MAHIA PENINSULA, New Zealand—The next generation of satellite executives dream of firing a rocket a week into the skies. But they’re running up against an unusual problem for star trekkers. A lack of space.

“We went to all the launch ranges in America,” said Peter Beck, a wiry-haired engineer who a decade ago founded Calif.-based aerospace company Rocket Lab. “They just didn’t allow the frequency that we needed in order to make space accessible for everybody.”

...