Not at all a poor use of a preposition. Perhaps it's somewhat idiomatic, but into is a commonly-used preposition when talking about rockets and missles, whether those are being fired into space, into the ocean, or into enemy territory.
Commercial and military satellites are frequently fired by rockets into orbit
Source: Peter P. Wegener, What Makes Airplanes Fly?: History, Science, and Applications of Aerodynamics, 1997
We build huge bridges and concrete dams and send mammoth rockets into space
Source: E.J. Hearn, Mechanics of Materials Volume 1, 1997
Von Braun recognized that shooting rockets into the heavens could arouse fear and religious anxiety
Source: James Gilbert, Redeeming Culture: American Religion in an Age of Science, 1997
Four Turkish F-100 fighter planes buzzed concentrations of National Guardsmen and fired rockets into the sea
Source: Andrew Faulds, 1988
Lebanese terrorist groups lobbed rockets into Israel's northern settlements and tried to penetrate the border
Source: Ira Sharkansky, Policy Making in Israel: Routines for Simple Problems and Coping with the Complex, 1997
Against von Braun's fervent hope that this would not happen, German military forces launched more than thirteen hundred V-2s at targets in England, and more than sixteen hundred V-2s into Belgium and France
Source: Stuhlinger & Ordway, Wernher von Braun, Crusader for Space, 1994
The preposition at is common when specifying a particular target, but into is frequently used to indicate that a missile or rocket landed inside a particular region or country.