde to circularize into the new orbit. Though it requires an additional burn compared to the Hohmann transfer, it may require less Δv as long as the ratio of the original and new orbits' semi-major axes (the average of the apsides) is 11.94 or greater and the intermediary elliptical orbit is correctly chosen.
Aerobraking/Aerocapture
Aerobraking refers to the capability of a planet's atmosphere to slow an approaching craft. As a craft transfers from one celestial body's sphere of influence to another, it usually is travelling much too fast to maintain a steady orbit. Normally this would be adjusted by firing retrograde at periapsis to stabilize the orbit. On planets with atmosphere, however, this is not entirely necessary; one can save fuel by setting one's periapsis to just slightly inside the atmosphere of the planet and letting air resistance slow the craft to a point where a more stable orbit can be attained, a process referred to as aerocapture. This is an extremely difficult and risky process, and is usually infeasible to do without program add-ons to do the calculations automatically.
Lithobraking
When all else fails, one can always depend on a good chunk of planet to slow a craft's descent. Doing so is often accompanied by rapid spectacular disassembly, and may void your Kerbals' warranties.
References
Joystiq - "The atypical story of Kerbal Space Program's indie flight to success"