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------------ 2750 - LAGRANGE POINTS - in space travel?
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- Let’s say you want to put a 4,000 pound spacecraft on the Moon. How much would it cost? The going rate is $250,000 per pound. That brings the cost to $1,000,000,000. It takes only 3 days to travel to the Moon, but, $1 billion is pretty expensive for the trip. It is 250,000 miles to get there traveling at 7,200 miles per hour it takes 35 hours. That is only 1 ½ days. Right, but the trip does not go in a straight line.
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- The trip starts with a launch into Earth orbit. Then, to escape this orbit and escape the Earth’s gravity rockets are fired to reach the speed of 7,200 miles per hour ( 2 miles per second).
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- When the spacecraft gets to the Moon the process has to be reversed. The ship turns itself around and fires its rockets to slow down and get captured by the Moon’s gravity. This slow-down maneuver alone costs $130,000,000 in fuel.
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- The whole mission is simple to calculate for astronomers. It can be done on a pocket calculator. And, it has worked successfully several times. The disadvantage, it is expensive. How can we make the trip and not cost so much?
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- Using more supplicated mathematics it should be possible to define a trajectory that continually surfs the gravitational flows between the Earth and the Moon. If we get the right trajectory we should be able to coast into orbit around the Moon. Theoretically there should be no need to even use reverse thrusters to get into Moon orbit.
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- After the launch into Earth orbit the spaceship slowly spirals out using a low continuous thrust. The spiral orbit continues out until it reaches a gravitational tug from the Moon. Once there the Moon will pull the ship into orbit.
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- The real trick in the calculation is when the gravity of Earth and the gravity of the Moon cancel out. Mathematically this calculation becomes one of “chaos theory” for a “3-body problem“. ( Earth, Moon, and spacecraft). The slightest nudge in any direction can amplify the trajectory tremendously.
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- In addition to the math getting difficult the time it takes extends to a 2 year trip. Compared to a 3 day trip this cheap trip may be too cheap. NASA said we like the math, thanks, but no thanks.
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- Then a Japan launch of an unmanned spacecraft ran awry. One vehicle was a relay station for the trip to the Moon. The other craft was supposed to fly to the Moon, but, it lost radio contact and left the mission. The relay station had very little fuel. NASA needed a way to salvage the mission.
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- The mathematics brought in another character, the Sun. Working backwards from the Moon orbit they bound a trajectory using the Sun’s gravity that was only 1 million miles away from the relay station.
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- Now, the math had a “4-body problem” to solve with 3 boundaries of chaos theory. The idea still worked. The Spacecraft slowly worked its way out to the Earth-Sun boundary. Then, with a little bit of fuel nudged the rocket toward the Earth-Moon Boundary. Another little nudge and off to the Moon. The Japanese spacecraft “Hiten” safely arrived at Moon October 2, 1991 after a 5 month trajectory. It was all done with the math and minimum use of fuel.
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- Now with this astonishing success, astronomers are looking at navigating the entire Solar System by surfing on the gravitational boundaries between the planets. It takes a lot of math but the trade off can be worth the effort in making the mission possible.
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- The gravity boundaries are called “ Lagrangian points”, Joseph-Louis Lagrange (1736 - 1813). Like trash collecting in the currents meeting in the Pacific Ocean, there are asteroids and space junk collecting in the gravity boundaries.
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- They are called “Trojan asteroids” and they follow the planets around in their orbits. The Sun-Earth boundary is 930,000 miles from Earth. The Earth-Moon boundary is 38,200 miles from the Moon.
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- That is how the math can make new space missions possible minimizing the fuel needed to be carried.
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- May 31, 2020 1143 2750
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--------------------- Sunday, May 31, 2020 -------------------------
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