# How much delta v does it take to get to the Sun-Earth Lagrange 3 point?

How much delta v does it take to get to the Sun-Earth Lagrange 3 point?

Also, Would higher delta-v allow a craft to get there much quicker?

Would two hohmann transfer orbits be the most efficient path from Earth to L3?

How much delta-v per year would be needed for station keeping?

For a transfer using a minimum of propellant, the required $\Delta v$ is very close to Earth's escape velocity. At only a very small $v_{inf}$, you can still have a solar orbit with an orbital period slightly less than a year, making you slowly crawl ahead of Earth, eventually reaching L3, where only a close to zero $\Delta v$ burn is needed to halt. This route however is very time consuming.

If you are willing to spend more $\Delta v$, the transfer can indeed be made quicker. For non-brachistocrone transfers, the fastest route is to enter an orbit with a period of 1/2 year and a periapse of 0.26 AU, entering L3 after only one revolution. This requires a $v_{inf}$ of $10.65 km/s$, that must be paid in full at L3, and also costing a $\Delta v$ of a mere $4.26km/s$ on top of Earth escape velocity.

Total cost: $14.9 km/s$ + escape velocity
Transfer time: 1/2 year

A little less costly is entering an orbit with a period of one and a half year, reaching an apoapsis of 1.62 AU. That increases the transfer time three times, but reduces the $v_{inf}$ to $3.34km/s$.

Total cost: $3.8 km/s$ + escape velocity
Transfer time: 1 + 1/2 year

Add more revolutions to taste, trading a $\Delta v$ reduction for a longer transfer time. For instance, two revolutions in a 1.25 year period orbit further reduces the $v_{vinf}$ to $2.0km/s$, and the total $\Delta v$ to $2.18km/s$ + escape velocity, at a transfer time of 2 + 1/2 year.

• Brachistochrone - yay! I learned a new word today. – uhoh May 31 '16 at 3:51