Table combining the critical properties of these planetoids... links on the names go to Mike Brown's page on each object.
| Name | a | H | Moon? | R/Rpluto | Size_method |
| 2003 UB313 | 67.7 | n/a | ? | 1-2 | radiometric(limit) |
| 2003 EL61 | 43.4 | 0.30 | yes | 0.7 | moon_orbit |
| Orcus (2004 DW) | 39.4 | 2.30 | ? | ~0.5 | radiometric(limit) |
| Sedna | 502.8 | 1.57 | ? | ~0.7 | radiometric(limit) |
| Quaoar | 43.5 | 2.70 | ? | 0.5 | resolved(HST) |
| Pluto | 39.5 | n/a | Charon | 1 | resolved |
To get the detailed orbits including an orbital diagram, enter the designation into the DASTCOM browser.
Here is a description of how sizes are measured using observed brightness and visible and infrared wavelengths.
Observations at visible wavelengths tell us the amount of light reflected
back to the Earth from an object. This will depend on how shiny the object
is, how big it is, and what fraction of the object is illuminated at the
time of observation. The shininess of an object is measured as a quantity
called "albedo", usually written with symbol A or sometimes pV, that measures
the fraction of light incident on the object that is reflected back to us.
The size of the object is pi*R^2 where R is the radius. And the decrease
in brightness that occurs when we see more of the "night" side of an
object is characterized as its phase function. Thus the brightness of an
object in reflected light may be written as follows:
FV = pV * pi*R^2 * P(phi) * Fsun / Delta^2
where P is the phase function and phi is the phase angle, the angle between
the line from the Sun to the object and the line from the object to the
observer (Sun-Target-Observer). Fsun is the flux of sunlight on the surface,
and Delta is the distance from the object to the observer. The phase function
may seem complicated in this equation, and indeed it can be very complicated
in detail, but for outer Solar System objects the phase angle is usually
small because the objects are so distant. So what we really need is the
phase function for nearly zero phase. Barring any funny effects for
near-zero phase (effects that DO occur for most surfaces but usually
only at VERY small phase, so worth keeping in mind but generally
glossed over for rough estimates), then we can say P=1.
If we only know the visible brightness, then we can only determine the size by assuming the albedo. Comets are dark and have pV~0.04, while Pluto is relatively bright and some Kuiper Belt objects are found to have pV~0.2. So in lack of other information, a good guess is pV~0.1. If the object turns out to be as dark as a comet, then this guess will have overestimated pV, and the object must have actually had a radius that is 60% than our guess. If the object turns out to have pV=0.2, then we will have underestimated and the object will actually have a radius that is 40% SMALLER. To avoid this uncertainty, it's obviously best to constrain the albedo, which is done with infrared observations.
Observations at infrared wavelengths tell us the fraction of light that
is absorbed (and subsequently re-radiated) by an object. If we measure the
total infrared flux, and all the energy absorbed by the object is reradiated
in the infrared, then we measured the
FIR = (1-A) * pi*R^2 * Fsun / Delta^2.
where A is now, specifically, the "Bond albedo" which is the fraction of
incident light that is reflected (so 1-A is the fraction absorbed). We
pretty much never measure the total infrared flux; instead we measure
at one or a few wavelengths. To convert from observations at one wavelength
to the total flux is an interesting story and has an uncertainty of about
a factor of 2 (if only one wavelength is measured) or less if multiple
wavelengths are used.
There is a standard relation between the bond Albedo, A, and the visible
geometric albedo, pV, measured for asteroids and the Moon, usually
written as A=pV*q.
If this holds for the object that we are working on,
then the SUM of the visible and infrared flux is
Ftot = FIR + FV * q/P = [A + (1-A) ] * pi*R^2 * Fsun / Delta^2
= pi * R^2 * Fsun/Delta^2
Since we know the solar flux and the distance to the object, we directly
measure the size of the object, R^2.
The ratio of the visible to infrared flux gives the albedo of the
object. Specifically,
FV / FIR = pV * P / (1-A) = [A / (1-A) ] * P/q
so if we adopt a phase curve and know P and q, we solve for the Bond albedo,
A; equivalently we could solve for the geometric albedo, pV.
In practice, we usually have only limited observations of the thermal
radiation, covering a small part of the spectrum. For outer Solar System
objects, the bulk of the enery is emitted in the 50-180 micron range.
The Spitzer/MIPS instrument has bands at 70 and 160 microns. In order to
use observations at those wavelengths to constrain the size and albedo of
the object, we must take into account the details of how the absorbed
energy is distributed across the object's surface. These details are
extremely significant for determining how much energy is emitted at
the wavelengths less than or near near the peak of the spectrum.
The peak emission will occur around
wavelength_peak = 15 sqrt(r) microns
so for objects at r=40 AU (like Pluto) the peak is around 90 microns,
and for 2003 UB313 at r=97 AU, the peak is around 140 microns.
The infrared emission is reasonably well matched by a simple model, called the "Standard Thermal Model," in which it is assumed that the object rotates slowly and has low surface thermal conductivity. Then the temperature of a given point on the illuminated surface depends only on how much sunlight is hitting it, and the night side is completely cold. The subsolar point is hottest, and the temperature falls off as cos^(1/4)(theta), where theta is the latitudinal angle with respect to the subsolar point. The basic model initially failed to predict the observed emission, so an extra tuning parameter, eta, was introduced. This extra parameter allows scales the subsolar temperature, while keeping the temperature distribution the same as the orignal standard thermal model. In the calculations below, we refer to the IRAS Standard Thermal Model (STM), which was determined by fitting a large number of asteroids at 12-100 micron wavelength using data from IRAS. The eta=0.756 in this model.
More recently it has been found that the IRAS STM does not match the spectral energy distribution of near earth objects. The parameter eta was allowed to be free again, and a value of eta=1 (or sometimes a bit higher than 1) has been found to match these small bodies. We refer to the Standard Thermal Model with parameters tuned to match near Earth asteroids as the NEATM.
If the object rotates relatively quickly (with respect to the time it takes to spread heat across the surface), then a different temperature distribution is established. Assuming the rotation axis is perpendicular to the orbital plane, one obtains a simple temperature distribution that is only a function of the latitude. The equator is hottest and the poles coldest. There is no day-night asymmetry in this limit. Atmospheres will tend to move bodies toward this limit. It appears that Pluto is closer to this limit than to the STM or NEATM.
For a given geometric albedo assumption, we use a diameter that yields
the correct absolute magnitude (i.e. the correct optical brightness)
taken from DASTCOM. Note that since the geometric albedo does not uniquely
specify the Bond albedo, which is what we need for the thermal modeling.
Therefore, for each assumed geometric albedo, there are also different
results for different assumption of the phase curve. For the pV=0.5 case,
we give the results for three possible phase curve shapes (G=0.15, 0.3, 0.9)
that should span what we have seen from dark asteroids (low G) to icy satellites (high G).
The predictions are in mJy.
For each object, the there are three lines. The first one gives the predictions for the IRAS STM, the second one is for NEATM, and the third one is for the FRM.
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.074 0.024 0.186 105.606 176.790 6974
0.000 0.000 0.032 56.833 130.872
0.000 0.000 0.001 17.758 77.846
2005fy9 2005-Jun-21 51.88 51.87 0.281 0.090 10.004 482.093 410.615 4013
0.000 0.000 2.763 305.005 324.112
0.000 0.000 0.204 131.364 216.007
2003el61 2005-Jun-22 51.24 50.93 0.273 0.088 10.111 467.344 393.686 3832
0.000 0.000 2.813 296.334 310.932
0.000 0.000 0.211 128.300 207.596
sedna 2004-Jan-01 89.55 88.91 0.009 0.003 0.032 12.962 19.641 2039
0.000 0.000 0.006 7.133 14.660
0.000 0.000 0.000 2.336 8.870
orcus 2005-May-14 47.68 47.45 0.052 0.017 2.443 89.037 70.455 1457
0.000 0.000 0.711 57.346 55.998
0.000 0.000 0.059 25.580 37.774
quaoar 2005-Apr-05 43.34 43.01 0.053 0.017 3.300 89.057 65.149 1212
0.000 0.000 1.017 58.473 52.168
0.000 0.000 0.095 27.077 35.644
assumed pV= 0.100000,G= 0.150000 (A= 0.0392600), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.074 0.024 0.047 31.529 55.806 4026
0.000 0.000 0.008 16.753 41.109
0.000 0.000 0.000 5.098 24.219
2005fy9 2005-Jun-21 51.88 51.87 0.281 0.090 2.661 147.934 130.954 2317
0.000 0.000 0.713 92.749 103.022
0.000 0.000 0.050 39.220 68.226
2003el61 2005-Jun-22 51.24 50.93 0.273 0.088 2.693 143.473 125.576 2212
0.000 0.000 0.727 90.159 98.852
0.000 0.000 0.052 38.330 65.585
sedna 2004-Jan-01 89.55 88.91 0.009 0.003 0.008 3.885 6.209 1177
0.000 0.000 0.001 2.112 4.613
0.000 0.000 0.000 0.675 2.766
orcus 2005-May-14 47.68 47.45 0.052 0.017 0.655 27.405 22.495 841
0.000 0.000 0.186 17.499 17.822
0.000 0.000 0.015 7.671 11.950
quaoar 2005-Apr-05 43.34 43.01 0.053 0.017 0.894 27.500 20.825 699
0.000 0.000 0.268 17.909 16.626
0.000 0.000 0.024 8.157 11.296
assumed pV= 0.300000,G= 0.150000 (A= 0.117780), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.074 0.024 0.022 16.728 31.517 3119
0.000 0.000 0.003 8.763 23.089
0.000 0.000 0.000 2.589 13.457
2005fy9 2005-Jun-21 51.88 51.87 0.281 0.090 1.242 80.936 74.816 1794
0.000 0.000 0.322 50.230 58.638
0.000 0.000 0.021 20.807 38.556
2003el61 2005-Jun-22 51.24 50.93 0.273 0.088 1.259 78.535 71.757 1714
0.000 0.000 0.329 48.856 56.276
0.000 0.000 0.022 20.350 37.074
sedna 2004-Jan-01 89.55 88.91 0.009 0.003 0.004 2.071 3.513 912
0.000 0.000 0.001 1.110 2.596
0.000 0.000 0.000 0.345 1.541
orcus 2005-May-14 47.68 47.45 0.052 0.017 0.309 15.044 12.868 651
0.000 0.000 0.085 9.514 10.159
0.000 0.000 0.006 4.089 6.766
quaoar 2005-Apr-05 43.34 43.01 0.053 0.017 0.425 15.152 11.928 542
0.000 0.000 0.124 9.777 9.491
0.000 0.000 0.010 4.372 6.408
assumed pV= 0.500000,G= 0.150000 (A= 0.196300), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.076 0.024 0.017 15.308 30.177 3119
0.000 0.000 0.002 7.937 22.018
0.000 0.000 0.000 2.295 12.733
2005fy9 2005-Jun-21 51.88 51.87 0.289 0.093 1.035 75.730 72.236 1794
0.000 0.000 0.262 46.656 56.462
0.000 0.000 0.016 19.040 36.933
2003el61 2005-Jun-22 51.24 50.93 0.281 0.090 1.050 73.511 69.292 1714
0.000 0.000 0.268 45.398 54.196
0.000 0.000 0.017 18.632 35.521
sedna 2004-Jan-01 89.55 88.91 0.009 0.003 0.003 1.901 3.368 912
0.000 0.000 0.000 1.009 2.479
0.000 0.000 0.000 0.307 1.460
orcus 2005-May-14 47.68 47.45 0.054 0.017 0.259 14.111 12.435 651
0.000 0.000 0.069 8.861 9.792
0.000 0.000 0.005 3.755 6.490
quaoar 2005-Apr-05 43.34 43.01 0.054 0.017 0.360 14.249 11.539 542
0.000 0.000 0.103 9.134 9.159
0.000 0.000 0.008 4.030 6.155
assumed pV= 0.500000,G= 0.300000 (A= 0.247600), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.081 0.026 0.007 9.778 24.275 3119
0.000 0.000 0.001 4.812 17.352
0.000 0.000 0.000 1.248 9.638
2005fy9 2005-Jun-21 51.88 51.87 0.320 0.103 0.415 54.160 60.657 1794
0.000 0.000 0.092 32.141 46.754
0.000 0.000 0.004 12.153 29.777
2003el61 2005-Jun-22 51.24 50.93 0.310 0.100 0.423 52.672 58.225 1714
0.000 0.000 0.095 31.341 44.914
0.000 0.000 0.005 11.924 28.667
sedna 2004-Jan-01 89.55 88.91 0.010 0.003 0.001 1.234 2.726 912
0.000 0.000 0.000 0.623 1.968
0.000 0.000 0.000 0.171 1.116
orcus 2005-May-14 47.68 47.45 0.060 0.019 0.107 10.219 10.490 651
0.000 0.000 0.026 6.192 8.152
0.000 0.000 0.001 2.440 5.268
quaoar 2005-Apr-05 43.34 43.01 0.061 0.019 0.155 10.459 9.782 542
0.000 0.000 0.040 6.481 7.668
0.000 0.000 0.003 2.670 5.033
assumed pV= 0.500000,G= 0.900000 (A= 0.452800), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.082 0.026 0.006 8.558 22.768 3119
0.000 0.000 0.000 4.146 16.175
0.000 0.000 0.000 1.041 8.875
2005fy9 2005-Jun-21 51.88 51.87 0.327 0.105 0.318 49.033 57.632 1794
0.000 0.000 0.068 28.773 44.236
0.000 0.000 0.003 10.633 27.946
2003el61 2005-Jun-22 51.24 50.93 0.317 0.102 0.324 47.712 55.333 1714
0.000 0.000 0.070 28.075 42.505
0.000 0.000 0.003 10.441 26.913
sedna 2004-Jan-01 89.55 88.91 0.010 0.003 0.001 1.086 2.562 912
0.000 0.000 0.000 0.540 1.839
0.000 0.000 0.000 0.143 1.030
orcus 2005-May-14 47.68 47.45 0.061 0.020 0.083 9.287 9.981 651
0.000 0.000 0.019 5.567 7.725
0.000 0.000 0.001 2.147 4.954
quaoar 2005-Apr-05 43.34 43.01 0.062 0.020 0.120 9.543 9.321 542
0.000 0.000 0.030 5.853 7.279
0.000 0.000 0.002 2.362 4.743
assumed pV= 0.500000,G= 1.03801 (A= 0.500000), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.082 0.026 0.003 3.775 13.438 2735
0.000 0.000 0.000 1.714 9.300
0.000 0.000 0.000 0.375 4.845
2005fy9 2005-Jun-21 51.88 51.87 0.327 0.105 0.085 24.929 35.932 1574
0.000 0.000 0.014 13.955 27.092
0.000 0.000 0.000 4.681 16.535
2003el61 2005-Jun-22 51.24 50.93 0.317 0.102 0.087 24.315 34.529 1503
0.000 0.000 0.015 13.653 26.059
0.000 0.000 0.001 4.612 15.944
sedna 2004-Jan-01 89.55 88.91 0.010 0.003 0.000 0.489 1.524 799
0.000 0.000 0.000 0.228 1.067
0.000 0.000 0.000 0.053 0.569
orcus 2005-May-14 47.68 47.45 0.061 0.020 0.023 4.797 6.260 571
0.000 0.000 0.004 2.749 4.764
0.000 0.000 0.000 0.967 2.957
quaoar 2005-Apr-05 43.34 43.01 0.062 0.020 0.034 5.013 5.883 475
0.000 0.000 0.007 2.946 4.522
0.000 0.000 0.000 1.090 2.857
assumed pV= 0.650000,G= 1.03801 (A= 0.650000), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.082 0.026 0.003 1.158 6.916 2465
0.000 0.000 0.000 0.469 4.566
0.000 0.000 0.000 0.080 2.165
2005fy9 2005-Jun-21 51.88 51.87 0.327 0.105 0.019 9.827 20.418 1418
0.000 0.000 0.001 5.060 14.905
0.000 0.000 0.000 1.428 8.542
2003el61 2005-Jun-22 51.24 50.93 0.317 0.102 0.019 9.625 19.653 1355
0.000 0.000 0.001 4.974 14.364
0.000 0.000 0.000 1.415 8.256
sedna 2004-Jan-01 89.55 88.91 0.010 0.003 0.000 0.156 0.796 721
0.000 0.000 0.000 0.065 0.533
0.000 0.000 0.000 0.012 0.260
orcus 2005-May-14 47.68 47.45 0.061 0.020 0.004 1.945 3.595 515
0.000 0.000 0.000 1.029 2.653
0.000 0.000 0.000 0.307 1.552
quaoar 2005-Apr-05 43.34 43.01 0.062 0.020 0.006 2.095 3.418 428
0.000 0.000 0.001 1.141 2.552
0.000 0.000 0.000 0.361 1.525
assumed pV= 0.800000,G= 1.03801 (A= 0.800000), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.082 0.026 0.003 0.253 3.219 2324
0.000 0.000 0.000 0.087 1.982
0.000 0.000 0.000 0.010 0.816
2005fy9 2005-Jun-21 51.88 51.87 0.327 0.105 0.012 3.089 11.022 1337
0.000 0.000 0.000 1.408 7.665
0.000 0.000 0.000 0.308 3.992
2003el61 2005-Jun-22 51.24 50.93 0.317 0.102 0.011 3.044 10.634 1277
0.000 0.000 0.000 1.394 7.407
0.000 0.000 0.000 0.308 3.872
sedna 2004-Jan-01 89.55 88.91 0.010 0.003 0.000 0.036 0.379 679
0.000 0.000 0.000 0.013 0.237
0.000 0.000 0.000 0.002 0.101
orcus 2005-May-14 47.68 47.45 0.061 0.020 0.002 0.637 1.972 485
0.000 0.000 0.000 0.300 1.390
0.000 0.000 0.000 0.070 0.743
quaoar 2005-Apr-05 43.34 43.01 0.062 0.020 0.002 0.717 1.907 404
0.000 0.000 0.000 0.349 1.364
0.000 0.000 0.000 0.088 0.748
assumed pV= 0.900000,G= 1.03801 (A= 0.900000), and used the values of H in Horizons
Object Date R Delta F4.5 F8 F24 F70 F160mJy Diam(km)
2003ub313 2005-Aug-23 96.91 96.44 0.081 0.026 0.003 0.044 1.361 2205
0.000 0.000 0.000 0.012 0.770
0.000 0.000 0.000 0.001 0.266
2005fy9 2005-Jun-21 51.88 51.87 0.323 0.104 0.011 0.816 5.587 1269
0.000 0.000 0.000 0.321 3.661
0.000 0.000 0.000 0.052 1.692
2003el61 2005-Jun-22 51.24 50.93 0.314 0.101 0.011 0.810 5.406 1212
0.000 0.000 0.000 0.321 3.549
0.000 0.000 0.000 0.052 1.649
sedna 2004-Jan-01 89.55 88.91 0.010 0.003 0.000 0.007 0.164 644
0.000 0.000 0.000 0.002 0.095
0.000 0.000 0.000 0.000 0.034
orcus 2005-May-14 47.68 47.45 0.060 0.019 0.002 0.177 1.020 460
0.000 0.000 0.000 0.072 0.679
0.000 0.000 0.000 0.013 0.324
quaoar 2005-Apr-05 43.34 43.01 0.061 0.020 0.002 0.209 1.007 383
0.000 0.000 0.000 0.089 0.683
0.000 0.000 0.000 0.017 0.337
assumed pV= 1.00000,G= 0.964912 (A= 0.950000), and used the values of H in Horizons
For a given type of thermal model, visible magnitude, and assumed phase curve, there is a unique combination of albedo and diameter that matches the observations at a given wavelength. The primary uncertainty in this radiometric diameter determination is therefore from the CHOICE of thermal model and phase curve. This uncertainty is significantly reduced if observations are available at more than one wavelength, with at least one of the wavelengths near the peak. For the icy planetoids of the outer Solar System, it is therefore critical that measurements in the 50-200 micron wavelength range are performed. In fact if both 70 and 160 micron detections are made, then the SUM of 70 and 160 micron fluxes can be used to constrian the diameter, and the result has a much smaller uncertainty due to choice of thermal model. (No matter how the energy from incident sunlight is distributed over the surface, it all has to be radiated away at some infrred wavelength.)