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The Physics of Space Travel and Orbital Maneuvers

This capstone examines the physics associated with interplanetary travel, orbital maneuvers, landing on the Moon, and more. Demonstrations are done with the game Kerbal Space Program. "Kerbal Space Program is a realistic space simulator that allows players to plan, build, launch, pilot, and experiment with their own spacecraft."

Wikipedia Article On KSP

KSP Wiki Page

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Basic Terms

Apoapsis: The point of an orbit in which an orbiting mass is farthest from its parent body

Periapsis: The point of an orbit in which an orbiting mass is closest to its parent body

Retrograde: The direction opposite of motion

Transfer orbits: An orbit used to change the altitude of another, original orbit

*The terms apoapsis and periapsis are subject to change based on the parent body. For example, an object orbiting the Earth would have an apogee and a perigee. Similarly, an object orbiting the sun would have an aphelion and a perihelion.*

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The diagram below explains the mathematics and manuevers behind the Hohmann transfer

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We can use these equations to raise the orbit of a satellite from 100 km to 200 km.

The parent body is the planet Kerbin in Kerbal Space Program. It has a mass of and an equatorial radius of .      Both values are positive because we are raising our orbit. Both engine impulses will be in the prograde direction.

The animation below demonstrates the previous calculations. The left half of the image represents (the first burn) and the initiation of the transfer orbit. This phase puts the craft into an elliptic orbit (see the red curve of the diagram above) with a perikee of 100 km and an apokee of 200 km. The right half of the image represents (the second burn) and the circularization phase of the orbit (see the purple curve in the diagram above).

Notice the orbital speed, apoapsis, and periapsis values for each phase. The difference in orbital speeds before and after each burn should be almost exactly the 's calculated above. (Any inaccuracies are primarily due to piloting error.)

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