Orbits of Main-Belt Asteroids

Apart from the major planets, the Solar System contains a large number of smaller bodies. The asteroids (i.e. the minor planets) are the small rocky objects that are found mainly between the orbits of Mars and Jupiter. So far over 700,000 have been catalogued. The largest, Ceres, has a diameter of 1000 km (i.e. 30% of the Moon diameter).

The aim of the project is to independently determine the orbits of several (~8) asteroids by making a series of positional measurements. This is achieved by measuring the asteroid's position on a CCD image relative to that of catalogued stars. Asteroids typically move about 10 arcmin per 24 hours. By tracking an asteroid over the term its orbit can be well determined. The goal will be to obtain about 10 observations per asteroid.

By reference to the UCAC4 star catalog, astrometry measurements can be made with uncertainties of better than 0.1 arcsec. The plot below compares the measured astrometric positions with the asteroid positions predicted from the JPL Horizons On-line Ephemeris. JPL's formal +/− 1, 2, 3 standard-deviation uncertainties are shown as error ellipses; these are described as "optimistic" (see Horizons Manual).

The minor planet Chloe was observed on seven different occasions during the 2005 Epiphany term by Astrolab students (David and Rob). Their results table for Chloe is given here. This table illustrates the type of positional measurements that can be obtained for this project.

Having measured the positions of a set of Main Belt asteroids over a few week period, the orbital parameters (and their uncertainties) can be derived and a 3D model for their orbits constructed. The figure below shows the heliocentric view of the orbits of nine asteroids studied in 2018 (Left). The scale is in AU. With a 3D model, the uncertainty in the position as a function of time can be calculated (Right). This has implications for missions to asteroids. With the orbital properties (and uncertainties) constrained, one of the goals of the project is to design a mission to an asteroid (either for scientific research, or for mining purposes), taking in to account the orbital uncertainties.

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