Final answer:
A 1000 kg spaceship would have the same weight on Planet X as it does on Earth because Planet X has the same gravitational acceleration (g = 9.8 m/s²) as Earth, resulting in the same force of gravity acting on the spaceship's mass.
Step-by-step explanation:
The question concerns where a 1000 kg spaceship would weigh the same as it does on Earth. Weight is the force of gravity acting on an object's mass, which can be calculated using the equation weight = mass × acceleration due to gravity (g). The acceleration due to gravity on Earth is 9.8 m/s². Therefore, for the spaceship to have the same weight elsewhere, it would need to be on a planet with the same gravitational acceleration.
Answer choices A, B, and C are incorrect because Mars and the Moon have different gravitational accelerations (3.6 m/s² and 1.6 m/s² respectively), and the spaceship's mass remains the same everywhere, though its weight will change depending on the local gravity. As gravity varies, so does weight.
The correct answer is D. Planet X (g=9.8) because it has the same gravitational acceleration as Earth. On Planet X, the 1000 kg spaceship would weigh the same as it does on Earth.