Cruithne

Click on the images to start them moving. Stop them again before moving on to the next image. Drag on the images to change the viewpoint.

Here are some simulations of Cruithne, also known as asteroid 3753, or 1986 TO, or "Earth's second moon". Many thanks to Graeme Waddington who supplied the xyz coordinates of Cruithne and the planets as of February 26 2000, and Paul Wiegert, Kimmo Innanen, and Seppo Mikkola whose research is responsible for most of what we know about Cruithne. (The coordinates are embedded in this html file, they are parameters to the gravitational simulation applet. Units are 10e28 pounds, astronomical units, and astronomical units per day.)

Cruithne is not really a moon, because Earth and Cruithne are not gravitationally bound. (Luna IS a real moon.) But Cruithne is locked into a 1::1 resonance with Earth. (Another resonance in the solar system is the 3::2 resonance of Neptune and Pluto. That means Neptune makes 3 orbits for every 2 of Pluto.) Cruithne's nearest pass to Earth is .1 AU (40 moon lengths), although right now it never comes closer than .3 AU. It is 5 kilometers (3 miles) wide.

Paul Wiegert says that two more asteroids in earth-resonant orbit have been found, 1998 UP1 and 2000 PH5. (If I find position-velocity XYZ coordinates for those and the inner planets at some point in time, I'll put up applets of those too.)
First, the normal view of solar system. Cruithne is the purple ellipse. Earth is the blue circle. This simulation includes all the planet, but doesn't handle relativity, and the earth/moon system are lumped into one point.

You can use the mouse to start and stop the image, and to move the view point (by dragging).

Sun Mercury Venus Cruithne Earth+Moon barycentre Mars Jupiter Saturn Uranus Neptune Pluto
Next, the most informative view my applet can manage, a strobe version drawn once per Earth year. Since every year Earth comes back to the same point in its orbit, and this is drawn once per year, Earth appears to stay fixed. Cruithne also has an orbit of almost one year, that's why consecutive purple dots are close to one another. (2014: I adjusted the masses to match the claimed units, and I fudged the gravitational constant by about 1/4000 to give the simulated earth an orbit of 365.24 days.)

Cruithne has an orbit slightly less than a year at first, then when it approaches Earth it slows down to slightly more than a year, and back and forth and back and forth. The little wobbles in Cruithne's orbit are apparently due to Jupiter.

I didn't include any planets beyond Jupiter, for speed.

Sun Mercury Venus Cruithne Earth+Moon barycentre Mars Jupiter
Strobe version again. Side view. Earth remains a blue dot. Note that Cruithne is pretty far out of the main plane of the solar system. All the planets are included. You can drag the image if you want to try different viewpoints.

The numbers in the upper lefthand corner are number of years, and energy difference from the start of the simulation. (Ideally energy is conserved, but my simulator isn't perfect.) Official estimates say Cruithne should leave this orbit in around 5000 years. This simulation says it stays in about the same orbit, but resonance gets spotty around 5000 years and goes away entirely around 10000.

Sun Mercury Venus Cruithne Earth+Moon barycentre Mars Jupiter Saturn Uranus Neptune Pluto
Here's the same thing again, but with coordinates supplied by Paul Weigert, who is studying the orbit of Cruithne. Are this simulation and the previous one noticably different (other than having slightly different viewpoints)?

I'm not accounting for relativity. My simulation says the oscillation takes about 760 years. The official estimate is 770 years. Is that due to relativity or a bug in my simulator?

Sun Mercury Venus Earth/Moon Mars Jupiter Saturn Uranus Neptune Cruithne

This is the perspective from Earth, actually where all the object appear in the sky. The one on screen all the time is Pluto. The purple one is Cruithne. This isn't very informative, although it does give you a chance to see Mars do its retrograde orbit thingy. It would be more interesting for Cruithne if I could put the eye on earth, like this, plus keep the sun at a fixed point in the sky. I can't do that yet.

Sun Mercury Venus Cruithne Earth+Moon barycentre Mars Jupiter Saturn Uranus Neptune Pluto
Finally, the normal view again, no strobe, no trails. Everything beyond Jupiter was removed for speed. Planets are drawn bigger than they really are. Sun Mercury Venus Cruithne Earth+Moon barycentre Mars Jupiter


Robert Vanderbei's simulations of Cruithne, which use a rotating frame to hold the earth fixed and keep the sun at a constant angle.
A stable figure-8 orbit
All orbit simulations in this site
Ye Olde Catalogue of Boy Scout Skits
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