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D. J. Tholen, R. J. Whiteley (Inst. for Astronomy, Univ. of Hawaii)
We had previously described a technique for computing orbits and ephemerides using just two observations. The technique involves assuming values for the topocentric distance and projection angle of the topocentric velocity vector onto the plane of the sky, along with using measured values for the right ascension, declination, and their time derivatives at the mid-observation time, to solve for a suite of orbits that could be used to compute future ephemeris positions. We have since generalized this technique to allow more than two observations. The topocentric distance and projection angle are still assumed, but we now use a least-squares approach to find the best-fit values of the initial right ascension, declination, and their time derivatives. With just two observations, it is always possible to find a perfect fit, so the resulting orbits are usually constrained to be elliptical and prograde (though these restrictions can be relaxed for special cases). With more than two observations, the resulting orbits are constrained by their RMS residuals. We will present several test cases involving NEOs that demonstrate the success of this method in predicting the positions of these typically fast-moving objects. One object, 1999 XA152, was recovered an amazing thirty days after its initial six-minute observational arc (bad weather had prevented more immediate recovery). Even when the individual orbital elements appear to be unconstrained, they collectively can still constrain the ephemeris prediction rather well. In particular, we will show that all orbit solutions for 1998 DK36 with RMS residuals of less than 1 arcsec have aphelion distances between 0.97 and 0.99 AU, despite having perihelion distances ranging from 0.14 to 0.76 AU and semimajor axes ranging from 0.56 to 0.87 AU, which reinforces the case for this object being the first asteroid known to have an orbit entirely interior to the Earth's orbit. We acknowledge NASA Grant No. NAG5-4524 for portions of this work.
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