Final answer:
The spaceship is likely headed towards Mars, as the topographical and geographical clues such as local 8 km peaks, a massive core, little tectonic activity, and heat align with known characteristics of Mars.
Step-by-step explanation:
Based on the provided clues, such as a topographical map showing local peaks with an altitude of about 8 km, valleys that are not incredibly deep, little to no plate movement, a massive core, and a distinct heat radiating, it is likely that the spaceship is headed towards Mars. Mars is known for its large volcanic features, like Olympus Mons, which is the tallest volcano and mountain in the solar system at approximately 22 km high. Although the 8 km peak seen in the topographical map may not be Olympus Mons itself, it does suggest a Martian-like terrain. The absence of significant plate tectonics aligns with current scientific understanding of Mars, and the heat could be due to atmospheric conditions or the ship's approach towards the planet. Mars has been extensively mapped, displaying a range of geographical features, including highland areas, volcanic plains, and a monumental elevation range, which indicates that other peaks could be higher than the one observed. Coupled with the known reddish hue of Mars due to iron oxides, this fits the information provided.