Captain Kidd's ship sails through the Terrestrial, interplanetary and Martian atmospheres down to the surface of Mars where the inhabitants, for a change, are not humanoid but crab-like. (We know that we will get Martians but not what they will be like.)
We are not unfamiliar with interplanetary atmospheres. A breathable atmosphere stretches between planets with a common orbit in an ERB work and Larry Niven's Smoke Ring is a torus of breathable gasses encircling a star at a planetary distance. However, Levine's Solar atmosphere requires different laws of gravity. Thus, this story about an alternative Mars also presents an alternative history and cosmology. The cosmology could be the premise of another themed anthology.
If Poul Anderson had contributed to such an anthology, then I would expect his story to outline the alternative laws of physics enabling the Solar gravitational field to hold a breathable atmosphere enclosing the particular planetary atmospheres. Anderson might also have presented a natural philosopher speculating about an alternative universe where the planets were instead separated by the Lucretian void. Anderson's vast corpus of works enables us to speculate about how he might have contributed to later trends in sf.