As a response to popular request (actually, no one asked except Jon Goff), I’ve cleaned up and uploaded my spreadsheet.
Other than the astonishing results themselves, the only thing that makes me suspicious is that the total delta V required for the mission with the stop for gas is less than that required for the direct trip (about seven km/s for the latter and about six for the former). But I’ve looked at it multiple times, and don’t see anything wrong with what I did. I’m guessing that, if this is right, it has something to do with the oddities of patched conics. But it would be nice to get some more eyes looking at the problem.
[Update a few minutes later]
Don’t waste too much time looking at that. I just noticed some problems. I’ll update when I’ve fixed.
[Update a few minutes later]
OK, I’ve uploaded a new version. The good news is that I found the problem, and the total delta V is now more for the trip with the gas stop than without (which it seemed it should have been). It’s now about four and a half kilometers per second for the direct case, and about six for the gas stop. The bad news is that the advantage has dropped significantly. The propellant ratio, rather than ten and more than twenty for the EML1 and LEO cases without refueling, is now more like three and five. Still, it’s a significant improvement.
I should note that this is an excellent example of a need to have a feel for the numbers, and not just trust what comes out of a computer (as I fear too many young people do these days). If you don’t know intuitively proper orders of magnitude, or recognize suspicious results, you’re likely to make a lot of errors when doing complex calculations, particularly if you are operating in an environment of confirmation bias (I really, really liked the first, incorrect results). I’m looking at you, climate modelers…
[Update a few minutes later]
One more update to the spreadsheet. I noticed that in fixing the calculations, my delta Vs had become unbalanced, so I adjusted the gas station orbit slightly to rebalance them. The new orbit is 1.256 AU.
out. David Brooks describes the premises.