# Observation arc

In observational astronomy, an observation arc (or arc length) is the time period between the earliest and the latest observations, used for tracing the body's path. It is usually given in days or years. The term is mostly used in the discovery and tracking of asteroids and comets. Arc length has the greatest influence on the accuracy of an orbit. The number and spacing of intermediate observations has a lesser effect.

## Short arcs

A very short arc could describe objects in a wide variety of orbits, at many distances from Earth. In some cases, there have been objects whose initial arc was insufficient to determine if the object was in orbit around the Earth, or orbiting out in the asteroid belt. With a 1-day observation arc, 2004 PR107 was thought to be a trans-Neptunian dwarf planet, but is now known to be a 1 km main-belt asteroid. With an observation arc of 3 days, 2004 BX159 was thought to be a Mars-crossing asteroid that could be a threat to Earth, but it is now known to be a main-belt asteroid.

A relatively modest observation arc may allow finding an older "precovery" photo, providing a much longer arc and a more precise orbit.

An observation arc less than 30 days can make it difficult to recover an Inner Solar System object more than a year after the last observation, and may result in a lost minor planet. Due to their greater distance from the Sun and slow movement across the sky, trans-Neptunian objects with observation arcs less than several years often have poorly constrained orbits.[1]

Long-period/Oort cloud objects such as 2013 CA134 (eccentricity of 1.8±1.3 and observation arc of 3 days)[2] can require an observation arc of several weeks to refine the uncertainties and know if the orbital period is thousands or millions of years.

## Interstellar objects

Interstellar objects generally require an observation arc of 2–3 weeks using hundreds of observations to confirm that an interloper has a hyperbolic excess velocity (interstellar speed) of more than a few km/s. Comet C/2008 J4 (McNaught) was only observed 22 times over an observation arc of 15 days, and due to an insufficient number of observations generates a low inbound interstellar speed of 3.9 km/s, but the uncertainties in the eccentricity easily produce a closed orbit with ${\displaystyle e<1}$.[3] Comet C/1999 U2 (SOHO) with an almost meaningless observation arc of 1 day shows a very dubious interstellar speed of 17 km/s, but could easily have a closed orbit with an eccentricity as low a 0.7.[4]

## Earth approaches

Uncertainty in Earth approach distance by comets currently further than Uranus
that have not been observed in the last ~20 years
Comet Observation
arc
Number of
observations
Uncertainty
parameter
Earth
approach date
Uncertainty in
distance from Earth
Reference
Comet Swift–Tuttle 257 years 652 0 2126-Aug-05 ±10 thousand km data
C/2001 OG108 0.9 years 886 2 2147-Mar-23 ±2 million km data
C/1991 L3 (Levy) 1.6 years 125 3 2094-Aug-01 ±15 million km data

With an observation arc of 257 years, the uncertainty in Comet Swift–Tuttle's closest approach to Earth on 5 August 2126 is about ±10 thousand km.[5] With an observation arc of ~1 year, the uncertainty in C/2001 OG108's closest approach to Earth on 23 March 2147 is about ±2 million km.[6] Even though C/1991 L3 (Levy) has a longer observation arc than C/2001 OG108, it has significantly fewer observations which generates a greater uncertainty.