Paradox

Poul Anderson, "A Little Knowledge" IN Anderson, David Falkayn: Star Trader (Riverdale, NY, 2010), pp. 599-630.

A subjovian planet should retain a large quantity of hydrogen and helium. However, the extra-solar subjovian, Paradox, captured an asteroid which became a moon with an eccentric orbit. Passing through the Paradoxical atmosphere, the moon blew large numbers of lighter molecules into space before breaking up and crashing onto the surface. Metallic atoms spread across the planet might have combined with any remaining hydrogen. The atmosphere became early terrestroid: carbon dioxide, water vapor, methane, ammonia etc, except for more helium than usual. Life and photosynthesis began, generating an oxynitrogen atmosphere. Despite fifteen Terrestrial masses, Paradox is solid with a humanly breathable atmosphere.

Another large planet that loses its hydrogen and helium, gaining an inhabited solid surface, is Ramnu. (Scroll down.)

Under The Moons Of Vanessa

"Norman Bean" was ERB's pen name. "Under The Moons of Mars" by Norman Bean was republished as A Princess Of Mars by Edgar Rice Burroughs.

In the following passage, the planet Vanessa seems to me to reflect ERB's Mars/Barsoom:

"Dinner was served in the roof turret, which had a view like being outdoors. By night Vanessa took on beauty. Both moons were aloft, small and swift, turning the land to a fantasy of dim silver and moving shadows. The lake gleamed, the native towers looked like giant blossoms. Overhead, the sky was splendid with stars..."
-"A Sun Invisible," IV, p. 289.

Over dinner, Falkayn mentions and explains rogue planets. They will be crucial to the plot.

Cynthia And Woden

Cynthia
"Oh, treetop highways under the golden-red sun of Cynthia!"
-Poul Anderson, "How To Be Ethnic In One Easy Lesson" IN Anderson, The Van Rijn Method (Riverdale, NY, 2009), pp. 175-197 AT p. 183.

"Oh, to be back on Ta-chih-chien-pi, Lifehome-under-Sky, again in a treetop house among forest perfumes!"
-Poul Anderson, "The Trouble Twisters" IN Anderson, David Falkayn: Star Trader (Riverdale, NY, 2010), pp. 77-208 AT VI, p. 138.

"Ta-chih-chien-pi - 02 Eridani A II or Cynthia to humans - felt even more distant than it was, warm ruddy sunlight and rustling leaves around treetop homes lost in time as well as space."
-Poul Anderson, "Day of Burning" IN David Falkayn: Star Trader, pp. 209-272 AT pp. 224-225.

"'Light across a sea of leaves, but down below full of shapes and mysteries, a cry of color on wings and petals, a glen where a rill comes joyful -...'"
-Poul Anderson, Mirkheim IN Anderson, Rise Of The Terran Empire (Riverdale, NY, 2011), pp. 1-291 AT XXI, p. 289.

Woden
"Adzel's thoughts turned sentimentally back to Woden, the dear broad plains under the brilliant sun, where his hooves spurned kilometers..."
"The Trouble Twisters," V, p. 132.

"'That wild bright openness where the winds run loose, horizons endlessly before us but also flowers underfoot, a land that that is the living Nirvana -...'"
-Mirkheim, p. 289.

I will quote more about either planet if I find it.

Beauty On Ikananka

"The Trouble Twisters."

Tidal action has forced one hemisphere of the small, eccentrically orbiting, librating planet Ikrananka to face its red dwarf sun but such slow rotation generates a weak magnetic field so that the planet retains an atmosphere although most of its water has frozen on the cold side making the warm side a slowly deteriorating desert whose inhabitants, struggling for survival in their season-less, rhythm-less environment, regard nature as hostile, believing in demons but not in gods, whereas dwellers on the edge of the Twilight Zone with rain, snow, day, night and constellations, more conventionally believe in an annually dying and rising god and a single devil whose power can be neutralized. The latter are easier to trade with.
-copied from here.

As Falkayn and his Ershoka captors approach, then enter, the Twilight Zone:

they leave the wasteland;
the country grows greener;
mosslike growth carpets the foothills;
brooks become audible;
the wind sways "...forests of plumed stalks..." (p. 156);
mountains glow in the red light;
there are "...snow peaks and glaciers..." (ibid.);
stars and a planet become visible;
slopes reflect heat;
ice melts;
rivers foam down cliffs;
the royal purple sky blackens;
the city, Rangakora, occupies a plateau above a mountain pass;
a road joins mountaintops, city and green, gold, glimmering, misty sea;
above the city, rainbows crown a waterfall;
then forest hides the river as it flows near the city wall;
Falkayn is impressed;
so am I.