Talk:3753 Cruithne

"Cruithne shares Earth's orbit, but does not actually orbit the Earth. Instead, it follows a spiralling path that moves along the Earth's orbit in a horseshoe shape, the two ends of the horseshoe approaching either side of Earth but not quite reaching it. It takes Cruithne 385 years to complete one such horseshoe orbit."

- Not to sound stupid but I am not following this dicussion of Cruithne's orbit. Huh?  :-) (I think we need to specify: horseshoe-shaped as observed from where?)

Take a look at the diagrams and animation of Cruithne's orbit in the external link provided at the bottom of the page. If you can come up with a simple textual description of that, you are most welcome to replace the one above. :) -BD (Actually, since the images on the page are © Paul Wiegert, I'll email him and see if I can get permission to use them in Wikipedia. I don't think that a simple textual description is possible, period. :)

Good God! If I'm understanding that right, it IS horseshoe-shaped!!

Well, only from the perspective of the Earth. From the perspective of an observer who isn't viewing the situation from a point orbiting the sun at Earth's orbital radius, Cruithne is actually following a relatively conventional elliptical orbit around the sun. But since that elliptical orbit has almost exactly the same period as Earth's, it behaves as if it's orbiting around the Earth in this weird manner. I've just emailed Dr. Weigert for permission to use some of his diagrams here, when I get a response I'll see about trying to explain this more clearly. It's cool. :) -BD

"a relatively conventional elliptical orbit", Okay, thanks, that restores my faith in God and Newton.  :-)

Not forgetting Kepler, if you please! - Lee M 01:28, 4 Sep 2003 (UTC)

"But since that elliptical orbit has almost exactly the same period as Earth's, it behaves as if it's orbiting around the Earth in this weird manner."

NO IT DOESN'T! Have another look at the animation - even if you hold the Earth still, Cruithne KEEPS TO ONE SIDE of the Earth - it does not orbit AROUND the Earth. The horseshoe slowly migrates until it's edge comes close to the Earth, whereupon it reverses direction so that the effect can repeat itself with the other edge of the horseshoe after another 385 years (orbital inclination notwithstanding). There is a myth out there the Cruithne is a moon of the Earth, and I think everything possible needs to be done to kill this myth. (I know that Paul Wiegert says "The near-Earth asteroid 3753 Cruithne is in an unusual orbit about that of the Earth" - I think his choice of the word "about" is unfortunate, I think he probably means "in relation to").

No, he means "an unusual orbit about the orbit of the Earth". HTH HAND --Phil | Talk 14:58, Dec 23, 2004 (UTC)

Temperatures

The article gives the average surface temperature of Cruithne as 378 Kelvin, that's well above the boiling point of water. How can that be for an object orbiting the sun at an average distance comparable to earths distance and without an atmosphere for any greenhouse effects? Does anyone have an explanation for this? 84.160.196.181 14:23, 27 Feb 2005 (UTC)

The low albedo is responsible. The temperature estimate is computed from the albedo and assumes the surface reaches thermal equilibrium over multiple rotations, using the semi-major axis distance.

Urhixidur 18:47, 2005 Feb 27 (UTC)

A good discussion of the physics involved is, for example, Marco Delbo's The nature of near-earth asteroids from the study of their thermal infrared emission Chapter 2: Sizes and albedos of asteroids: the radiometric method and asteroid thermal models (http://www.diss.fu-berlin.de/2004/289/Chapter2.pdf).

Urhixidur 22:20, 2005 Feb 27 (UTC)

Thanks for the explaination. I'm not quite satisfied because when looking at the moon its albedo (0.12) is even slightly lower than Cruithnes but the everage temperature is much colder. Hm, when realylooking at the moon it is quite bright so the albedo of 0,12 seems wrong. 84.160.223.61 15:05, 5 Mar 2005 (UTC)

The calculation goes like this. Assume thermal equilibrium, which means there is as much energy being absorbed per unit of time (from the Sun's rays) as is being emitted. The energy flux absorbed is a fraction of the solar luminosity (L_o = 3.827×10²⁶ W) determined by the ratio of the asteroid's presented surface (πd²/4, where d is the asteroid's diametre) to the orbital sphere (4πR², where R is the orbital radius). The albedo intervenes at this point; the energy flux absorbed is the fraction (1-A). Obviously, an albedo of 1 (perfect reflector) means no energy flux is absorbed. The energy emitted is the asteroid's surface (πd²) times the all-wavelength energy flux per unit surface, given by (σT⁴), where σ is the Stefan-Boltzmann constant (5.670 399 102 108 67×10^-8 W/m²K⁴). This is true for a black body (perfect radiator); for asteroids, an emissivity ε of 0.9 is assumed. Thus we have:

<math>\sigma T^4 \pi d^2 \epsilon = \frac{(1 - A) L_o d^2}{16 R^2}<math>

hence

<math>T^4 = \frac{(1 - A) L_o}{16 \pi R^2 \sigma \epsilon}<math>

For the Earth, this calculation yields an average temperature of 255 K (actual average: 287 K); for the Moon, it yields 277 K (vs 250 K). This gives an idea of the error inherent in these estimates.

By the way, thanks for having me take a look at these again; it allowed me to spot a mistake that has resulted in systematically too high estimated temperatures in the asteroid articles!

Urhixidur 15:53, 2005 Mar 5 (UTC)

Thanks again. Now I have a better understanding. The T⁴ causes the average temperature to fall when maximum and minimum temperatures differ more strongly. Thus heat transport on the asteroid as well as the rotation period might have a significant impact.

By the way, when in some decades the first human will set foot on Cruithne I will proudly be telling my grandchildren that it was me that gave the crucial hint on not going too lightly clothed and better be wearing a double pair of woolen socks ;-) 84.160.223.61 19:11, 5 Mar 2005 (UTC)

Note that in the case of a strongly eccentric orbit, the definition of "average" temperateure used here is wrong --we're using the semi-major axis, whereas the time-averaged orbital radius is actually a(1+e²/2) (see here). Considering the asteroid's actual thermal regime (i.e., thermal inertia) complicates the calculation even further.

Urhixidur 01:44, 2005 Mar 6 (UTC)

Pronunciation

Paul Wiegert's page about Cruithne (http://www.astro.uwo.ca/~wiegert/3753/3753.html) gives a different pronunciation than that given here. He says it has just two syllables, with the stress on the first. Who's right? --agr 05:17, 20 Jun 2005 (UTC)