Awesome choice!
I’ll add:
Frank Black - Places Named After Numbers
Beep Beep - Louis Prima
Fly Me to the Moon - Frank Sinatra
One more I forgot: The Reverse Engineers - Mercury in Retrograde
53 Miles West Of Venus - The B-52’s
Phone Call From The Moon - Adrian Belew
Moon Rocks - Talking Heads
UFO’s, Big Rigs & BBQ - Mojo Nixon
Mr. Spaceman
by The Byrds
A Space Boy Dream by Belle & Sebastian. It’s spoken word - but spoken in a Scottish accent. kewl
“Beautiful Zelda” by the Bonzo Dog Band
Jeff Wayne’s Musical Version of The War of the Worlds.
“Spaceman” by Harry Nilsson
“The Martian Hop” by the Randells
Outta’ Space (Instrumental)
by Billy Preston
Missing
(Amplified Heart CD)
by Everything But The Girl
“Now you’ve disappeared somewhere, like outer space, you’ve found some better place…”
Moon River Andy Williams
Space Cowboy Jamiroquai
Space Cowboy Steve Miller Band
Man on the Moon R.E.M.
Jonathan Coulton’s “Space Doggity”
13 Questions
by Seatrain
We’re On Our Way
by Chris Hodge
Pluto Bjork
Pluto Drive The Creatures
Moonraker Shirley Bassey
Venus Shocking Blue
Any song by Freddie Mercury? The Neptunes?
Neptune’s Call The Duke Spirit
Uranus, the Magician Gustav Holst amongst others (classical)
Uranus Rock Jimi Hendrix
Milky Way Cosmic Gate
Aquarius, Let the Sunshine In The 5th Dimension
Fuck dis shit! You want filk!
F’rinstance, “Fire in the Sky,” by Jordin Kare.
Or “Fly, Columbia!” by Dana Gallagher.
That one has such poignancy, now . . . 
Or, on a lighter note, for ST-TOS fans, Leslie Fish’s classic “Banned from Argo.”
“Planet Claire,” “There’s a Moon in the Sky (Called the Moon),” and “Hallucinating Pluto” – The B-52’s
“Bike Ride to the Moon” – The Dukes of Stratosphear (XTC in psychedelic drag)
“Another Satellite” – XTC
“Interstellar Overdrive” – The Vibrators. A mashup cover of Pink Floyd’s “I.O.” that segues into The Beatles’ “Daytripper”.
“The Third Sun” – Trey Gunn
“Lazy Old Sun” – The Kinks
“Bird Dream of the Olympus Mons” and “Planet of Sound” – Pixies
“Voyage Into Infinity” – Bad Brains. (Okay, that one’s more metaphysical than astronomical, but in a way space = time, right?)
And from Muse: “Shrinking Universe,” “Dead Star,” “Space Dementia,” “Knights of Cydonia,” “Starlight,” and doubtless others. Their fifth LP (The Resistance, due this Sept.) may have a 15-minute space rock song on it. Hey, they don’t call frontman and songwriter Matt Bellamy “Barmy Bellamy” and “Barking Mad Bellamy” for nothing. 
FTR. you can find any of the song I listed at http://listen.grooveshark.com/#
Space Cowboy
Steve Miller Band
Wow, thanks everybody! You guys make up for an improperly aligned telescope!
I can’t wait to check all these songs out–though I have to say, I do already have all the Bowie that’s been mentioned. What can I say, at least it’s an understandable obsession.