--- title: "Probability of Collision of satellites and space debris for short-term encounters: Rederivation and fast-to-compute upper and lower bounds" description: This study introduces a novel derivation based on first principles that naturally allow for tight and fast upper and lower bounds for the probability of collision. image: https://blog.neuraspace.com/hubfs/LinkedIn_Neura%20(1).png --- [Skip to content](https://blog.neuraspace.com/probability-of-collision-of-satellites#main-content) [![Neuraspace_Horizontal_Light](https://blog.neuraspace.com/hs-fs/hubfs/Neuraspace_Horizontal_Light.png?width=200&height=40&name=Neuraspace_Horizontal_Light.png)](https://www.neuraspace.com) - [Neuraspace Stories](https://blog.neuraspace.com/) Open main navigation Close main navigation - [Neuraspace Stories](https://blog.neuraspace.com/) - [Book a Demo](https://content.neuraspace.com/book-a-demo) [Book a Demo](https://content.neuraspace.com/book-a-demo) Dec 5, 2023 3:34:40 PM # Probability of Collision of satellites and space debris for short-term encounters: Rederivation and fast-to-compute upper and lower bounds ![Picture of Neuraspace](https://blog.neuraspace.com/hs-fs/hubfs/Untitled%20design-1.png?width=50&name=Untitled%20design-1.png) [Neuraspace](https://blog.neuraspace.com/author/neuraspace) Share: [facebook-f icon](http://www.facebook.com/share.php?u=https://blog.neuraspace.com/probability-of-collision-of-satellites) [linkedin-in icon](http://www.linkedin.com/shareArticle?mini=true&url=https://blog.neuraspace.com/probability-of-collision-of-satellites) [Twitter icon](https://twitter.com/intent/tweet?url=https://blog.neuraspace.com/probability-of-collision-of-satellites) [pinterest-p icon](http://pinterest.com/pin/create/link/?url=https://blog.neuraspace.com/probability-of-collision-of-satellites) [envelope icon](mailto:?body=https://blog.neuraspace.com/probability-of-collision-of-satellites) *![LinkedIn_Neura (1)](https://blog.neuraspace.com/hs-fs/hubfs/LinkedIn_Neura%20(1).png?width=1200&height=627&name=LinkedIn_Neura%20(1).png)* *\[In the Journal\]* *Authors:* - FCT-UNL, Portugal, [rjn.ferreira@campus.fct.unl.pt](mailto:rjn.ferreira@campus.fct.unl.pt) - FCT-UNL, Portugal, [claudia.soares@fct.unl.pt](mailto:claudia.soares@fct.unl.pt) - Neuraspace, Portugal, [marta.guimaraes@neuraspace.com](mailto:marta.guimaraes@neuraspace.com)  The accelerated increase in space debris in the low earth orbit (LEO) is a growing concern. Given the high speeds that these millions of fragments can reach, even the fragments that are a few millimetres in size, can cause fractures in a satellite’s hull or put a serious crack in the window of a space shuttle. The conventional method proposed by Akella and Alfriend in 2000 remains widely used to estimate the probability of collision in short-term encounters. This study introduces a novel derivation based on first principles that naturally allow for tight and fast upper and lower bounds for the probability of collision. Read the paper to know how we: - Derive from first principles the expression for the probability of collision - Introduce accurate and fast-to-compute upper and lower bounds of the probability of collision - Study the computational complexity of our method when compared with the naive one - Validate our approach on a real dataset of Conjunction Data Messages (CDM) ### Download the paper ## Related posts [![](https://blog.neuraspace.com/hs-fs/hubfs/Blog_LinkedIn_Neura%20(5).png?height=200&name=Blog_LinkedIn_Neura%20(5).png)](https://blog.neuraspace.com/forecasting-the-position-uncertainty-with-confidence-intervals) [Neuraspace](https://blog.neuraspace.com/tag/neuraspace) ## [Forecasting the position uncertainty with confidence intervals](https://blog.neuraspace.com/forecasting-the-position-uncertainty-with-confidence-intervals) ![Picture of Neuraspace](https://blog.neuraspace.com/hs-fs/hubfs/Untitled%20design-1.png?width=50&name=Untitled%20design-1.png) [Neuraspace](https://blog.neuraspace.com/author/neuraspace) Jun 6, 2024 10:36:14 AM Improved decision-making using Neuraspace PRO feature. Overview Satellite operators rely on... [Read more](https://blog.neuraspace.com/forecasting-the-position-uncertainty-with-confidence-intervals) [![SYNC](https://blog.neuraspace.com/hs-fs/hubfs/Blog_LinkedIn_Neura%20(12)-2.png?height=200&name=Blog_LinkedIn_Neura%20(12)-2.png)](https://blog.neuraspace.com/precise-satellite-tracking-and-orbit-prediction-neuraspace) [Neuraspace](https://blog.neuraspace.com/tag/neuraspace) ## [Precise Satellite Tracking and Orbit Prediction for a Commercial Satellite Operator](https://blog.neuraspace.com/precise-satellite-tracking-and-orbit-prediction-neuraspace) ![Picture of Neuraspace](https://blog.neuraspace.com/hs-fs/hubfs/Untitled%20design-1.png?width=50&name=Untitled%20design-1.png) [Neuraspace](https://blog.neuraspace.com/author/neuraspace) Oct 10, 2024 1:49:05 PM A satellite operator involved in launching and managing satellites in Low Earth Orbit (LEO)... [Read more](https://blog.neuraspace.com/precise-satellite-tracking-and-orbit-prediction-neuraspace) [![SYNC](https://blog.neuraspace.com/hs-fs/hubfs/Earth%20and%20Satellites%20in%20Space.png?height=200&name=Earth%20and%20Satellites%20in%20Space.png)](https://blog.neuraspace.com/case-study-ensuring-safe-operations-of-a-new-leo-constellation) [Neuraspace](https://blog.neuraspace.com/tag/neuraspace), [Case Study](https://blog.neuraspace.com/tag/case-study) ## [Case Study: Ensuring Safe Operations of a New LEO Constellation](https://blog.neuraspace.com/case-study-ensuring-safe-operations-of-a-new-leo-constellation) ![Picture of Neuraspace](https://blog.neuraspace.com/hs-fs/hubfs/Untitled%20design-1.png?width=50&name=Untitled%20design-1.png) [Neuraspace](https://blog.neuraspace.com/author/neuraspace) Oct 21, 2025 4:03:01 PM As the number of satellites in orbit continues to rise, ensuring mission safety and regulatory... [Read more](https://blog.neuraspace.com/case-study-ensuring-safe-operations-of-a-new-leo-constellation) --- [![Neuraspace_Horizontal_Light](https://blog.neuraspace.com/hs-fs/hubfs/Neuraspace_Horizontal_Light.png?width=200&height=41&name=Neuraspace_Horizontal_Light.png "Neuraspace_Horizontal_Light")](https://www.neuraspace.com) © 2026 Neuraspace [linkedin-in icon](https://www.linkedin.com/company/neuraspace/) [Follow us on Facebook](https://instagram.com/neuraspacehqhttps://) [Follow us on Facebook](https://instagram.com/neuraspacehqhttps://) [Follow us on Facebook](https://twitter.com/neuraspacehttps://) Connect info@neuraspace.com +351 239 700 346   [![PRR_Logotipos-white-hor-1](https://blog.neuraspace.com/hs-fs/hubfs/PRR_Logotipos-white-hor-1.png?width=224&height=80&name=PRR_Logotipos-white-hor-1.png "PRR_Logotipos-white-hor-1")](https://www.neuraspace.com/) [![LOGO_REPUBLICA_PORTUGUESA-01](https://blog.neuraspace.com/hs-fs/hubfs/LOGO_REPUBLICA_PORTUGUESA-01.png?width=257&height=110&name=LOGO_REPUBLICA_PORTUGUESA-01.png "LOGO_REPUBLICA_PORTUGUESA-01")](https://www.neuraspace.com/) [![PT Financiado pela Uniֶo Europeia_WHITE](https://blog.neuraspace.com/hs-fs/hubfs/PT%20Financiado%20pela%20Uni%D6%B6o%20Europeia_WHITE.png?width=306&height=80&name=PT%20Financiado%20pela%20Uni%D6%B6o%20Europeia_WHITE.png "PT Financiado pela Uniֶo Europeia_WHITE")](https://www.neuraspace.com/) ```json { "@context" : "https://schema.org", "@type" : "BlogPosting", "author" : { "@type" : "Person", "name" : "Neuraspace", "url" : "https://blog.neuraspace.com/author/neuraspace" }, "dateModified" : "2023-12-05T15:34:40.864Z", "datePublished" : "2023-12-05T15:34:40.000Z", "headline" : "Probability of Collision of satellites and space debris for short-term encounters: Rederivation and fast-to-compute upper and lower bounds", "image" : [ "https://blog.neuraspace.com/hubfs/LinkedIn_Neura%20(1).png" ], "mainEntityOfPage" : { "@id" : "https://blog.neuraspace.com/probability-of-collision-of-satellites", "@type" : "WebPage" }, "publisher" : { "@type" : "Organization", "logo" : { "@type" : "ImageObject", "url" : "https://blog.neuraspace.com/hubfs/Neuraspace_Dark-2.png" }, "name" : "Neuraspace" } } ```