1620 Geographos: A Tidally Distorted Asteroid?
Tidal forces can not only disrupt asteroids but distort them as well.
Using our model results (described elsewhere), we suggest that
1620 Geographos is a tidally distorted object. Here is some of
- 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
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.
Tidally distorted rubble-pile asteroid from our model
How do tidal forces make these unusual shapes?
- 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).
How was this image of 1620 Geographos made?
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.