What type of a maneuver would you need to perform to transfer from Earth to L5?

An object in L5 would be 60 degrees behind the Earth on the same orbit, traveling at the same speed as Earth.|||What you need to do is slow down and get into a higher orbit so that your period is 1 year and 2 months. You do this by firing your rockets in the same direction as earth's orbit and go into an ellipse. After one orbit you are exactly 60 degrees behind the earth. You then fire your rockets once more and slow down. Your are now at L5.





This is the least fuel to get L5 within a 1year and 2 months. If you had more time, you could save even more energy. If you had to get there fast, I could draw you up an orbit that would get you in place in 8 months, but the cost would be higher. It would be unresonably costly to get there in less than 8 months





Here is a how to drawing.: http://i278.photobucket.com/albums/kk114…





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For anyone who doesn't understand orbital mechanics, in my example the earth would travel 1 orbit plus 60 degrees in one year and 2 months while the statellite would only travel 1 orbit. It would therefore be 60 degrees behind the earth and in L5.





There are plenty of other orbits you could plot to accomplish this goal. Your goal is to end up 60 degrees behind the earth. (You do this by changing the thrust and the angular direction the satellite leave earth's gravitational field). Any less than 1 year and two months would take more energy and any more would take less energy. What I plotted was simplist way to understand what needs to be done|||short time but go slower overall. ;-)

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|||By slow down, I meant slowing down your angular rotation rate and increasing your period. Of course you do it, as you point out, by paradoxically increasing your speed to get into a higher orbit. You average speed in the higher orbit is slower than in earth's orbit. So you go faster for a ...

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|||L4 and L5 Lagrangian points are only stable when the largest of the three bodies is at least 24.96 times as massive as the the intermediate body. The sun-earth and earth-moon systems satisfy this condition. The sun's gravitational influence tends to destabilize the L4 and L5 points of the earth-moon system you are asking about smearing them into "volumes of space". As to the exact maneuver depends on where you start and what we are talking about as a vehicle. Check the dude below for from LEO by shuttle orbiter.





If ETs were real ("if" being the operative word), L4 %26amp; L5 would be sweet spots for parking probes for long-term study of the earth.|||does this helps ?





http://www.nas.nasa.gov/About/Education/…





am not astronomer only a dumb engineerng final year student :(|||You would need to do an ejection burn, in retrograde direction of Earth (also called inbound), with only slightly more eccentricity than one. This puts you safely at the border of Earths gravity field, with a little bit of excess velocity which you have to counter when you reach the L5.





An eccentricity of slightly less than 1 would not be enough - you would fall back to Earth before reaching the Lagrange point.|||Just my thinking on the matter... I've never bothered with the mathematics of it, but... It could be done without sending the object into a retrograde orbit. I'm not familiar with the physics involved mathematically, but an artificial satellite in LEO, if it were to make the proper propulsion adjustments, could still easilly "fall behind" the earth, if it were to orbit the sun (prograde) at a greater distance than 1AU. Once the L5 point "catches up" to this satellite (or very nearly so), a new adjustment in it's trajectory to put it back in the earth's orbit around the sun in the L5 point would be possible.





As the first answerer stated, these points are not stable.