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'Sail To The Moon' was written for Thom's son Noah, who was then still under a year old. The song feels like it's related to 'Pyramid Song', in the sense that it shares the overall atmosphere, the tricky time signatures, the prominent use of piano, and features a lyrical connection to the line "a moon full of stars and astral cars" from 'Pyramid Song'. The whole theme of the song is also reminiscent of the 'Pyramid Song' video.
In late 2001 or early 2002, Thom recorded a demo of the song. The band members apparently reacted differently to the demo. While Colin and Phil expressed their excitement over the simple beauty of it, Jonny said the song wasn't properly written at that point yet, and only grew to being something great when the band worked on it during the spring rehearsals.
On July 22nd 2002, the song was premiered in Lisboa, Portugal. The third line of the first verse was slightly different at this point ("and fell into the sun"), and would be developed to its final form for the next show on the 23rd, therefore only the premiere features this difference:

I sailed [to] the moon
I spoke too soon
and fell into the sun

I was dropped from
moonbeams
and sailed on shooting stars

maybe you'll
be president
but know right from wrong

or in the flood
you build an Ark
and sail us to the moon
sail us to the moon
sail to...


It sounds like Thom is singing "I sailed the moon" in the opening line, and perhaps changed it to "I sucked the moon" during the following sessions in september. Maybe fans speculated about the line on message boards and Thom then used what they thought they heard. He said that even during the OK Computer sessions he used lyrics the fans had misheard from low quality live recordings, so maybe this happened again here.
A sheet with several lyrical fragments, written by Thom in september 2002 in L.A. and taken from the 'scrapbook' section of radiohead.com, contains the alternate title 'Brush the Cobwebs out of the Sky':

Thom: "Well, it was written for my little boy, which I decided to sort of say, be honest about, 'cause it's fairly obvious, I suppose. It's just a very personal song, I think. I mean, I got back into singing. But as to where they [the vocals] were placed a lot of the time, and how they sounded, I really left that up to Nigel. I think he was sort of enjoying the fact, that I was just singing normally and not complaining. So he could just get on with it. I think the band did an amazing thing with that, because I never thought we'd get it off the ground, because all the counting and the timing on it is really funny. I mean, I guess you can't hear it, Maybe people can't hear it, but it's just a total nightmare. And everyone's having to count all the way through. 'Ok, this one's 7, this one's 6, this one's 5, bla bla bla'. But it doesn't really sound like that, they made it sound really effortless. So I was really happy about that, I was really proud of that."

Phil: "It's a track that we'd had quite a bit of difficulty arranging, 'cause we can't count beyond 4. But it's just one of those things that.. over to you Colin, on that one."

Colin: "What my brother Jonny says about it is, there are two kinds of songs we were working on with Thom. There are the ones which are sort of alright, and you do something that's really good. And then there's the ones like 'Sail To The Moon', that, when you hear the demo of it, you could just put that on the record and everyone would swoon. And it's a real case of 'don't walk on the grass, don't step on the flowers' when you're playing it. So you really just try and like play as little as possible to get in the way with the tracks, cause it's such a delicate sort of thing, such a beautiful thing. And it's great. And of course it's got like great James Bond sort of Moonraker vibe to it. When they switch the gravity machine off in the studio and everyone's floating around."

Phil: "I mean, it's a stunning song. As with so much of this record, I think Thom's voice has really been outstanding, being a real feature. And on the CDs, that he distributed amongst us before we actually started rehearsing, I think that was one of the stand-out songs, really. I think it's quite a good indication of where his head was at during this recording. 'Cause I mean, to actually give those kinds of performances you need to be very relaxed and very confident in what you're doing."
Thom: "That was written in five minutes. That's a love song, I think it's a bit lovely. There's a lot of that- about responsibility. Lots of looking to the future and seeing fuck all. That's probably a very good reason for people not to be interested in this record. If they don't want to hear that atmosphere I think they should go and buy something else. A general fear of the future, that it's being jeopardised, that it's difficult to do very much about, because things have been set in motion that seem unstoppable."
Thom: "It's a really hopeful song, and… quite personal, and that's about all I can say about it, really. 'Brush the cobwebs out of the sky' - that's from somewhere, but I can't remember… Oh yes, it's from 'Bagpuss'. I think it's one of those amazing Oliver Postgate songs, story things. I'm not sure."
Jonny: "For every song like 'I Will,' which arrived fully formed and was immediately perfect, there are songs like 'Sail to the Moon,' which weren't great. I'm not being rude, but 'Sail to the Moon' wasn't very well-written, and it had different chords and only half an idea. It only came together after the whole band worked on it and figured out how the structures should be, and Phil had some insight on how the song could be arranged. And then it became just about the best song on the record."
On March 30th 2003, the rough mix of the song leaked and it represents the state of work from February. This version is almost identical to the released version, but features a slightly different, longer ending:

On June 5th 2003, this clip of 'Sail to the Moon' was filmed from Jonny's corner on stage at the MTV $2 Bill show at the Beacon Theatre in New York City:
'Sail to the Moon' wasn't performed during the second half of touring for In Rainbows.
On November 28th 2008, Thom posted a piece called 'sailtothechop' on his page at w.a.s.t.e. central. It seems to be based on drum, bass and vocal tracks recorded for 'Sail to the Moon', but it's a bit hard to tell. At least the title suggests that that's what Thom is playing with:

Sailtothechop by CitizenInsane;