The key to writing a song about space in the 1970s required two crucial elements: atmospheric synthesizers and slide guitars. The best example (perhaps part of John and Taupin's inspiration for "Rocket Man") is David Bowie's 1969 single "Space Odditiy." Check out how clear the use of those effects is. When Major Tom, the astronaut in the song, lifts off, a slide guitar effect comes in, perhaps as a sort of "sonic boom" effect. After that, when Major Tom is actually in space, the song contains a synthesized string effect. The "synth" adds a sort of airy quality to the atmosphere of the song; you might even call it a floating or flying quality.
"Rocket Man" uses the same key sonic elements. The synth effect that leads into, "And all the science..." conveys a futurism with its processed artificial quality. "Rocket Man" really deploys the slide guitar to the best effect, though, using the instrument mainly to mimic atmospheric sounds. With the words, "I'm a rocket man," the slide guitar rolls on up the neck of the guitar, creating a soaring "lift off" effect. In the second verse, a guitar slide, nestled between the lines "In fact [Mars is] as cold as hell, / And there's no one there to raise them if you did," mimics the howling of the wind in a desolate, empty place.
At the same time, the slide guitar creates a more earthly vibe. If you've heard the slide guitar before, it's probably been in country or blues songs. The Allman Brothers, a country rock band of Elton John's era, made legendary use of the slide guitar, for example. So you can also connect the slide guitar effect to a country quality (this is on Honky Château after all) in the music.
That country quality makes sense when you think about the lyrics, which are spoken by a cowboy of a character. But an everyman feel shows up melodically as well. The melody—the way that Elton John sings the lines—has an almost spoken quality in the verses. That spoken quality is a dramatized mimicry of the natural cadence of English-speaking people. You think of this cadence as the meter when you study poetry. Some lines, like the opening "She packed my bags last night preflight," are sung in iambs. An iamb is a metrical foot that consists of a short syllable followed by a long syllable (as in "she packed"). John exaggerates this natural speech pattern in his singing, voicing the longer syllable at a higher pitch in addition to singing it two to three times as long. It's an almost Shakespearian way of singing… but it's important to remember that while we think of Shakespearian verse as ornate and fancy, the iambic meter in which Shakespeare wrote most of his dialogue was intended to mimic natural speech. That same spoken quality is clearly in the melody in "Rocket Man."