Heinlein, one of the very greatest sf authors, fortunately set many of his tales in the Old Solar System. The list below is not exhaustive. Heinlein's Future History stories are collected in The Past Through Tomorrow.
Poetic grandeur in Heinlein is not to be found in word or line or paragraph but rather in his work as a whole. The breadth of his knowledge, his fascination with the way things work, his flair for narrative and his prolific output remind one of Poul Anderson, though Anderson is more the scientist and Heinlein more the engineer. Both combine technical knowledge with romantic vision; however, unlike Anderson and the equally scientific (and even more poetical) Arthur C Clarke, Heinlein can be criticized for not conveying a sense of "place" in his planetary scenes: for example if you compare The Moon is a Harsh Mistress (an excellent yarn, a rousing tale of revolution in a lunar colony) with Clarke's Earthlight, you feel Heinlein's Moon is a mere prop, compared with Clarke's wonderful evocation.
But this stricture does not apply to Red Planet, which is a glorious success in any terms, one of the best evocations of Mars ever written.
Plying the space-lanes: The Green Hills of Earth
Venus: Space Cadet; Between Planets; Logic of Empire
Earth: The Man Who Sold The Moon (for the Old Space Program); sundry Future History stories
The Moon: many of his Future History short stories set on a colonized Moon; also, the novel The Moon is a Harsh Mistress.
Arthur C Clarke, Earthlight (1955); Robert A Heinlein, Between Planets (1951);Farmer in the Sky (1950); "Logic of Empire" (Astounding Science Fiction, March 1941);The Man Who Sold The Moon (written 1949, published 1951); The Moon is a Harsh Mistress (1966);Red Planet (1949); Space Cadet (1948); Double Star (1956); The Past Through Tomorrow (1967)
Logic of Empire is discussed by Dylan Jeninga in the Travelogue page, Slaves of Venus.
D D Harriman's longing for the Moon in Requiem is discussed in the Diary,
Cathexis in C S Lewis and Heinlein.