The discussion explores the hypothetical scenario of two identical Earth-like planets positioned opposite each other across the sun and whether they would eventually coalesce. It concludes that while the solar system is not entirely stable, the likelihood of the two planets colliding is extremely low due to their orbital dynamics, which would keep them in trojan and horseshoe orbits. Additionally, external influences from the Oort Cloud or other celestial bodies are not significant enough to disrupt their paths. The formation of planets in the solar system suggests that they developed singularly, indicating that multiple identical planets would not coexist in the same orbit. Overall, the consensus is that while theoretically possible, the coalescence of two identical planets is highly unlikely.