Final answer:
To estimate the maximum height of mountains on a planet with double the gravity of Earth, we recognize that increased gravity leads to a higher rate of erosion and stronger pull on mountain material, suggesting that such mountains would be notably shorter than Earth's. The exact heights are dependent on multiple factors but can be expected to be significantly lower than Earth's highest peaks.
Step-by-step explanation:
To estimate the maximum height of mountains on a hypothetical planet with twice the surface gravity of Earth, we can consider the concept of scale height. The scale height is a measure of how quickly atmospheric pressure decreases with altitude and is inversely proportional to the planet's gravity. For Earth, the average mountain height is limited by erosional processes and the strength of the materials composing mountains, with the tallest peak, Mount Everest, being about 8.848 km high.
Given the stronger gravity on the hypothetical planet, the mountains would likely be shorter, as the increased gravitational force would result in a higher rate of erosion and a stronger pull on the mountain's material, leading to an increased tendency for the material to collapse under its own weight.
Without a specific formula to calculate the mountain height relative to Earth's, we can make a qualitative estimate that the mountains on a planet with double the gravity of Earth could be significantly shorter than those on Earth because of these factors. The exact heights would depend on many other variables, such as tectonic activity, mountain composition, and erosional processes.