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Would the optimal time to launch be when the Moon was on the opposite side of the Earth from the Sun? What direction would be optimal leaving EM-L2, radially away from the moon?

Is the last line of this table a reasonable approximation of the delta-v required? enter image description here

If the launch used the minimal delta-v, and took place in the middle of Moon's umbra, how long would it take to emerge into the sunlight?

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    $\begingroup$ This is a great question! There are many Q&A here for how to calculate or estimate delta-v's for more classical transfer schemes based on a sequence of ellipses, and for low-thrust spirals from circular orbit to infinity (and beyond!) but I don't think we have self-contained answers within the site that explain how to address this kind of problem (libration-point start, end, or both) mathematically, without pointing off-site for the calculation itself. $\endgroup$ – uhoh Apr 16 at 3:14
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    $\begingroup$ @uhoh You said, "without pointing off-site for the calculations." I assumed you meant websites off of Stack Exchange. No matter. I didn't know about Pod Bay, I will check it out. Thanks. $\endgroup$ – Bob516 Apr 17 at 14:50
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    $\begingroup$ Oh, some users here answer questions with "the answer is in post x on my blog, where I have an excel file..." I meant that It would be great someone would answer with a real, proper Stack Exchange answer within this site. There is one blog though that may be of particular interest to you hopsblog-hop.blogspot.com the author is also a user here. @HopDavid. You can search the blog for key words, and search @HopDavid's questions and answers. $\endgroup$ – uhoh Apr 17 at 15:01
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    $\begingroup$ I just ran across an example of an "off-site answer" space.stackexchange.com/a/5316/12102 It's a perfectly fine answer, but you need to go off site and then run a spreadsheet in your computer to get the goodies. $\endgroup$ – uhoh Apr 18 at 0:40
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    $\begingroup$ no, you don't need to run anything. I was just showing that as an example of what I meant by an "off-site answer". It's not an answer to your main question, it just addresses the question you asked in this comment, nothing more. $\endgroup$ – uhoh Apr 19 at 0:20

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