1620 Geographos: A Tidally Distorted Asteroid?

Orbit: 1620 Geographos is an Apollo Earth-crossing asteroid with orbital paremeters (a = 1.25 AU; e = 0.34; i = 13.3 deg.). Its average encounter velocity with the Earth (~ 11 km/s) is slow enough that close encounters make susceptible to the Earth's tidal forces.

Rotation: Geographos has a rotation period of 5.22 hours, short when compared to many other Earth-crossing asteroids (i.e. the median rotation period for ECAs is ~ 6 hours). In addition, Geographos is so elongated that each end is nearly rotating faster than the theoretical break-up limit for rubble-piles. Our model results show that fast rotators tend to tidal disrupt more readily.

Shape: Geographos is almost 3 times as long as it is wide (5.1 x 1.8 km, or 2.8 x 1.0 normalized), making it the most elongated body that we know of in the solar system. Our model results show that elongated bodies disrupt more readily than spherical bodies if they have the right orientation at encounter. This delay-doppler radar image also the Geographos has an "S" or a "pinwheel" shaped structure, with small "hooks" seen near the ends of the body. For a better view of Geographos, see below.

Summary image of 1620 Geographos

Note: This image is the sum of many high-res images covering roughly one full rotation period. It was created to define the entire pole-on silhouette. The disadvantage of superposing large numbers of images together is that youe smear any features "inside" the silhouette. Also, if the coregistration of images is not perfect, you also smear the silhouette itself a little bit. The 30-deg-summed images shown below show Geographos's "hooks" at each end better than this image's silhouette.

Using one endstate from our model, we can match both Geographos's elongated shape and its pinwheel-like structure.

When a point mass encountering the Earth reaches periapse, the gravitational acceleration pulling the object towards Earth equals the centrifugal force trying to throw it from the Earth.

For real bodies such as our elongated rubble-pile asteroid, however, this balance is lost. Instead of experiencing equal forces, the end of the asteroid nearest to Earth experiences a slight excess of gravitational force pulling it radially towards Earth, while the end of the asteroid furthest from Earth experiences a slight excess of centrifugal force pulling it radially away from Earth. This differential force results in a torque which pulls the asteroid's long axis towards the radial line stretching from the asteroid's center of mass to the Earth's center. Longer moment arms at periapse are more susceptible to tidal torque (i.e. spherical bodies have uniformly small moment arms, elongated asteroids have moment arms which vary depending on their orientation at periapse). In many cases, tidal torque may accelerate the asteroid's rotation rate and increase its length.

If the torque is strong enough, the ends of the distorted asteroid may be lost into space along the asteroid's equatorial plane. Keplerian shear (wherein bodies closer to the asteroid's center of mass orbit faster than those further away) among these ejected bodies produces spiral deformations similar to those seen in models of stellar collisions (Benz and Hills 1987; Benz et al. 1989).

The delay-Doppler radar transmit-receive cycle (run) by Steve Ostro et al. (JPL/NASA) produced an image of 1620 Geographos with phase resolution of about 1 degree. The low-resolution and high-resolution single run images were noisy enough that they rotated several images into co-registration with each other and added them together. For this figure, they summed 30-degree blocks of images.

In any radar image, we only see the radar-facing part of the asteroid, and the image is the projection of the illuminated surface regions onto the apparent equatorial plane. For Geographos, the radar was in the asteroid's equatorial plane, so the geometry is relatively easy to understand: you can pretend that you are looking along the spin axis and that you can see the illuminated parts of Geographos in both the northern and southern "hemispheres", superposed as a double exposure. There is no ambiguity in the definition of the asteroid's silhouette, but a single image only shows part of the silhouette.