ViaSat Inc. is betting that a pair of behemoth spacecraft operating far from earth can provide better Internet connectivity to far-flung regions than a swarm of small, low-altitude satellites envisioned by its rivals.

Over the years, various traditional satellite-broadband initiatives have faltered either because steep charges discouraged widespread use, or in other cases because customers were turned off by what they considered frustratingly slow Internet or video links. This has prompted many airlines to offer airborne...