The Story of Topography

NEAR Science Update

September 07, 2000

While we may get excited about topography for many reasons, one of them is that topography provides important clues to the structure and evolution of an object. Topography deals with the irregularity of an object's shape, meaning the extent to which the shape differs from that of simple solids like the sphere or the ellipsoid. What is so special about these particular shapes? A fluid body that is not rotating will be spherical because of its own gravity. If it is fluid, it has no strength, so it resists pure compression but not other types of deformation. If a hill forms on a fluid body, there is no strength to support the hill, and it spreads out at the bottom, decreases in height and disappears. If a valley forms in such a body, the walls collapse, and again the body returns toward a spherical shape.

However, if a fluid body rotates, then centrifugal force distorts the shape from spherical to ellipsoidal. The faster the rotation is, the greater the distortion. In the case of large objects like the Earth and the Moon, the crushing force of gravity dominates even the strength of rocks, and gravity forces the shape of the Earth to be almost spherical, although Earth's equatorial radius of 6378 km is about 21 km larger than its polar radius because of centrifugal distortion. However, the gravity small bodies like asteroids is much weaker and is not able to enforce a nearly spherical shape. We find that objects larger than a few hundred kilometers in diameter are nearly spherical, whereas smaller objects like Eros are irregular. An object the size of the Earth could not hold the shape of Eros - with its dimension about 32.7 km and its smallest (from the bottom of the 5 km crater to the bottom of the saddle) under 7 km. Unless such an object were made of material much stronger than any rock, it would collapse to a more spherical shape. However, the story of topography and how it forms on a planet is much more than a brute contest among strength, gravity, and centrifugal force. On Earth and the other terrestrial planets, the mountains and the continents are not supported solely by strength. Rather, these topographic highs are supported in large part by buoyancy, because they are made of rocks which are of lower density than those comprising the underlying mantle. Hence on Earth, the continents float in the mantle, like icebergs floating in the ocean. The rock in the mantle is solid but is nevertheless able to flow over geologic time - albeit very slowly and under great duress. Circulation in the mantle is driven by heat escaping from the interior of the Earth, and it drags the continents around the world at the majestic rate of centimeters per year, causing the so-called continental drift. To be a bit more precise, the continents are carried on rafts which we call plates and which make up the uppermost, relatively cool and rigid, layer of the mantle. Circulation occurs in the hotter, lower layers of the mantle. The entire crust of the Earth is carried on plates in relative motion, with thinner crust on plates under the oceans and thicker crust on plates holding the continents. Some plates collide, and these monstrous collisions build mountain ranges, produce earthquakes, and induce volcanism, thereby driving much of the geologic activity on Earth. Plates are continually being recycled, with new plate material forming at ocean ridges and old plate material being pulled down into the mantle at ocean trenches.

This picture of moving plates is called plate tectonics, and in this form, it is found only at Earth. However, various types of tectonism, meaning crustal deformations, are found at Mercury, Venus, and Mars as well. The origins of topography are different for each of these worlds, but we cannot go into details here.

For us the point is that none of the types of geologic activity that we have looked at, that are associated with plate tectonics in particular, could ever have occurred on Eros. This is the implication of the composition measurements made by NEAR, that showed Eros to have a primitive, undifferentiated composition. Eros, and its parent body if there was one, never underwent complete melting and never separated into a distinct crust and mantle. Nothing like plate tectonics could ever have occurred. However, some form of volcanism associated with partial melting is still not ruled out, although we have yet to find any compositional signatures of such volcanism, and we are looking hard.

As a small primitive body, then, Eros would not be expected to show much in the way of topography other than that which would result from impacts. In this view, the familiar processes on planets that push up mountains and make valleys simply do not happen on small bodies like Eros, although there is always impact cratering, and possibly a catastrophic impact that broke apart a parent body of Eros. But this view is wrong - it is incomplete, and the story of topography at Eros is not simply a tale of endless battering by impacts of other small bodies. The delightful truth is that Eros displays a great variety of topographic features, including some - ridges and troughs - that indicate tectonic deformations. But now we ask, what is the story of topography at Eros? What caused the tectonic deformations, and when did they occur? We can't yet read the story of topography at Eros, but it is marvelous.

Andrew Cheng
NEAR Project Scientist
and member of the
NEAR-Shoemaker Laser Rangefinder Science Team

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