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Orbital Mechanics, The Liftoff, The Turnover, The Retrograde Burn

Here's a nice graphic illustrating some basic maneuvers in orbital mechanics:

As far as I know, the first description of rocket-powered space flight, a rocket-assisted takeoff into the heavens occurs in A Voyage to the Moon, by Cyrano de Bergerac, published in 1657:

I made a machine which I fancied might carry me up as high as I pleased, so that nothing seeming to be wanting to it, I placed myself within, and from the Top of a Rock threw my self into the Air: But because I had not taken my measures right, I fell with a sosh into the Valley below...

...Then having taken a dram of Cordial Waters to strengthen my Heart, I went back to look for my Machine; but I could not find it, for some Soldiers, that had been sent into the Forest... had carried it into the Fort. Where after a great deal of guessing what it might be, when they had discovered the invention of the Spring, some said, that a good many Fire-Works should be fastened to it, because their force carrying them up on high, and their Force carrying them up on high, and the Machine playing its large Wings, no Body but would take it for a fiery dragon... I ran to the Souldier that was giving Fire to it... and in great rage threw my self into my Machine, that I might undo the Fire-Works that they had stuck about it; but I came too late, for hardly were both my Feet within, then whip, away went I up in a Cloud.

...as soon as the Flame had devoured one tier of Squibs, which were ranked six by six, by means of a Train that reached every half-dozen, another tier went off, and then another...

The first description of the turnover move that positions a rocket's engines to retard its forward motion, as far as science fiction fans are concerned, comes from Skylark of Space (1928) by EE 'Doc' Smith, who described negative acceleration with the associated maneuver thusly:

"If that misguided mutt thinks he can pull off a stunt like that and get away with it, he's got another think coming," asserted Seaton, after making a reading on the other car after several days of the flight. "He went off half-cocked this time, for sure, and we've got him foul. We'd better put on some negative pretty soon hadn't we, Mart? Only a little over a hundred light-years now."

Crane nodded agreement and Seaton continued:

"It'll take as long to stop, of course, as it has taken to get out here, and if we ram them—GOOD NIGHT! Let's figure it out as nearly as we can."

They calculated their own speed, and that of the other vessel, as shown by the various readings taken, and applied just enough negative acceleration to slow the Skylark down to the speed of the other space-car when they should come up with it. They smiled at each other in recognition of the perfect working of the mechanism when the huge vessel had spun, with a sickening lurch, through a complete half-circle, the instant the power was reversed. Each knew that they were actually traveling in a direction that to them seemed "down," but with a constantly diminishing velocity, even though they seemed to be still going "up" with an increasing speed.

Here's another illustration and description from Buck Rogers, 2431, published 10-Sep-1931:

(Interplanetary Turn Over from 'Buck Rogers, 2431' by Nowlan and Calkin)

Compare to turnover from Off the Beam (1944) by George O. Smith and skew-flip turnover from Have Space Suit - Will Travel (1958) by Robert Heinlein.

If you want to come to a full stop on the surface of a planet, you're going to need retro-rockets, which according to NASA were invented by Jules Verne in From the Earth to the Moon (1867).

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