Elon Musk’s Space Exploration Technologies Corp. is raising another $500 million in funding amid internal questions about the viability of an internet-via-satellite business considered key to the company’s growth.

The fundraising, outlined in a regulatory filing last week, comes four months after a similarly sized deal for the closely held company, which is trying to accelerate development of its ambitious satellite venture, called Starlink, along with work on various rocket and spacecraft projects.

Mr....