2867 Steins (APOD 08 Sep 2008)

[pcstarship]

I kinda expected there would be some attitude instability. But the flyby video indicates that this body doesn't tumble. Wonder why?

[bystander]

http://antwrp.gsfc.nasa.gov/apod/ap080908.html

Perhaps the rate of closure was too high.

[orin stepanek]

http://apod.nasa.gov/apod/ap080908.html

If it is tumbling; the rate may have been too negligent for the photo to capture. I couldn't find much on not tumbling on google; as most sites suggested that asteroids do tumble. 8)

Orin

[Chris Peterson]

If it is tumbling; the rate may have been too negligent for the photo to capture. :? I couldn't find much on not tumbling on google; as most sites suggested that asteroids do tumble.

Most asteroids do not tumble, but simply rotate about their principal axis. Tumbling means the asteroid rotates about more than one axis, a type of motion that induces repetitive internal strain that damps out the motion over time. So tumblers tend to either be the result of recent collisions, or are found in very slowly rotating asteroids that haven't had time for the motion to get completely damped. 2867 Steins is a typical asteroid rotating about a single axis with a period of about six hours. Since the actual flyby was only a few minutes long, it would be hard to pick out the rotation visually.

[henk21cm]

I kinda expected there would be some attitude instability. But the flyby video indicates that this body doesn't tumble. Wonder why?

Did you see the presentation of H. Uwe keller? On page/sheet 5 a light curve is drawn. The horizontal scale is in Modified Julian Date and the vertical scale is the "magnitude". There is a fluctuation in magnitude in length about 0.1 MJD visible, so roughly 2.5 hours, which could be interpreted as rotational. But if you look very carefully you will see a plateau in the magnitude at 13.95 left and right, which is not visible in the central period. The time between the two plateaus may be interpreted as a full rotational period of 1.03-0.77 = 0.26 days (6 hours).

So you are correct: it is tumbling. Now why don't we see it tumbling?

The time from start to end of the sequence of images can be infered from elsewhere at the ESA site. At 20h43m the distance to Steins is 7500 km, the closest approach is on 20h58m at 800 km. At 20h38 m the spacecraft is flipped for fly-by operation. The video could not have been started earlier. My estimation -yours or someone elses may be better- is that the actual sequence of images is about half an hour. That is rather short compared to the rotational period of a quarter of a day. That supports the arguments of orin and bystander.

<Re-editted>
When i was writing Chris Peterson gave a similar answer and arguments.
</Re-edited>

[neufer]

I kinda expected there would be some attitude instability. But the flyby video indicates that this body doesn't tumble. Wonder why?

Did you see the presentation of H. Uwe keller? On page/sheet 5 a light curve is drawn. The horizontal scale is in Modified Julian Date and the vertical scale is the "magnitude". There is a fluctuation in magnitude in length about 0.1 MJD visible, so roughly 2.5 hours, which could be interpreted as rotational. But if you look very carefully you will see a plateau in the magnitude at 13.95 left and right, which is not visible in the central period. The time between the two plateaus may be interpreted as a full rotational period of 1.03-0.77 = 0.26 days (6 hours).

So you are correct: it is tumbling. Now why don't we see it tumbling?

The time from start to end of the sequence of images can be infered from elsewhere at the ESA site. At 20h43m the distance to Steins is 7500 km, the closest approach is on 20h58m at 800 km. At 20h38 m the spacecraft is flipped for fly-by operation. The video could not have been started earlier. My estimation -yours or someone elses may be better- is that the actual sequence of images is about half an hour. That is rather short compared to the rotational period of a quarter of a day. That supports the arguments of orin and bystander.

This is probably why we don't see 2867 Šteins ROTATING.

However, TUMBLING implies a more chaotic motion:
------------------------------------------
Tumble, v. i. [OE. tumblen, AS. tumbian to turn heels over head, to dance violently;
akin to D. tuimelen to fall, Sw. tumla, Dan. tumle, Icel. tumba;
and cf. G. taumeln to reel, to stagger.]

1. To roll over, or to and fro; to throw one's self about; as, a person on pain tumbles and tosses.

2. To roll down; to fall suddenly and violently; to be precipitated; as, to tumble from a scaffold.

3. To play tricks by various movements and contortions of the body; to perform the feats of an acrobat.
------------------------------------------
This more chaotic type of rotation is sometimes observed in asteroids that are:

• 1) slowly rotating
  2) oblong AND
  3) in resonance with Jupiter.

A.k.a., 4179 Toutatis:
--------------------------------------------------
http://en.wikipedia.org/wiki/4179_Toutatis

<<4179 Toutatis is an Apollo, Alinda, and Mars-crosser asteroid with a chaotic orbit produced by a 3:1 resonance with the planet Jupiter. Due to its very low orbital inclination (0.47°) and its orbital period of very nearly 4 years, Toutatis makes frequent close approaches to Earth, with a currently minimum possible distance (Earth MOID) of just 0.006 AU (2.3 times as far as the Moon). The approach on September 29, 2004 was particularly close, at 0.0104 AU (within 4 lunar distances) from Earth, presenting a good opportunity for observation.

http://antwrp.gsfc.nasa.gov/apod/ap041002.html

Its rotation combines two separate periodic motions into a non-periodic result; to someone on the surface of Toutatis the Sun would seem to rise and set in apparently random locations and at random times at the asteroid's horizon. It was first sighted on February 10, 1934 as object 1934 CT and then promptly lost. It was recovered on January 4, 1989 by Christian Pollas and was named after the Celtic god Toutatis/Teutates, known to popular culture as Astérix's village-god.

Radar imagery has shown that Toutatis is a highly irregular body consisting of two distinct "lobes", with maximum widths of about 4.6 km and 2.4 km respectively. It is hypothesized that Toutatis formed from two originally separate bodies which coalesced at some point, with the resultant asteroid being compared to a "rubble pile".>>
------------------------------------------
http://en.wikipedia.org/wiki/Toutatis

<<Toutatis or Teutates was a Celtic god worshipped in ancient Gaul and Britain. On the basis of his name's etymology, he has been widely interpreted to be a tribal protector. Today, he is best known under the name Toutatis through the Gaulish catchphrase "By Toutatis!", invented for the Asterix comics by Goscinny and Uderzo. The spelling Toutatis, however, is authentic and attested by about ten ancient inscriptions. Under the spelling Teutates, the god is also known from a passage in Lucan. According to later commentators, victims sacrificed to Teutates were killed by being plunged headfirst into a vat [large Stein?] filled with an unspecified liquid.>>

[Chris Peterson]

Did you see the presentation of H. Uwe keller? On page/sheet 5 a light curve is drawn. The horizontal scale is in Modified Julian Date and the vertical scale is the "magnitude". There is a fluctuation in magnitude in length about 0.1 MJD visible, so roughly 2.5 hours, which could be interpreted as rotational. But if you look very carefully you will see a plateau in the magnitude at 13.95 left and right, which is not visible in the central period. The time between the two plateaus may be interpreted as a full rotational period of 1.03-0.77 = 0.26 days (6 hours).

So you are correct: it is tumbling. Now why don't we see it tumbling?

Do you know of any descriptive text to go along with the presentation you link? The light curve as shown there looks nothing like any of the previous OSIRIS light curves for this object. The one in the presentation was from August 20, 2008, so still a couple of weeks from the flyby. All the other curves I've seen show only a six hour period, with no sign of other periodic components. In other words, there has been nothing to suggest that Steins is tumbling. I'd be interested in seeing some discussion about why the light curve in the presentation looks so different.

[Chris Peterson]

This is probably why we don't see 2867 Šteins ROTATING.

However, TUMBLING implies a more chaotic motion...

In the case of asteroids, tumbling can't be taken as implying chaotic motion. Tumbling means that there is rotation about more than one axis, which is not typically chaotic. The actual motion may be chaotic in the long term as the result of gravitational perturbations from Jupiter or other bodies, or as the result of internal mass shifts (many asteroids appear to be nothing but rubble piles, not rigid bodies).

I am not aware of any known tumbling asteroids that show chaotic motion.

[henk21cm]

Do you know of any descriptive text to go along with the presentation you link?

Unfortunately not. The webstreaming of the press conference, well its gone. See http://www.esa.int/rosetta or i'm missing a player.

In a later (September 6th) article on the ESA website an e-mail address is mentioned for further info.

I could drop them a line. You can ask them as well.

[orin stepanek]

No sign of tumbling observed by ORISIShttp://www.physorg.com/news93617655.html(The observations show that Steins rotates with a spin period of slightly more than six hours, in agreement with previous earth-based observations. The asymmetry of the light curve suggests an irregular shape of Steins. However, OSIRIS found no evidence for a ‘tumbling’ motion of the asteroid or the presence of a satellite. Work is ongoing to construct the orientation of the spin axis of Steins from a combination of the OSIRIS observations with ground-based data. )

Orin

[henk21cm]

I'd be interested in seeing some discussion about why the light curve in the presentation looks so different.

Thought experiment. Take a cylinder (soda can), paint it white and let it rotate around an axis, perpendicular to the symmetry axis. Let some light shine on it, e.g. from the back side of the observer. (Full moon idea). The light curve will show a double period, since the cylinder has a rotation by 180° symmetry.

That could explain the double period of the light curve.

[Chris Peterson]

Thought experiment. Take a cylinder (soda can), paint it white and let it rotate around an axis, perpendicular to the symmetry axis. Let some light shine on it, e.g. from the back side of the observer. (Full moon idea). The light curve will show a double period, since the cylinder has a rotation by 180° symmetry.

That could explain the double period of the light curve.

Except, it doesn't appear to me that we see a double period. There is a 2.6 hour main cycle, and that pair of plateaus which are 6 hours apart. The earlier published light curves from the same instrument show only the 6 hour cycle, and the analysis I've seen indicates no other periodicity.

Your example does demonstrate the challenge of analyzing asteroid light curves, since they always have shape and albedo features superimposed. It's not too difficult to extract those in the case of simple rotation, but for tumblers it can be a real effort.

[henk21cm]

Except, it doesn't appear to me that we see a double period. There is a 2.6 hour main cycle, and that pair of plateaus which are 6 hours apart. The earlier published light curves from the same instrument show only the 6 hour cycle, and the analysis I've seen indicates no other periodicity.

Did some googling and found a light curve of March 11th 2006, in stead of August 20th 2008 in the Uwe Keller press conference. It shows the same double periodicity and the plateau, although the plateau is less striking as in the August 20th light curve.

Do you have references (URL) to another light curve?

[Chris Peterson]

Did some googling and found a light curve of March 11th 2006, in stead of August 20th 2008 in the Uwe Keller press conference. It shows the same double periodicity and the plateau, although the plateau is less striking as in the August 20th light curve.

Looking more closely at the published curves, I think they are all showing the same thing. What's confusing is the use of different units. The curves that use rotational phase need to provide additional information about the phase period, which some do and some don't. The period is 6.052 hours. The faster cycle shows rotational artifacts, either because of shape or albedo variations. But the faster cycle isn't half the full cycle; the curve isn't symmetric.