MOON
INTRODUCTION
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In September of 1968, the Soviets used their Proton-K rocket to launch Zond 5, a mission that sent the first biological specimens on a circumlunar flight that flew on a free-return trajectory round the Moon before returning safely to Earth with all its biological cargo still in tact. This was a precursor for what the Americans believed would be a lunar orbit mission using humans. Determined to get there first, NASA selected the crew of Apollo 8 that same year to execute such a mission on the first manned flight of the enormous Saturn V rocket. Frank Borman, Jim Lovell, and Bill Anders set out for the Moon in late December of 1968, entering lunar orbit approximately 70 hours later and remaining in orbit for an additional 20. This mission was of great significance, in that the United States proved that humans had the power and navigational technology to get to lunar orbit and return safely. This in turn paved the way for all future Apollo missions destined for the Moon, while also achieving the goal of getting there first.
Lunar MISSION
MISSION ARCHITECTURE
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When engineering such a mission, the basic logistics are not overly complicated. A heavy lift rocket is needed, as is enough food, water, and oxygen (life support) for 3 adult crew members. For example the weight of the Apollo 8 launch vehicle fully loaded was 6,221,823 lbs, only 1.5% of which was actual payload. The rest was the launch vehicle.
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The crew is launched on an elongated elliptical orbit, where it will eventually cross into the lunar sphere of influence. The Moon's gravity takes over and brings the spacecraft closer and faster, until the crew performs an engine burn to slow their orbital velocity into that of a circular orbit. After remaining in orbit for a predetermined time, the crew reignites the engine to thrust the spacecraft back toward Earth.
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PROCEDURE
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1. The spacecraft is launched from Earth and is put into a 185km x 185km parking orbit
2. The spacecraft then uses a one-tangent burn called Trans Lunar Injection (TLI) with a final velocity of over 10.8 km/s, placing it into a highly elliptical orbit around Earth with a semi-major axis of approximately 289,000 km. As the spacecraft gets farther from Earth, its relative velocity will decrease as well.
3. At a distance of 64,374 km from the Moon, the gravity from the Moon becomes stronger than that of the Earth, making the spacecraft "fall" to the Moon on a hyperbolic trajectory.
4. About 15 hours later, the spacecraft performs an orbital maneuver called Lunar Orbit Insertion (LOI), which slows the spacecraft down into an orbit around the Moon with a nominal altitude of 111 km (although the Apollo missions used an elliptical lunar orbit first before circularizing it).
CALCULATIONS
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Let's look at a mission like Gemini VII, which took two crew members (Jim Lovell and Frank Borman) into space for almost 14 days. Their spacecraft had a launch mass of approximately 3670 kg, which contained an adequate amount of consumables and life support for a 2-man crew over a duration of 2 weeks. My calculations show that a Gemini-sized spacecraft (or atleast one of a similar core mass) with added fuel, tanks, engines, and a larger heat shield could be launched on a Falcon Heavy to lunar orbit with 2 humans, and then using it's own propulsion system, execute a burn out of lunar orbit onto trans Earth injection.
I have also put together a more formal written and illustrated outline of this mission in my paper entitled "FH Lunar Mission" which can be downloaded below. In this paper, I breakdown the components that are involved in planning such a mission. I have also included my own calculations for the Falcon Heavy launch vehicle. My calculations prove that this rocket alone provides adequate power to execute the first half of such a mission, atleast getting it's payload to lunar orbit. This begs the question, "How long will it be until we return to the Moon?"
