“Whoa! It’s like Spotify but for academic articles.”

Instant Access to Thousands of Journals for just $40/month

Try 2 weeks free now

Orbit determination with the two-body integrals



We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed body and their time derivatives at a given epoch; we call this set of data attributable . Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two attributables belong to the same body ( linkage problem ). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results from the observation error statistics. The performance of this method has been investigated by using a large set of simulated observations of the Pan-STARRS project.



Celestial Mechanics and Dynamical AstronomySpringer Journals

Published: Jul 1, 2010

DOI: 10.1007/s10569-010-9271-9

Free Preview of First Page

Loading next page...

You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy unlimited access and
personalized recommendations from
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $40/month

Try 2 weeks free now

Explore the DeepDyve Library

How DeepDyve Works

Spend time researching, not time worrying you’re buying articles that might not be useful.

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.

All the latest content is available, no embargo periods.

See the journals in your area

Simple and Affordable Pricing

14-day free trial. Cancel anytime, with a 30-day money-back guarantee.

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Best Deal — 25% off

Annual Plan

  • All the features of the Professional Plan, but for 25% off!
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

billed annually