A Spanish entrepreneur wants to give you a glimpse of the black expanse of space and the curvature of the earth from a most unusual vantage point — a balloon.

José Mariano López-Urdiales, the founder of zero2infinity, is offering what he calls the “near-space” experience of viewing the planet and the space beyond it from 36 km [22 miles] above the earth. He hopes to have the first passengers aloft in the near-space vehicle called a “bloon” — the company doesn’t appear to be big on capital letters — by the middle of this decade.

That altitude is a long ways from the height of more than 100 km...