Collision Probabilities for Keplerian Orbits

Collision Probabilities for Keplerian Orbits We present a new derivation of the probability of collisions between spherical satellites occupying Keplerian orbits. The equations follow from the central concept of the instantaneous collision rate, an expression that describes the occurrence of collisions by using a Dirac δ-function. The derivation proceeds by showing how this instantaneous collision rate can be averaged over orbital mean anomaly angles and, additionally, over orbital precession angles to generate expressions appropriate for intermediate and long time scales. Collision rates averaged over mean anomalies tend to be non-zero during relatively brief collision seasons, when the peak collision probability may exceed the long-term average by several orders of magnitude. Derived precession-angle averages have a functional form similar but not identical to the collision probability expression derived using the spatial density approach of Kessler (Icarus, 48: 39–48, 1981), and the two methods have been found to yield numerical results to within 1% for all cases examined. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Space Debris Springer Journals

Collision Probabilities for Keplerian Orbits

Loading next page...
 
/lp/springer_journal/collision-probabilities-for-keplerian-orbits-2pzGWQC07f
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Engineering; Automotive Engineering; Law of the Sea, Air and Outer Space; Astronomy, Observations and Techniques
ISSN
1388-3828
eISSN
1572-9664
D.O.I.
10.1023/A:1022916401768
Publisher site
See Article on Publisher Site

Abstract

We present a new derivation of the probability of collisions between spherical satellites occupying Keplerian orbits. The equations follow from the central concept of the instantaneous collision rate, an expression that describes the occurrence of collisions by using a Dirac δ-function. The derivation proceeds by showing how this instantaneous collision rate can be averaged over orbital mean anomaly angles and, additionally, over orbital precession angles to generate expressions appropriate for intermediate and long time scales. Collision rates averaged over mean anomalies tend to be non-zero during relatively brief collision seasons, when the peak collision probability may exceed the long-term average by several orders of magnitude. Derived precession-angle averages have a functional form similar but not identical to the collision probability expression derived using the spatial density approach of Kessler (Icarus, 48: 39–48, 1981), and the two methods have been found to yield numerical results to within 1% for all cases examined.

Journal

Space DebrisSpringer Journals

Published: Oct 8, 2004

References

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 affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off