Measuring the size and shape of Ceres using stellar occulations.

Ceres is the largest body in the Main Asteroid Belt, containing approximately one fifth of the total mass found there. It is the only body in the Main Asteroid belt to be accorded the status of ‘Minor Planet’, which indicates that it is thought to be large enough to have adopted a roughly spherical shape due to its own gravity, but not large enough to have cleared all other material from its approximate orbit. The other bodies in our Solar System to have been designated as Minor Planets are all Kuiper Belt Objects such as Pluto, Eris and Makemake. This has profound implications for the structure of Ceres; while it is thought that the majority of Main Asteroid Belt objects are simply large rocks, or rubble piles held loosely together by microgravity, Ceres is thought likely to have a differentiated, layered structure which may contain ice layers or even liquid water beneath the surface.

Stellar occulations, situations in which a Solar System body passes in front of a star causing a measurable dimming of its light, are a powerful tool in the study of small Solar System bodies, and have been used to measure the sizes of a number of bodies in the Main Asteroid Belt and even the Kuiper Belt. The method relies on having a number of observatories on Earth measuring the dimming of the star, and using synchronized time recordings to compare the dimming observed from each station, in order to build a picture of its size and shape. This method has been used once previously to measure the size and shape of Ceres, when data from a 1984 occulation was used to determine that Ceres was an oblate spheroid (slightly flattened sphere), with an equatorial diameter of 959 km and an oblateness of 0.05 (i.e. its diameter measured on the north-south access is 5% smaller than its diameter measured at the equator). This is comparible to measurements obtained with the Hubble Space Telescope and Keck and Very Large Telescopes, but a little smaller and less oblate than these other observations suggest.

In a paper published the arXiv database at Cornell University Library on 20 April 2015, and in the Monthly Notices of the Royal Astronomical Society on 19 April 2015, a team of astronomers led by Altair Gomes-Júnior of the Observatório do Valongo in Rio de Janeiro, discuss the results obtained two further stellar occulations by Ceres, in August 2010 and October 2013.

On 17 August 2010 Ceres occulated the magnitude 11.55 star TYC 6833-163-1 (or UCAC4 313-111823); an occulation which was visible from the southern coastal area of Brazil. This was observed from five locations; Belo Horizonte CEAMIG, Pico dos Dias LNA, São José dos Campos INPE, Ponta Grossa UEPG and Florianópolis UFSC, though in the event Florianópolis turned out to be outside the area from which the occulation was visible and only part of the occulation was observed from São José dos Campos.

Post-occultation reconstruction of Ceres' shadow path on Earth for the 2010 August 17 event. The big red dot is the geocentric closest approach at 22:40:25 UT. The small red ones represent the centre of the shadow separated by one minute, shadow moves from the left to the right. Blue dots are the sites that have observed the event. UFSC had a negative chord. Gomes-Júnior et al. (2015).

All of the observations were made with instruments which used charged-couple devices to record the times with an accuracy good to within a few hundredths of a second. Since this was an exceptionally slow occulation, with the shadow of Ceres moving at velocity of 3.9 kilometres per second in the plane of the sky, and the observing stations were spaced evenly across the width of the observational area, this enabled very accurate measurements to be made, resulting in a calculated equatorial diameter of 972 km and an oblateness of 0.08.

The best elliptical fit for the occultation chords for the event of 2010 using the times and the pole constrained solution. The arrow indicates the direction of motion, blue lines are the observed chords, the red segments are the ingress, egress and mid-occultation error bars at 1σ level. Gomes-Júnior et al. (2015).

On 25 October 2013 Ceres occulated the magnitude 10.05 star TYC 865-911-1 (or UCAC4 496-058191), an event visible from much of the eastern United States. This was observed from nine locations, Hampton, Topsfield, Brookline, Winchester, Greenbelt, Alexandria, Owings, Mechanicsville and Varina.

Post-occultation reconstruction of Ceres' shadow path on Earth for the 2013 October 25 event at the east coast of USA. Upper view of the occultation over the sites that observed the event (blue dots). Red points are the centre of the shadow separated by 15 seconds. Gomes-Júnior et al. (2015).

On this occasion Ceres was moving much faster relative to the Earth, and its shadow travelled at a speed of 42.6 kilometers per second. For this reason all of the observations were made using video equipment, and timed in slightly different ways at different stations. At Greenbelt and Owings a GPS unit was used to directly insert a time stamp into each frame. At Brookline the time was inserted via an internet server, and at, Hampton, Topsfield, Winchester, Alexandria, Mechanicsville and Varina the event was initially timed with the internal clock on a camcorder and this was then calibrated with a GPS unit.

In the event the method used at Brookline proved to be a failure, with the internet server losing its connection and inserting a delay of about 64 seconds. The Brookline observations were not therefore used in the final calculations. The timings obtained from the Varina observations also appeared to be erroneous, possibly due to a failure of the camcorder timer and GPS timer to correspond properly, so this set of observations were also discarded. Finally the observations made from Owings also seem to be inaccurate, delayed relative to nearby observations from Alexandria and Greenbelt, but very close to those from Mechanicsville, about a hundred kilometres to the south. This is harder to explain as the time-stamp was inserted into the Owings observations directly be GPS, and Gomes-Júnior et al. suggest that it may have been caused by some surface feature on Ceres. The Owings observations were also excluded from the final calculations.

The best elliptical fit for the occultation chords for the event of 2013 using timing from Table 3 and the pole-constrained solution. The arrow indicates the direction of motion, blue lines are the observed chords, the red and green segments are the ingress, egress and mid-occultation error bars at 1σ level. The chords with green error bars were not used during the limb fit process. The chord of Brookline is shifted by -64s. Gomes-Júnior et al. (2015).

The 2013 North American Ceres occulation observations therefore contained data from more observation stations than any previous set of similar observations, but these were not well distributed and were particularly week compared to the asteroids southern hemisphere. Nevertheless Gomes-Júnior et al. were able to calculate the size and shape of Ceres from these observations, coming up with an equatorial diameter of 971 km and an oblateness of 0.08.

Combining the data from all the observations in the two studies Gomes-Júnior et al. were able to come up with an equatorial diameter of 972 km and an oblateness of 0.08 for Ceres. This is comparable to a 2014 study which used direct observations of the asteroid from Keck Observatory and the Very Large Telescope (equatorial diameter 967 km, oblateness 0.078), and a 2004 study using the Hubble Space Telescope (equatorial diameter 975 km, oblateness 0.067), but not so well with the previous 1984 occualtion study (equatorial diameter 959 km, oblateness 0.05) or a 2008 study using data from Keck Observatory alone (equatorial diameter 959 km, oblateness 0.074).

To some extent all of these observations are now spurious, as NASA’s Dawn Spacecraft has now moved into orbit around Ceres, and is likely to produce much more accurate observations and measurements of the asteroid in the near future. However this does provide a good test for the methodology involved, which has been used on a great number of other asteroids and Solar System bodies, the vast majority of which have no prospect of being visited by a space mission in the foreseeable future.

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