by Robert J. Vanderbei
Recently NASA’s Wide-field Infrared Survey Explorer (WISE) space telescope discovered an interesting asteroid named 2010 SO16.
The asteroid is in a so-called “horseshoe” orbit with respect to Earth. Essentially that means the asteroid is in the same orbit as Earth but, at the moment, it trails us in our yearlong journey around the sun by about two weeks.
The asteroid’s center of mass is currently slightly closer to the sun than our center of mass here on Earth. Hence it is going around the sun slightly faster than we are.
In other words, 2010 SO16 is catching up to us.
Luckily, the asteroid will not hit us. Instead, as it nears us, the space rock will start to feel the gravitational attraction of Earth. Since we are ahead of it, we will accelerate it forward.
This would seem bad, but what happens is that the asteroid will get slung to a higher orbit and actually start going slower. This is a weird, counter-intuitive feature of the laws of gravity: Hit the accelerator and you end up going slower—but in a higher orbit, so at least something was gained!
Asteroid 2010 SO16 is doing this transition right about now and will soon be in a higher, slower orbit.
In about 175 years we will be the ones approaching from behind, as by then we will have almost lapped the asteroid.
At that time the dynamic will work in the opposite manner: The asteroid will start to feel the Earth tugging on it from behind. This will cause the asteroid to decelerate, and it will drop back to the original, lower orbit and return to its faster pace.
In total, the asteroid’s orbital path traces a horseshoe shape relative to Earth. This process is stable and can continue indefinitely.
There are a few other previously known asteroids that exhibit similar interesting orbits relative to Earth. One is called Cruithne, and another is called 2002 AA29.
I’ve constructed an animation of these three asteroids as they orbit the sun using a JAVA applet.
To run it, you will need to install Sun Microsystem’s JAVA on your computer. Installation instructions can be found here and instructions on how to enable JAVA in your favorite browser can be found here.
Once that’s squared away, click here to view the horseshoe-orbits animation.
In addition to the asteroids, the animation shows the inner planets Venus, Earth, and Mars—as well as our moon and the outer planet Jupiter.
By default, Earth is at the center of the animation window and the sun is held fixed directly to its left. To hold the sun and Earth fixed means that our “point of view” is counter-rotating.
Objects closer to the sun (such as Venus) orbit faster and therefore appear to move counterclockwise around the sun. Objects farther from the sun (such as Mars) orbit more slowly and therefore appear to move in a clockwise fashion.
If you change “center on” from 2 to 0, then the sun will be placed at the center of the window, counter-rotation is disabled, and all bodies will move counterclockwise.
By default, the animation shows where the bodies are at the time shown in the bottom left corner of the animation window. To see orbital trails, click “Show Trails.”
—Screen grab by Robert J. Vanderbei
You will notice that the orbits have a rather “loopy” appearance. This is because the planets’ orbits about the sun are not perfect circles—they are ellipses.
We are holding Earth fixed in the center. The fact that its orbit is elliptical is seen in the fact that the sun wobbles slightly.
Venus’s orbit is nearly circular. The smearing of the green Venusian trails is a combination of both Venus’s and Earth’s ellipticity.
Mars, on the other hand, has a much more elliptical orbit, which is clearly illustrated by the “fatness” of the red trail.
Note that Cruithne’s orbit is sometimes closer to the sun than Venus’s and is sometime farther from the sun than Mars’s. Yet on average its distance from the sun is almost the same as Earth’s, and so it classifies as an Earth-coorbital asteroid.
Asteroids 2002 AA29 and 2010 SO16 have paths that are much more like the idealized “horseshoe” orbit described above.
You can speed up the animation by giving a larger “warp” value. The “+” and “-” buttons also allow you to zoom in and out, respectively.
If you zoom in by clicking “+” a number of times (with Earth at the center by default), you will be able to see the moon orbiting Earth. If you zoom out with a few clicks on “-” you will find Jupiter—it is just too far from the sun to be seen at the default zoom level.
Once you have JAVA installed and have explored the horseshoe orbits, you might want to check out several other orbital animations I have assembled.
Robert J. Vanderbei is chair of the Operations Research and Financial Engineering department at Princeton University and co-author of the National Geographic book Sizing Up the Universe. Vanderbei has been an astrophotographer since 1999, and he regularly posts new images on his astro gallery website.