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# Standard asteroid physical characteristics

## From Wikipedia, the free encyclopedia

For the majority of numbered asteroids, almost nothing is known apart from a few physical parameters and orbital elements and some physical characteristics are often only estimated. The physical data is determined by making certain standard assumptions.

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• ✪ Eugene Bagashov: Asteroid Missions and Crumbling Theories | Space News
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#### Transcription

Welcome to Space News from the Electric Universe, brought to you by The Thunderbolts Project™ at Thunderbolts.info Today, two spacecraft exploring two separate asteroids may provide critical data that could change scientists' thoughts about these mysterious rocky worlds. Since June of 2018, the Japanese spacecraft Hayabusa2 has surveyed the surface of the asteroid Ryugu and recently Japan's space agency performed a touchdown on the object to collect physical samples, which will reach the Earth late next year. Meanwhile, NASA's OSIRIS-REx spacecraft is exploring an asteroid of remarkably similar size, called Bennu, with dust samples from the asteroid scheduled to return to Earth in 2023. Already, what the spacecraft have found has surprised scientists on Earth, including the "surprisingly dry" surface of Ryugu, and recently, the completely unexpected emission of "energetic plumes" of particles from the asteroid Bennu. In part 1 of this three-part presentation, physicist Eugene Bagashov explores in detail what the missions have already found, and he suggests from the Electric Universe perspective what forthcoming discoveries might reveal. Recently, there has been quite a surge of research papers published in journals Science and Nature regarding the preliminary results of OSIRIS REx and Hayabusa2 missions to the asteroids Bennu and Ryugu correspondingly. Here I wish to review some of these results and their possible implications for the Electric Universe paradigm. Firstly, I'd like to give a rough description of what astronomers currently believe is the origin of these objects so that all the following findings and surprises could be placed in the proper context. So from what I've read in these 10 papers, it follows that both Bennu and Ryugu are supposed to have formed in the inner asteroid belt, some hundreds of millions of years ago or perhaps a billion years ago, being the results of a disruption of larger bodies, approximately 100-kilometer-sized asteroids. And supposedly, of course, these disruptions were caused by impact events so the material released during these impacts reaccreted to form what is now known as Bennu and Ryugu, then for some unknown reason these asteroids migrated to the inner solar system; for Bennu the current estimate for that is about 10 million years ago and for Ryugu it's about 40 million years ago. And since then they both are found here, roughly between the orbits of Earth and Mars. With regards to their internal structure and composition, astronomers refer to them as "rubble piles" and it is supposed that they are composed of multitude of poorly connected pieces that have appeared after the disruptions of their parent bodies. From that, I think we might already see that it is acknowledged that some catastrophic events should predate the appearance of these objects, so many of the conclusions that the astronomers arrive at would not directly contradict the usually assumed Electric Universe scenarios. In my opinion, the same thing might have happened in the EU catastrophism. Indeed, it is not impossible that a large asteroid might have been destroyed and its pieces later formed some other bodies; it's just the exact reason for its destruction might have been different, namely electrical. Yet, at the same time one might pursue a line of thinking that is more divergent from that, namely that both Ryugu and Bennu are not the aggregates of pieces of a larger asteroid but rather single chunks torn away from a big planet like Earth, Venus or Mars for example, or maybe the Moon or Mercury. As far as this scenario potentially provides more contradicting predictions with respect to the nebular hypothesis, I would choose to mostly stick to it although again with the caveat that it is possible to choose a version of the origins of Ryugu and Bennu in the EU paradigm that is less disagreeable with the nebular-hypothesis-astrophysics. Now let's get into more details. First of all it's worth noting how similar these two objects are. Their size is comparable, the average diameter of Ryugu is just a bit below 1 km and the diameter of Bennu is about 0.5 km, they both are very dark, almost completely black reflecting almost identical amount of solar light of only about 4.5% which places them among the darkest known objects in the solar system and they both demonstrate what the scientists refer to as "spinning top shape." That is in particular a pretty peculiar uplift in the equatorial region which makes them not quite spherical. Here we might mark the first line of separation between what the astronomers believe to be the reason for that shape and what the more extreme EU scenarios of the planetary excavation might provide. So the idea currently adopted by research teams of both Hayabusa 2 and OSIRIS-REx is that this shape came into being because of the rotation of these supposed rubble piles so that the poorly bound material just accumulated in the equatorial region due to the centrifugal force. But what about the electrical scenario? Could the electricity produce the same shape, at least potentially? I believe it could and in support of this statement I wish to remember one paper that described the application of electric fields to fluids. The authors of this paper have found that under some conditions, the electric fields caused the droplets of fluid to squash almost into a pancake shape; notably at this time they also released some material from the equatorial region in the form of smaller droplets, or even rings, but when the field disappears, the droplets assume the more relaxed spherical shape again. Of course, that has some implications to the oblate shape of Saturn and the possible emergence of its rings due to the previous electric stresses. I even once had an idea that one day we might learn to use these rings almost like in tinder dendrochronology to determine the space climate so to speak, the electromagnetic conditions in the past of the solar system from the ring density and the size of the gaps between them etc. But anyway, returning to Ryugu and Bennu, I think it might have been possible to achieve this same shape through application of the electric fields during the time of their formation. It is possible again that the asteroids therefore do not represent piles of rubble but rather a more or less homogeneous objects with quite good internal strength that was able to retain this peculiar shape since the time of their formation. Of course, the paper I am referring to had dealt with liquids, but at least I believe the general pattern is there and at the moment it is unclear what might happen to the crustal rock during extremely intense electric discharges. Perhaps they might undergo a sequence of phase transitions or other types of structural transformations etc. I should note how symmetric and regular they look; both these objects almost look like monolithic crystals rather than a bunch of irregular rocks randomly stuck together with microgravity. Let's talk now about densities of Ryugu and Bennu. They are quite remarkably the same, 1,190 kg/m³ for both of the bodies. In my opinion, this incredible similarity would be quite hard to achieve if both of them were the result of sticking together of a bunch of different rocks forming the proverbial rubble pile that the researchers keep talking about. Such similarity, in my opinion, would indicate that perhaps both of these bodies originate from the same type of initial rock that again, according to the scenario discussed above, might have belonged to a large planet and have been excavated from it electrically. What is also interesting is that this density figure is much lower than the one usually assumed for an average asteroid that is about 2,000 kg/m³ and much closer to the cometary nuclei that have densities in the region of about 800 kg/m³. And just as in case of cometary nuclei, here the researchers assume that the low density is the result of high porosity which is estimated to be 50% or even bigger. However, they assume that high porosity is the result of this rubble pile type of inner structure rather than the property of the rock itself, but I wish to repeat my point from the previous recent videos on Mars, I think that the higher porosity might be the consequence of internal transformations of the crustal planetary rock under the influence of extremely strong electric discharges. In order to validate the rubble pile scenario, the researchers from OSIRIS REx team propose that there might be some internal inhomogeneities in the asteroid Bennu. In particular, they say that their measurements "...correspond to about 0.1% shift in the center of mass and an approximately 0.1 degree offset of the principal axis with respect to a constant density shape, and they indicate heterogeneity in the mass distribution." Well OK, let's suppose that the measurements are correct, though in my opinion that is not guaranteed, but is 0.1% shift of the center of mass and 0.1 degree offset of the axis with respect to the constant density shape such a big deal? Is this a good piece of evidence for any significant inhomogeneity? It is only my opinion but I would say that quite the contrary, such a miniscule offset indicates a pretty homogeneous and incredibly ordered object, especially given its size. Objects less than 1 km in size should be nowhere near as ordered if their shapes are maintained by gravitation alone. Only bodies of few hundreds of kilometers in size might assume spherical form gravitationally. Moreover, even if you look at Earth, we have about 2.5 km offset of the center of mass with respect to the center of figure, which in terms of percent translates into 0.04. Is therefore Earth a rubble pile or is it still highly structured? Other point that the OSIRIS REx team makes with regards to density is that "...at 50-60%, Bennu's high total porosity is incompatible with a monolithic body and may be the strongest evidence for a rubble-pile interior." Well, it's a shame that these people don't even read their colleagues' papers, otherwise they would know that Rosetta mission has shown that the nucleus of the comet 67P is internally highly homogeneous and at the same time it has even higher porosity of more than 70%. So it seems that this argument is also invalid. With regards to that, it's probably worth to remember the unexpectedly strong material of the comet 67P nucleus. As you probably know, the MUPUS penetrator, on board of Philae lander, failed to insert itself into the nucleus and even the SD2 instrument drill seems to have failed to make a hole in it just lifting the lander instead. In my opinion, the same underestimation might happen with asteroids Ryugu and Bennu, if the hypothetical rubble pile scenario would prove to be wrong. In the next two videos, we'll discuss some other hints that it might be the case, but so far I wish to note that this potentially has some implications for the upcoming impactor release event that Hayabusa2 team is currently planning to conduct in early April. In my opinion, the estimates of the depth of crater that this impactor would create are higher than what would be actually observed, as the strength of the rock of Ryugu is most likely underestimated. So perhaps the crater would be flatter and wider rather than deeper and narrower, even though the impactor is a 2.5 kilogram copper projectile that is going to be shot into Ryugu at the astonishing speed of 2 km/s. Now some might say that the discharge between the impactor and the surface of Ryugu is also possible but I have some doubts about that, given the fact that Hayabusa 2 was orbiting the asteroid for a few months already and it even had a touchdown on the surface in February. On a final note, I'd like to say that of course it's quite hard to predict exactly the properties of rock that has undergone the processes that we don't observe today so maybe I would be wrong in my conclusions, even though the initial ideas would be correct.

## Dimensions

Data from the IRAS minor planet survey[1] or the Midcourse Space Experiment (MSX) minor planet survey[2] (available at the Planetary Data System Small Bodies Node (PDS)) is the usual source of the diameter.

For many asteroids, lightcurve analysis provides estimates of pole direction and diameter ratios. Pre-1995 estimates collected by Per Magnusson[3] are tabulated in the PDS,[4] with the most reliable data being the syntheses labeled in the data tables as "Synth". More recent determinations for several dozens of asteroids are collected at the web page of a Finnish research group in Helsinki which is running a systematic campaign to determine poles and shape models from lightcurves.[5]

These data can be used to obtain a better estimate of dimensions. A body's dimensions are usually given as a tri-axial ellipsoid, the axes of which are listed in decreasing order as a×b×c. If we have the diameter ratios μ = a/b, ν = b/c from lightcurves, and an IRAS mean diameter d, one sets the geometric mean of the diameters ${\displaystyle d=(abc)^{\frac {1}{3}}\,\!}$ for consistency, and obtains the three diameters:

${\displaystyle a=d\,(\mu ^{2}\nu )^{\frac {1}{3}}\,\!}$
${\displaystyle b=d\,\left({\frac {\nu }{\mu }}\right)^{\frac {1}{3}}\,\!}$
${\displaystyle c={\frac {d}{(\nu ^{2}\mu )^{\frac {1}{3}}}}\,\!}$

## Mass

Barring detailed mass determinations,[6] the mass M can be estimated from the diameter and (assumed) density values ρ worked out as below.

${\displaystyle M={\frac {\pi abc\rho }{6}}\,\!}$

Such estimates can be indicated as approximate by use of a tilde "~". Besides these "guesstimates", masses can be obtained for the larger asteroids by solving for the perturbations they cause in each other's orbits,[7] or when the asteroid has an orbiting companion of known orbital radius. The masses of the largest asteroids 1 Ceres, 2 Pallas, and 4 Vesta can also be obtained from perturbations of Mars.[8] While these perturbations are tiny, they can be accurately measured from radar ranging data from the Earth to spacecraft on the surface of Mars, such as the Viking landers.

## Density

Apart from a few asteroids whose densities have been investigated,[6] one has to resort to enlightened guesswork. See Carry[9] for a summary.

For many asteroids a value of ρ~2 g/cm3 has been assumed.

However, density depends on the asteroid's spectral type. Krasinsky et al. gives calculations for the mean densities of C, S, and M class asteroids as 1.38, 2.71, and 5.32 g/cm3.[10] (Here "C" included Tholen classes C, D, P, T, B, G, and F, while "S" included Tholen classes S, K, Q, V, R, A, and E). Assuming these values (rather than the present ~2 g/cm3) is a better guess.

## Surface gravity

### Spherical body

For a spherical body, the gravitational acceleration at the surface (g), is given by

${\displaystyle g_{\rm {spherical}}={\frac {GM}{r^{2}}}\,\!}$

Where G = 6.6742×10−11 m3s−2kg−1 is the gravitational constant, M is the mass of the body, and r its radius.

### Irregular body

For irregularly shaped bodies, the surface gravity will differ appreciably with location. The above formula then is only an approximation, as the calculations become more involved. The value of g at surface points closer to the center of mass is usually somewhat greater than at surface points farther out.

### Centripetal force

On a rotating body, the apparent weight experienced by an object on the surface is reduced by the centripetal force, when one is away from the poles. The centripetal acceleration experienced at a latitude θ is

${\displaystyle g_{\rm {centrifugal}}=-\left({\frac {2\pi }{T}}\right)^{2}r\sin \theta }$

where T is the rotation period in seconds, r is the equatorial radius, and θ is the latitude. Its magnitude is maximized when one is at the equator, and sinθ=1. The negative sign indicates that it acts in the opposite direction to the gravitational acceleration g.

The effective acceleration is

${\displaystyle g_{\rm {effective}}=g_{\rm {gravitational}}+g_{\rm {centrifugal}}\ .}$

### Close binaries

If the body in question is a member of a close binary with components of comparable mass, the effect of the second body may also be non-negligible.

## Escape velocity

For surface gravity g and radius r of a spherically symmetric body, the escape velocity is:

${\displaystyle v_{e}={\sqrt {\frac {2GM}{r}}}}$

## Rotation period

Rotation period is usually taken from lightcurve parameters at the PDS.[11]

## Spectral class

Spectral class is usually taken from the Tholen classification at the PDS.[12]

## Absolute magnitude

Absolute magnitude is usually given by the IRAS minor planet survey[1] or the MSX minor planet survey[2] (available at the PDS).

## Albedo

Astronomical albedos are usually given by the IRAS minor planet survey[1] or the MSX minor planet survey[2] (available at the PDS). These are geometric albedos. If there is no IRAS/MSX data a rough average of 0.1 can be used.

## Surface temperature

### Mean

The simplest method which gives sensible results is to assume the asteroid behaves as a greybody in equilibrium with the incident solar radiation. Then, its mean temperature is obtained by equating the mean incident and radiated heat power. The total incident power is:

${\displaystyle R_{\mathrm {in} }={\frac {(1-A)L_{0}\pi r^{2}}{4\pi a^{2}}},}$

where ${\displaystyle A\,\!}$ is the asteroid albedo (precisely, the Bond albedo), ${\displaystyle a\,\!}$ its semi-major axis, ${\displaystyle L_{0}\,\!}$ is the solar luminosity (i.e. total power output 3.827×1026 W), and ${\displaystyle r}$ the asteroid's radius. It has been assumed that: the absorptivity is ${\displaystyle 1-A}$, the asteroid is spherical, it is on a circular orbit, and that the Sun's energy output is isotropic.

Using a greybody version of the Stefan-Boltzmann law, the radiated power (from the entire spherical surface of the asteroid) is:

${\displaystyle R_{\mathrm {out} }=4\pi r^{2}\epsilon \sigma T^{4}{\frac {}{}},}$

where ${\displaystyle \sigma \,\!}$ is the Stefan-Boltzmann constant (5.6704×10−8 W/m²K4), ${\displaystyle T}$ is the temperature in kelvins, and ${\displaystyle \epsilon \,\!}$ is the asteroid's infra-red emissivity. Equating ${\displaystyle R_{\mathrm {in} }=R_{\mathrm {out} }}$, one obtains

${\displaystyle T=\left({\frac {(1-A)L_{0}}{\epsilon \sigma 16\pi a^{2}}}\right)^{1/4}\,\!}$

The standard value of ${\displaystyle \epsilon }$=0.9, estimated from detailed observations of a few of the large asteroids is used.

While this method gives a fairly good estimate of the average surface temperature, the local temperature varies greatly, as is typical for bodies without atmospheres.

### Maximum

A rough estimate of the maximum temperature can be obtained by assuming that when the Sun is overhead, the surface is in thermal equilibrium with the instantaneous solar radiation. This gives average "sub-solar" temperature of

${\displaystyle T_{ss}={\sqrt {2}}\,T\approx 1.41\,T,}$

where ${\displaystyle T}$ is the average temperature calculated as above.

At perihelion, the radiation is maximised, and

${\displaystyle T_{ss}^{\rm {max}}={\sqrt {\frac {2}{1-e}}}\ T,}$

where ${\displaystyle e\,\!}$ is the eccentricity of the orbit.

### Temperature measurements and regular temperature variations

Infra-red observations are commonly combined with albedo to measure the temperature more directly. For example, L.F.Lim et al. [Icarus, Vo. 173, 385 (2005)] does this for 29 asteroids. However, it should be pointed out that these are measurements for a particular observing day, and that the asteroid's surface temperature will change in a regular way depending on its distance from the Sun. From the Stefan-Boltzmann calculation above,

${\displaystyle T={\rm {constant}}\times {\frac {1}{\sqrt {d}}},}$

where ${\displaystyle d\,\!}$ is the distance from the Sun on any particular day. If the day of the relevant observations is known, the distance from the Sun on that day can be obtained online from e.g. the NASA orbit calculator,[13] and corresponding temperature estimates at perihelion, aphelion, etc. can be obtained from the expression above.

### Albedo inaccuracy problem

There is a snag when using these expressions to estimate the temperature of a particular asteroid. The calculation requires the Bond albedo A (the proportion of total incoming power reflected, taking into account all directions), while the IRAS and MSX albedo data that is available for asteroids gives only the geometric albedo p which characterises only the strength of light reflected back to the source (the Sun).

While these two albedos are correlated, the numerical factor between them depends in a very nontrivial way on the surface properties. Actual measurements of Bond albedo are not forthcoming for the majority of asteroids because they require measurements from high phase angles that can only be acquired by spacecraft that pass near or beyond the asteroid belt. Some complicated modelling of surface and thermal properties can lead to estimates of the Bond albedo given the geometric one, but this far is beyond the scope of a quick estimate for these articles. It can be obtained for some asteroids from scientific publications.

For want of a better alternative for most asteroids, the best that can be done here is to assume that these two albedos are equal, but keep in mind that there is an inherent inaccuracy in the resulting temperature values.

How large is this inaccuracy?

A glance at the examples in this table shows that for bodies in the asteroid albedo range, the typical difference between Bond and geometric albedo is 20% or less, with either quantity capable of being larger. Since the calculated temperature varies as (1-A)1/4, the dependence is fairly weak for typical asteroid Ap values of 0.05−0.3.

The typical inaccuracy in calculated temperature from this source alone is then found to be about 2%. This translates to an uncertainty of about ±5 K for maximum temperatures.

## Other common data

Some other information for large numbers of asteroids can be found at the Planetary Data System Small Bodies Node.[14] Up-to-date information on pole orientation of several dozen asteroids is provided by Doc. Mikko Kaasalainen,[5] and can be used to determine axial tilt.

Another source of useful information is NASA's orbit calculator.[13]

## References

1. ^ a b c "IRAS Minor Planet Survey  Supplemental IRAS Minor Planet Survey". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-02. Retrieved 2006-10-21.
2. ^ a b c "Midcourse Space Experiment (MSX) Infrared Minor Planet Survey". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-02. Retrieved 2006-10-21.
3. ^ Magnusson, Per (1989). "Pole determinations of asteroids". In Richard P. Binzel; Tom Gehrels; Mildred S. Matthews (eds.). Asteroids II. Tucson: University of Arizona Press. pp. 1180–1190.
4. ^ "Asteroid Spin Vectors". Archived from the original on 2006-09-02. Retrieved 2006-10-21.
5. ^ a b Modeled asteroids. rni.helsinki.fi. 2006-06-18.
6. ^ a b For example "Asteroid Densities Compilation". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-02. Retrieved 2006-10-21.
7. ^ Hilton, James L. (November 30, 1999). "Masses of the Largest Asteroids". Archived from the original on February 12, 2009. Retrieved 2009-09-05.
8. ^ Pitjeva, E. V. (2004). Estimations of masses of the largest asteroids and the main asteroid belt from ranging to planets, Mars orbiters and landers. 35th COSPAR Scientific Assembly. Held 18–25 July 2004. Paris, France. p. 2014. Bibcode:2004cosp...35.2014P.
9. ^ Benoit Carry, Density of asteroids, Planetary & Space Science to be published (accessed Dec. 20, 2013
10. ^ Krasinsky, G. A.; Pitjeva, E. V.; Vasilyev, M. V.; Yagudina, E. I. (July 2002). "Hidden Mass in the Asteroid Belt". Icarus. 158 (1): 98–105. Bibcode:2002Icar..158...98K. doi:10.1006/icar.2002.6837.
11. ^ "Asteroid Lightcurve Parameters". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-02. Retrieved 2006-10-21.
12. ^ Asteroid Taxonomies PDS Asteroid/Dust Archive. 2006-10-21.
13. ^ a b "Orbit Diagrams". NASA. Retrieved 2006-06-18.
14. ^ "Asteroid Data Sets". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-28. Retrieved 2006-10-21.
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