Editing Palermo scale (section)

== Risk calculation ==
{{multiple image
 |direction = vertical
 |align     = right
 |width1    = 300
 |width2    = 300
 |image1    = Apophis ellipse.svg
 |image2    = Impact probability of Apophis as function of uncertainty.jpg
 |footer    = ''Top:'' example of the shrinking and changing position of the 3-sigma uncertainty region relative to Earth in the B-plane<br>''Bottom:'' theoretical (blue and dashed red) and observational (crosses and triangles) evolution of impact probability as a function of uncertainty in the close approach distance for a bypass and an impact case, based on a planetary defense exercise using adapted real observations of [[99942 Apophis]]
}}

For [[NASA]], a unit of the [[Jet Propulsion Laboratory]] (JPL), the [[Center for Near-Earth Object Studies]] (CNEOS) calculates impact risks and assigns ratings in its [[Sentry (monitoring system)|Sentry Risk Table]],<ref name="sentry-list">{{cite web |title=Sentry: Earth Impact Monitoring. Impact Risk Data |publisher=NASA JPL CNEOS |url=https://cneos.jpl.nasa.gov/sentry/ |access-date=2025-03-10}}</ref> while another unit of JPL, Solar System Dynamics (SSD) provides orbital and close approach data.<ref name="sbdb">{{cite web |title=Small-Body Database Lookup |publisher=NASA JPL SSD |url=https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/ |access-date=2025-02-08}}</ref> For [[European Space Agency|ESA]], similar services are provided by its [[Near-Earth Object Coordination Centre]] (NEOCC), which maintains its own Risk List<ref name="NEOCC-risk-list">{{cite web |title=Risk List |publisher=ESA NEOCC |url=https://neo.ssa.esa.int/risk-list |access-date=2025-02-08}}</ref> and Close Approaches List.<ref name="NEOCC-close-approach-list">{{cite web |title=Close Approaches |publisher=ESA NEOCC |url=https://neo.ssa.esa.int/close-approaches |access-date=2025-02-08}}</ref>

The basis for the risk evaluation is the most recent orbit calculation based on all known reliable observations. Along the calculated orbit, close approaches with Earth are determined. Due to measurement and model imprecision, the orbit calculation has an uncertainty, which can be quantified for the close approach distance. Assuming a two-dimensional [[normal distribution|Gaussian probability distribution]] in the plane perpendicular to the asteroid's orbit (the B-plane), the uncertainty can be characterised by the [[standard deviation]] (sigma) the close approach point in the directions along the asteroid's orbit and perpendicular to it, where the former is usually much larger. The one-sigma margin, which is used by ESA NEOCC one-sigma,<ref name="NEOCC-help">{{cite web |title=Help: Object |publisher=ESA NEOCC |url=https://neo.ssa.esa.int/objects/help |access-date=2025-02-08}}</ref> means that the close approach point is within those bounds with a 68.3% probability, while the 3-sigma margin, used by NASA JPL SSD, corresponds to 99.7% probability. The probability of an impact is the integral of the probability distribution over the cross section of Earth in the B-plane.

When the close approach of a newly discovered asteroid is first put on a risk list with a significant risk, it is normal for the risk to first increase, regardless whether the potential impact will eventually be ruled out or confirmed with the help of additional observations.<ref name="Smithsonian_no-panic">{{Cite news |first=Margherita |last=Bassi |title=Astronomers Raise Odds of Asteroid Impact in 2032 to 2.3 Percent—Here's Why You Shouldn't Panic |date=6 February 2025 |work=[[Smithsonian (magazine)|Smithsonian]] |url=https://www.smithsonianmag.com/smart-news/astronomers-raise-odds-of-asteroid-impact-in-2032-to-2-3-percent-heres-why-you-shouldnt-panic-180985949/ |access-date=2025-02-08 }}</ref> After discovery, Earth will be close to the center of the probability distribution, that is, the 3-sigma uncertainty margin will be much bigger than the nominal close encounter distance. With additional observations, the uncertainty will decrease, thus the 3-sigma uncertainty region will shrink, thus Earth will initially cover an increasing part of the probability distribution, resulting in increased risk, and an increasing rating. If the real orbit bypasses Earth, with further observations, Earth will only intersect the tail of the probability distribution (the 3-sigma region will shrink to exclude the Earth) and the impact risk will fall towards zero; while in case the asteroid will hit the Earth, the probability distribution will contract towards its intersection (the 3-sigma region will shrink into Earth's intersection in the B-plane) and the risk will rise towards 100%.<ref name="Reddy2022">{{cite journal |first1=Vishnu |last1=Reddy |first2=Michael S. |last2=Kelley |first3= Jessie |last3=Dotson |display-authors=etal |title=Apophis Planetary Defense Campaign |journal=[[The Planetary Science Journal]] |volume=3 |issue=5 |at=id. 123, 16 pp. |date=May 2022 |doi=10.3847/PSJ/ac66eb |doi-access=free |bibcode=2022PSJ.....3..123R }}</ref>