On Mars, the difference in elevation between the highest point (the summit of Olympus Mons) and the lowest point (the bottom of the Hellas Planitia basin) is \(30 \mathrm{~km}\). On Earth, the corresponding elevation difference (from the peak of Mount Everest to the bottom of the deepest ocean) is only \(20 \mathrm{~km}\). Discuss why the maximum elevation difference is so much greater on Mars.

The study of Mars topography reveals a planet with striking surface features that tell a story of its geological past. Olympus Mons stands as a colossal shield volcano, measuring an impressive 22 km in height, much taller than Mount Everest, Earth's highest peak at approximately 8.848 km. Hellas Planitia, on the other hand, is a massive impact crater that dips about 8 km below Mars' datum (the average elevation level from which elevation is measured).

The significant difference in elevation between these two landmarks on Mars is a clear indication of the diverse and dramatic Martian landscape. The vast height of Olympus Mons is supported by Mars’ lower gravity, which at approximately 38% of Earth’s, exerts less force on geological structures. This enables features on Mars to potentially reach greater heights and depths than those on Earth before the materials comprising them succumb to gravitational collapse.

Mars, with its stark topographical contrasts, poses fascinating questions about its historical geological dynamics. Understanding the history encoded in its topography could provide insights into the planet's past climate and the possibility that it may have once harbored life.

Gravitation plays a key role in determining the structural integrity of a planet's surface features. On rocky planets like Earth and Mars, it dictates how tall mountains can grow before the rocks at their bases can no longer support the weight above. With Mars having lower gravitational pull, geological formations do not experience the same degree of downward force as they would on Earth.

This concept of gravity's effect on elevation is essential to understanding why Olympus Mons can tower to such commanding heights compared to any mountain on Earth. A lower gravity not only means that mountains can grow higher, but erosion processes are also less intense, allowing surface features to retain their shape and elevation over much longer timescales. As explained in the exercise improvement, the gravitational forces also impact how deep features like valleys and basins can become, given the lower pull allowing greater retention of depth and definition in these features on Mars.

The tectonic activity of a planet is a reflection of its internal dynamism—manifesting as volcanic eruptions, the shifting and folding of crust, and the creation of mountains and rift valleys. Earth is a hub of tectonic activity, with its surface divided into moving plates that contribute to the continuous reshaping of its topography. In contrast, Mars appears to lack similar active plate tectonics at present.

The relative tectonic inactivity on Mars allows for its giant structures to remain unaltered for eons. Unlike on Earth, where the constant churning of the surface can decrease the lifespan of large geological structures, on Mars, landmarks like Olympus Mons and Hellas Planitia are free from such a cycle of destruction and renewal. Due to this tectonic stagnation, erosion and sediment deposition are the primary forces that gradually modify the Martian surface, causing its topography to be more static and maintaining extreme elevation differences over geological time periods.