Cruithne, Earth's "2nd Moon"Cruithne is an asteroid that is sometimes referred to as Earth's 2nd moon. While this might be stretching the definition of moon a bit, Cruithne does have a very interesting orbit which is heavily influenced by Earth.
The simulation cruithne.gsim shows Cruithne in a rotating frame. Watch as it orbits the Sun in a kidney bean shape orbit. The Earth has a noticable effect on Cruithne's orbit, sometimes repelling it as it gets too close. Cruithne's kidney bean-shaped "orbit" then spends centuries travelling all the way around the Sun, just to meet the Earth from the other side. Earth once again repels the kidney bean-shaped orbit. Cruithne's kidney-bean orbit repeats this process over and over again.
Starting conditions were obtained using JPL Horizons Ephemeris Computation Service.
(You need to have the program Gravity Simulator installed on your computer first. Click Here to download Gravity Simulator.)
Cruithne has an orbit that stretches from the orbit of Mercury to beyond the orbit of Mars. But remarkably, Cruithne's period is almost exactly the same as Earth's. This sets the table for some interesting orbital interactions.
Cruithne's orbit is highly inclined compared to the the orbits of the planets.
In this simulation the Earth and Moon trace an oval in a rotating frame that match's their solar period. Because the Earth's orbit is slightly elliptical, sometimes it is closer to the Sun than its average distance, and sometimes it is further. When it is closer, it also moves slightly faster in its orbit, causing it to advance slightly from its average position. When it is further from the Sun, it moves slightly slower, causing it to fall behind its average position. This is why the Earth / Moon system traces an oval instead of appearing as a fixed point.
In 1997, Cruithne's horseshoe orbit causes it to make close encounters with Earth on an annual basis. But Cruithne's kidney bean-shaped orbit is distancing itself from the Earth with each orbit.
In the year 2110, Cruithne traces its kidney bean-shaped orbit around Earth's Lagrange 3 point.
In the year 2277, Cruithne's kidney bean-shaped orbit encounter Earth. Earth's gravity raises Cruithne's orbit slightly. The higher orbit means Cruithne has a slower speed in its orbit around the Sun. Cruithne begins to retreat from the Earth. Cruithne will return to this point 752 years later in the year 3029.
Three centuries later, Cruithne's kidney bean-shaped "orbit" approached Earth from the other direction, and the leading edge advanced past Earth. Because of Cruithne's inclination, the asteroid was well below Earth at the time. Out of Earth's gravitational grasp, the asteroid's kidney bean-shaped "orbit" continued to march clockwise.
In the year 2647 the trailing edge of Cruithne's kidney bean-shaped "orbit" approached the Earth. This time, Cruithne's inclination was not sufficient to keep Cruithne a safe distance from Earth's gravitational grasp. Earth's gravity slowed the asteroid down. But the slowdown was only temporary. It actually caused Cruithne to drop into a faster orbit. Once again, its kidney bean-shaped "orbit" reversed direction.