Tag Archives: Rotation

Rotation and activity of a comet

Hi there! We, Earthians, are regularly visited by periodic comets, the most famous one being probably 1P/Halley, which will visit us in 2061. Since we cannot wait, we study others of that kind. Today I tell you about 49P / Arend-Rigaux. This is the opportunity for me to present you The rotation and other properties of Comet 49P/Arend-Rigaux, 1984 – 2012, by Nora Eisner, Matthew M. Knight and David G. Schleicher. This study has recently been published in The Astronomical Journal.

The comet 49P / Arend-Rigaux

The comet 49P / Arend-Rigaux has been discovered in February 1951 at the Royal Observatory of Belgium, by Sylvain Arend and Fernand Rigaux. It is a periodic comet of the Jupiter family, i.e. with a period smaller than 20 years. Its period is actually 6.71 years, its semimajor axis 3.55 AU (astronomical units, 1 AU being 150 millions km, i.e. the Sun-Earth distance), its eccentricity 0.6, and its orbital inclination 19°, with respect to the ecliptic. These numbers are extracted from the JPL Small-Body Database Browser, and are calculated at the date Apr 6, 2010. I have plotted below the distances Sun-comet and Earth-comet.

Distance to the Sun.
Distance to the Sun.
Distance to the Earth.
Distance to the Earth.

The distance to the Sun clearly shows the periodic variations. The orbit of the Earth is at 1 AU, the one of Mars at 1.5 AU, and the one of Jupiter at 5.2 AU. Every 6.71 years, the comet reaches its perihelion, i.e. minimizes its distance to the Sun. This proximity warms the comet and provokes an excess of cometary activity, i.e. sublimation of dirty ice. At these occasions, the distance with the Earth is minimized, but with variations due to the orbital motion of the Earth. We can see for instance that the comet gets pretty close to the Earth in 1951 (when it was discovered), in 1984, and in early 2032. These are favorable moments to observe it. The paper I present you today is mainly (but not only) based on photometric observations made between January and May 2012, at Lowell Observatory.

Observations at Lowell Observatory

Lowell Observatory is located close to Flagstaff, AZ (USA). It was founded by the famous Percival Lowell in 1894, and is the place where Clyde Tombaugh discovered Pluto, in 1930. Among its facilities is the 4.28 m Discovery Channel Telescope, but most of the data used in this study were acquired with the 1.1 m Hall telescope, which is devoted to the study of comets, asteroids, and Sun-like stars. The authors also used a 79 cm telescope. The observations were made in the R(ed) band.

The data

Besides these 33 observation nights during the first half of 2012, the authors used data acquired close to the 1984 and 2005 perihelion passages, even if the 2005 ones revealed unusable. The observations consists to measure the magnitude (somehow, the luminosity) of the comet, in correcting for atmospheric problems, so as to be able to detect the variations of this magnitude. You can find below an example of data:

Magnitude of 49P / Arend-Rigaux measured in April 2012.
Magnitude of 49P / Arend-Rigaux measured in April 2012.

Of course, the data have holes, since you cannot observe during the day. Moreover, the comet needs to be visible from Arizona, otherwise it was just impossible to observe it and make any measurements.

We can see a kind of periodicity in the magnitude, this is a signature of the rotation of the comet.

Measuring the rotation

Most of the planetary bodies are kinds of triaxial ellipsoids. Imagine we are in the equatorial plane of one of them. We see an alternation of the long and short axes of its equatorial section. If the albedo of the surface element we face depends mainly on its curvature (it depends on it, but mainly may be an overstatement), then we should see two peaks during a period. As a consequence, the period of the lightcurve we observe should be half the rotation period of the comet.

In combining all the measurements, the authors managed to derive a rotation period of 13.45 ± 0.01 hour. For that, they used two different algorithms, which gave very close results, giving the authors confidence in their conclusions. The first one, Phase Dispersion Minimization (PDM), consists to assume a given period, split the measurements into time intervals of this period, and overlap them. The resulting period gives to the best overlap. The other algorithm is named Lomb-Scargle, following its authors. It is a kind of Discrete Fourier Transform, but with the advantage of not requiring uniformly sampled data.

In addition to this rotation period, the authors detected an increasing trend in the 2012 data, as if the spin of the comet accelerated. This is in agreement with an alteration of the measured rotation from the Earth, which moves, and reveals a retrograde rotation, i.e. an obliquity close to 180°. In other words, this is an illusion due to the motion of the observer, but this illusion reveals the obliquity.

Moreover, in comparing the 2012 data with the ones of 1984, the authors managed to detect a variation in the rotation period, not larger than 54 seconds. This is possible regarding the fact that the comet is altered by each perihelion passage, since it outgasses. In this case, that would imply a change of at the most 14 seconds of the rotation period between two passages. Such variations have also been detected for at least 4 other comets (2P/Encke, 9P/Tempel 1, 10P/Tempel 2, and 103P/Hartley 2, see Samarinha and Mueller (2013)).

Comet Period (h) Variation (s)
2P/Encke 11 240
9P/Tempel 1 41 -840
10P/Tempel 2 9 16.2
103P/Hartley 2 18 7200
49P/Arend-Rigaux 13.45 -(>14)

Finally, since the lightcurve is a signature of the shape as well, the authors deduced from the amplitude of variation that the axial ratio of the nucleus, i.e. long axis / short axis, should be between 1.38 and 1.63, while an independent, previous study found 1.6.

Cometary activity

49P / Arend-Rigaux has a low activity. Anyway, the authors detected an event of impulse-type outburst, which lasted less than 2 hours. The analysis of the coma revealed an excess of cyanides with respect to the 1984 passage. Moreover, 49P / Arend-Rigaux is the first comet to show hydroxyde.

The study and its authors

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Indirect measurement of an asteroid’s pole

Hi there! Today, another paper on the Yarkovsky effect. You know, this non-gravitational force which acts on the asteroid, especially if it is close enough to the Sun. After reading this post, you will know how it can reveal us the obliquity of an asteroid. I present you Constraints on the near-Earth asteroid obliquity distribution from the Yarkovsky effect, by C. Tardioli, D. Farnocchia, B. Rozitis, D. Cotto-Figueiroa, S.R. Chesley, T.S. Statler & M. Vasile. This paper has recently been accepted for publication in Astronomy and Astronomy.

The way it works

Imagine you want to know the rotation of an asteroid… but you cannot measure it directly. However, you can measure the orbital motion of the asteroid, with enough accuracy to detect an effect (here Yarkovsky), which itself depends on the rotation… measuring Yarkovsky is measuring the rotation! Easy, isn’t it?

The rotation of an asteroid

As any planetary body, an asteroid has a rotational motion, which consists in spinning around one axis (actually 3, but you can safely neglect this fact), at a given rate. We can consider that we know its rotation when

  1. We know its spin rate, or its rotational period (let us assume it is constant),
  2. We know the orientation of its spin pole. We will call it the obliquity.

Usually the asteroids spin in a few hours, which is very fast since they need at least several months to complete one revolution around the Sun. The obliquity is between 0° and 180°. 0° means that the spin axis is orthogonal to the orbital plane, and that the rotation is prograde. However, 180° is the other extreme case, the spin axis is orthogonal, but with a retrograde rotation.

A direct measurement of these two quantities would consist in following the surface of the asteroid, to observe the rotation. Usually we cannot observe the surface, but sometimes we can measure the variations of the magnitude of the asteroid over time. This is directly due to the Solar light flux, which is reflected by the surface of the asteroid. Because the topography is irregular, the rotation of the asteroid induces variations of this reflection, and by analyzing the resulting lightcurve we can retrieve the rotational quantities.

Very well, but sometimes the photometric observations are not accurate enough to get these quantities. And other times, the measured rotational quantities present an ambiguity, i.e. 2 solutions, which would need an independent measurement to discriminate them, i.e. determine which of the two possible results is the right one.

It appears that the Yarkovsky effect, which is an alteration of the orbital motion of the body due to the inhomogeneity of its temperature, itself due to the Solar incident flux and the orientation of the body, i.e. its rotation, can sometimes be measured. When you know Yarkovsky, you know the obliquity. Well, it is a little more complicated than that.

Yarkovsky: A thermal effect

Since I have already presented you Yarkovsky with words, I give you now a formula.

The Yarkovsky effect, i.e. the thermal heating of the asteroid, induced a non-gravitational acceleration of its orbital motion. This acceleration reads A2/r2, where r is the distance to the Sun (remember that the asteroid orbits the Sun), and

A2 = 4/9(1-A)Φ(αf(θs)cos(ε)-f(θo)sin2(ε)),

where

  • A: albedo of the asteroid, i.e. quantity of the reflected light wrt the incident one,
  • Φ: Solar radiation,
  • α: an enhancement factor. This is a parameter…
  • ε: the obliquity (which the authors determined),
  • θs / θo: thermal parameters which depend on the spin period (s), and the orbital one (o), respectively.

If you know Yarkovsky, you know A2, since you know the distance r (you actually know where the asteroid is). If you know all the parameters except ε, then A2 gives you ε. In fact, some of the other parameters need to be estimated.

Measuring Yarkovsky

As you can see, this study is possible only for asteroids, for which you can know the Yarkovsky acceleration. Since it is a thermal effect, you can do it only for Near-Earth Asteroids, which are closer to the Sun than the Main Belt. And to measure Yarkovsky, you must simulate the orbital motion of the asteroid, which is perturbed by the main planets and Yarkovsky, with the Yarkovsky acceleration as a free parameter. A fit of the simulations to the actual astrometric observations of the asteroid gives you a number for the Yarkovsky acceleration, with a numerical uncertainty. If your number is larger than the uncertainty, then you have detected Yarkovsky. And this uncertainty mainly depends on the accuracy of your astrometric observations. It could also depend on the validity of the dynamical model, i.e. on the consideration of the forces perturbing the orbital motion, but usually the dynamical model is very accurate, since the masses and motions of the disturbing planets are very well known.
The first detection of the Yarkovsky acceleration was in 2003, when a drift of 15 km over 12 years was announced for the asteroid 6489 Golevka.

So, you have now a list of asteroids, with their Yarkovsky accelerations. The authors worked with a final dataset of 125 asteroids.

So many retrograde asteroids

The authors tried to fit a distribution of the obliquities of these asteroids. The best fit, i.e. which reduces the distance between the resulting obliquities and the Yarkovsky acceleration that they would have produced, is obtained from a quadratic model, i.e. 1.12 cos2(ε)-0.32 cos(ε)+0.13, which is represented below.

Distribution of the asteroids with respect to their obliquity.
Distribution of the asteroids with respect to their obliquity.

What you see is the number of asteroids with respect to their obliquity. The 2 maxima at 0° and 180° mean that most of the asteroids spin about an axis, which is almost orthogonal to their orbital plane. From their relative heights, it appears that there about twice more retrograde asteroids than prograde ones. This is consistent with previous studies, these obliquities actually being a consequence of the YORP effect, which is the influence of Yarkovsky on the rotation.

The study and its authors

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Equatorial cavities due to fissions

Hi there! Today I present you a theoretical study, which explains why some asteroids present cavities in their equatorial plane. The related paper, Equatorial cavities on asteroids, an evidence of fission events, by Simon Tardivel, Paul Sánchez & Daniel J. Scheeres, has recently been accepted for publication in Icarus.

When you see a cavity, i.e. a hole at the surface of a planetary, you… OK, I usually assume it is due to an impact. Here we have another explanation, which is that it spun so fast that it ejected some material. These cavities have been observed on the two NEOs (Near-Earth Objects) 2008 EV5 and 2000 DP107 α,for which the authors describe the mechanism.

The 2 asteroids involved

The following table gives you orbital and physical data relevant to these two bodies:

2008 EV5 2000 DP107 α
Semimajor axis 0.958 AU 1.365 AU
Eccentricity 0.083 0.377
Inclination 7.437° 8.672°
Orbital period 343 d 583 d
Spin period 3.725 h 2.775 h
Diameter 450 m 950 m

And you can see the shape model of 2008 EV5 on this video, from James Richardson:

They both are small bodies, which orbit in the vicinity of the Earth, and they spin fast. You cannot see that 2000 DP 107 α has a small companion, so this is the largest component (the primary) of a binary asteroid. Their proximity to the Earth made possible the acquisition of enough radar data to model their shapes. We know that they are top-shaped asteroid, i.e. they can be seen as two cones joined by their base, giving an equatorial ridge. Moreover, they both have an equatorial cavity, of diameters 160 and 400 m, and depths 20 and 60 meters, respectively. The authors estimate that given the numbers of potential projectiles in the NEO population, the odds are very small, i.e. one chance over 600, that these two craters are both consequences of impacts. Such an impact should have occurred during the last millions of years, otherwise the craters would have relaxed. This is why it must be the signature of another mechanism, here fission is proposed.

To have fission, you must spin fast enough, and this fast spin cannot be primordial, otherwise the asteroid would not have formed. So, something has accelerated the spin. This something is YORP, for Yarkovsky-O’Keefe-Radzievskii-Paddack.

Yarkovsky and YORP

When you are close enough to the Sun, the side facing the Sun warms, and then radiates in cooling. This is the Yarkovsky effect, which is a non-gravitational force, which affect the orbit of a small body. When you have an irregular shape, which is common among asteroids (you need to reach a critical size > 100 km to be pretty spherical), your response to the Sun light may be the one of a windmill to the wind. And your spin accelerates. This is the YORP effect.

These Yarkovsky and YORP effects have actually been measured in the NEO population.

Asteroid fission

When you spin fast enough, you just split. This is easy to figure out: the shape of a planetary body is a balance between its own gravity, its spin, and if applicable the tidal action of a large perturber. For our asteroids, we can neglect this last effect. So, we have a balance between the own gravity, which tends to preserve the asteroid, and the centrifugal force, which tends to destroy it. When you accelerate the rotation, you endanger the body. But it actually does not explode, since once some material is ejected, enough angular momentum is lost, and the two newly created bodies may survive. This process of fission is assumed to be the main cause of the formation of binaries in the NEO population.
2000 DP107 α belongs to a binary, while 2008 EV5 does not. But that does not mean that it did not experience fission, since the ejecta may not have aggregated, or the formed binary may not have survived as a binary.

Now, let us see how this process created an equatorial cavity.

Ejecting a protrusion

The author imagined that there was initially a mass filling the cavity. This mass would have had the same density as the remaining body, and they considered its size to be a free parameter. They assumed the smallest possible mass to exactly fill the cavity, the other options creating protrusion. As a consequence, the radius of the asteroid would have been larger at that very place, while it is smaller now. And this is where it is getting very interesting.

In accelerating the rotation of the asteroid, you move the surface limit, which would correspond to the balance between gravitation and spin. More exactly, you diminish its radius, until it reaches the surface of the asteroid… the first contact being at the protrusion. The balance being different whether you are inside or outside the asteroid, this limit surface would go deeper at the location of the protrusion, permitting the ejection of the mass which lies outside, and thus creating an equatorial cavity. Easy, isn’t it?

But this raises another question: this would mean that the cohesion at the equatorial plane is not very strong, and weaker than expected for an asteroid. How to solve this paradox? Thanks to kinetic sieving!

The kinetic sieving

The authors simulated a phenomenon that is known by geologist as reverse grading. In granular avalanches, the separation of particles occurs according to size, involving that the largest particles are expelled where the spin is faster, i.e. at the equator, which would result in a lowest tensile strength, which would itself facilitate the ejection of the mass, and create an equatorial cavity. This phenomenon has been simulated, but not observed yet. So, this is a prediction which should be tested by future space missions.

By the way, the size of the companion of 2000 DP107 α is consistent with a protruder of height 60m.

Summary

  1. Initial state: a Near-Earth Object, with irregular shape. Probably spins fast enough to be top-shaped, i.e. having an equatorial ridge,
  2. YORP accelerates the rotation, favoring the accumulation of large particles at the equator, while tropics are more sandy,
  3. A mass is ejected at the equator, leaving a cavity,
  4. You get a binary, which may survive or not.

More will be known in the next future, thanks to the space mission Osiris-REx, which will visit the asteroid (101955) Bennu in 2018 and return samples to the Earth in 2023. Does it have sandy tropics?

The Near-Earth Asteroid Bennu. © NASA.
The Near-Earth Asteroid Bennu. © NASA.

The study and the authors

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A new contact binary

Hi there! Today I will tell you on the discovery that an already known Trans-Neptunian Object is in fact probably a contact binary. This is the opportunity for me to present you 2004 TT357: A potential contact binary in the Trans-Neptunian Belt by Audrey Thirouin, Scott S. Sheppard, and Keith S. Noll. This study has recently been published in The Astrophysical Journal.

2004 TT357‘s facts

As suggested by its name, 2004 TT357 was discovered in 2004. More precisely in August by a team led by Marc W. Buie, at Kitt Peak Observatory, Arizona, USA, on the 4-m Mayall telescope. From its magnitude, its radius is estimated to be between 87 and 218 km, depending on the albedo of the asteroid, i.e. the fraction of Solar light which is reflected by its surface. This albedo is unknown. You can find below its orbital elements.

Orbital elements of 2004 TT357
Semimajor axis 54.97 AU
Eccentricity 0.43
Inclination
Orbital period 408 y

These elements show that 2004 TT357 is in a 5:2 mean-motion resonance in Neptune, i.e. it performs 2 revolutions around the Sun while Neptune makes 5. This makes 2004 TT357 a Scaterred Disc Resonant Object. Its high eccentricity is probably at least partly due to this resonance.

Contact binaries

In astronomy, a binary object is a group of two objects, which are so linked together that they orbit around a common barycenter. Of course, their separation is pretty small. There are binary stars, here we speak about binary asteroids.
A contact binary is a kind of extreme case, in which the two components touch each other. In some sense, this is a single object, but with two different lobes. This was probably a former classical binary, which lost enough angular momentum so that the two objects eventually collided, but slowly enough to avoid any catastrophic outcome. It is thought that there is a significant fraction of contact binaries in the Solar System, i.e. between 5% and 50%, depending on the group you are considering.

Characterizing a known object as a contact binary is not an easy task, particularly for the Trans-Neptunian Objects, because of their distance to us. Among them, only (139775) 2001 QG298 is a confirmed contact binary, while 2003 SQ317 and (486958) 2014 MU69 are probable ones. This study concludes that 2004 TT357 is a probable one as well.

Observations at Lowell Observatory

Lowell Observatory is located in Flagstaff, Arizona, USA. It has been founded by Percival Lowell in 1894, and among its achievements is the discovery of the former planet Pluto in 1930, by Clyde Tombaugh. Currently, the largest of its instruments is the 4.3-m Discovery Channel Telescope (DCT), which has been partly funded by Discovery Communications. This telescope has its first light in April 2012, it is located in the Coconino National Forest near Happy Jack, Arizona, at an altitude of 2,360 meters.

The Discovery Channel Telescope. © Lowell Observatory
The Discovery Channel Telescope. © Lowell Observatory

The authors used this telescope, equipped with the Large Monolithic Imager (LMI). They acquired two sets of observation, in December 2015 and February 2017, during which they posed during 600 and 700 seconds, respectively. 2004 TT357 had then a mean visual magnitude of 22.6 and 23, respectively.

The Large Monolithic Imager. © Lowell Observatory
The Large Monolithic Imager. © Lowell Observatory

Analyzing the data

You can find below the photometric measurements of 2004 TT357.

The first set of observations. The measurements are represented with the uncertainties.
The first set of observations. The measurements are represented with the uncertainties.
The second set of observations. The measurements are represented with the uncertainties.
The second set of observations. The measurements are represented with the uncertainties.

We can see pretty significant variations of the incoming light flux, these variations being pretty periodic. This periodicity is the signature of the rotation of the asteroid, which does not always present the same face to the terrestrial observer. From these lightcurves, the authors measure a rotation period of 7.79±0.01 h. From the curves, the period seems twice smaller, but if we consider that the asteroid should be an ellipsoid, then its geometrical symmetries tell us that our line of sight should be aligned twice with the long axis and twice with the short axis during a single period. So, during a rotation period, we should see two minimums and two maximums. This assumes that we are close to the equatorial plane.

Another interesting fact is the pretty high amplitude of variation of the incident light flux. If you are interested in it, go directly to the next section. Before that, I would like to tell you how this period of 7.79±0.01 h has been determined.

The authors used 2 different algorithms:

  • the Lomb periodogram technique,
  • the phase dispersion minimization (PDM).

Usually periodic signals are described as sums of sinusoids, thanks to Fourier transforms. Unfortunately, Fourier is not suitable for unevenly-spaced data. The Lomb (or Lomb-Scargle) periodogram technique consists to fit a sinusoid to the data, thanks to the least-squares method, i.e. you minimize the squares of the departure of your signal from a sinusoid, in adjusting its amplitude, phase, and frequency. PDM is an astronomical adaptation of data folding. You guess a period, and you split your full time interval into sub-intervals, which duration is the period you have guessed. Then you superimpose them. If this the period you have guessed is truly a period of the signal, then all of your time intervals should give you pretty the same signal. If not, then the period you have guessed is not a period of the signal.

Let us go back now to the variations in the amplitude.

Physical interpretation

The authors assume that periodic magnitude variations could have 3 causes:

  • Albedo variations
  • Elongation of the asteroid
  • Two bodies, i.e. a binary.

The albedo quantify the portion of Solar flux, which is reflected by the surface. Here, the variations are too large to be due to the variations of the albedo.

The authors estimate that, if 2004 TT357 were a single, ellipsoidal body, then a/b = 2.01 and c/a = 0.38, a,b, and c being the 3 axis of the ellipsoid. This is hardly possible if the shape corresponds to an equilibrium figure (hydrostatic equilibrium, giving a Jacobi ellipsoid). Moreover, this would mean that 2004 TT357 would have been ideally oriented… very unlikely

As a consequence, 2004 TT357 is probably a binary, with a mass ratio between 0.4 and 0.8. Hubble Space Telescope observed 2004 TT357 in 2012, and detected no companion, which means it is probably a contact binary. Another way to detect a companion is the analysis of a stellar occultation (see here). Fortunately for us, one will occur in February 2018.

A star occultation in February 2018

On 5 February 2018, 2004 TT357 shall occult the 12.8-magnitude star 2UCAC 38383610, in the constellation Taurus, see here. This occultation should be visible from Brazil, and provide us new data which would help to determine the nature of 2004 TT357. Are you interested to observe?

To know more

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The rotation of Fagus

Hi there! Today I will tell you on the rotation of the asteroid (9021) Fagus. The first determination of its spin period is given in Rotation period determination for asteroid 9021 Fagus, by G. Apostolovska, A. Kostov, Z. Donchev, and E. Vchkova Bebekovska. This study has recently been published in the Bulgarian Astronomical Journal.

(9021) Fagus’s facts

(9021) Fagus is a small, Main Belt asteroid. You can find below some of its characteristics:

Semimajor axis 2.58 AU, i.e. 386 millions km
Eccentricity 0.173
Inclination 13.3°
Orbital period 4.14 y
Diameter 13.1 km
Absolute magnitude 12.4
Discovery February 14, 1988

Its small magnitude explains that its discovery was acknowledged only in 1988. Once identified, it was found on older photographic plates, providing observations from 1973 (yes, you can observe an object before it was discovered… you just do not know that you observed it). This body is so small, that the authors of this study observed it by accident: in 2013, they observed in fact (901) Brunsia during two nights, which is brighter (absolute magnitude: 11.35), but Fagus was in the field. The collected photometric data were supplemented in March 2017 by two other nights of observations, which permitted the authors to determine the spin (rotation) period with enough confidence.

Measuring the rotation

I address the measurement of the rotation of an asteroid here. Such a small body may have an irregular shape, and tumble. But since it is very difficult to get accurate data for such a small body, it is commonly assumed that the body rotates around one principal axis, this hypothesis being confronted with the observations. In other words, if you can explain the observations with a rotation around one axis, then you have won.

The irregularity of the shape makes that the light flux you record presents temporal variations, i.e. the surface elements you face is changing, so the reflection of the incident Solar light is changing, which means that these variations are correlated with the rotational dynamics. If these variations are dominated by a constant period of oscillation, then you have the rotation period of the asteroid. Typically, the rotation period of the Main-Belt asteroids are a few hours. These numbers are strongly affected by the original dynamics of the planetary nebula, the despinning of the asteroids being very slow. This is a major difference with the planetary satellites, which rotates in a few days since they are locked by the tides raised by their parent planet. For comparison, the spin period of the Moon is 28 days.

Photometric observations

Detecting the photometric variations of the incident light of such a small body requires to be very accurate. The overall signal is very faint, its variations are even fainter. To avoid errors, the observer should consider:

  • The weather. A bright sky is always better, preferably with no wind, which induces some seeing, i.e. apparent scintillation of the observed object.
  • The anthropogenic light pollution.
  • The variations of the thickness of the atmosphere during the observation. If your object is at the zenith, then it is pretty good. If it is low in the sky, then its course during the night will involve variations of the thickness of the atmosphere during the observations.
  • Instrumental problems. Usually you use a chip of CCD sensors, these sensors do not have exactly the same response. A way to compensate this is to measure a flat, i.e. the response of the chip to a homogeneous incident light flux.

The observation conditions can be optimized, for instance in observing from a mountain area. The observer should also be disciplined, for instance many professional observatories forbid to smoke under the domes. In the past, this caused wrong detections. A good way to secure the photometric results is to have several objects in the fields, and to detect the correlations between their variations of flux. Intrinsic properties of an object would emerge from light variations, which would be detected for this object only.

The observation facilities

The observations were made at Rozhen Observatory, also known as Bulgarian National Astronomical Observatory. It is located close to Chepelare, Bulgaria, at an altitude of 1,759 m. It consists of 4 telescopes.

The 2013 observations were made with a 50/70 cm Schmidt telescope, and the 2017 ones with a 2m-Ritchey-Chrétien-Coude telescope. In both cases, the observations were made through a red filter. The faintness of the asteroid required exposure times between 5 and 6 minutes.

The Schmidt telescope used for the 2013 observations. Copyright: P. Markishky
The Schmidt telescope used for the 2013 observations. Copyright: P. Markishky
The 2m telescope, used for the 2017 observations. Copyright: P. Markishky
The 2m telescope, used for the 2017 observations. Copyright: P. Markishky

The softwares

The authors used two softwares in their study: CCDPHOT, and MPO Canopus. CCDPHOT is a software running under IDL, which is another software, commonly used to treat astrophysical data, and not only. With CCDPHOT, the authors get the photometric measurements. MPO Canopus could give these measurements as well, but the authors used it for another functionality: it fits a period to the lightcurve, in proving an uncertainty. This is based on a Fourier transform, i.e. a spectral decomposition of the signal. In other words, the lightcurves, with are recorded as a set of pairs (time, lightflux), are transformed into a triplet of (amplitude, frequency, phase), i.e. it is written as a sum of sinusoidal oscillations. If one of these oscillations clearly dominates the signal, then its period is the rotation period of the asteroid.

Result

And the result is this: the rotation period of (9021)Fagus is 5.065±0.002 hours. In practice, being accurate on such a number requires to collect data over several times this interval. An ideal night of observation would permit to measure during about 2 periods. Here, data have been collected over 4 nights.
Up to now, we had no measurement of the spin period of Fagus, which makes this result original. It not only helps to understand the specific Fagus, but it is also a new data in the catalog of the rotational periods of Main-Belt asteroids.

To know more…

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