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Observation arc

## Summary

In observational astronomy, the observation arc (or arc length) of a Solar System body is the time period between its earliest and 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 leaves a high uncertainty parameter. The object might be in one of many different orbits, at many distances from Earth. In some cases, the initial arc was too short 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 was later found to be another 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]

2018 AG37 which was discovered when 100+ AU from the Sun and has only been observed 9 times over 2 years[2] will require an observation arc of several years to refine the uncertainties in the orbital period and aphelion (furthest distance from the Sun).

1999 DP8 with only 4 observations over 1 day[3] has uncertainties so large that the error bars are not really meaningful and just show that the uncertainties are very large. On its discovery date 1999 DP8 is estimated to have been 52±1500 AU from Earth.

## 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 ${\displaystyle e<1}$.[4] 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.[5]

## 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.[6] 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.[7] 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.

## References

1. ^ TNOs really do require patience; 2-3 years is only just enough to say anything about the orbit parameters – Astronomer Michele Bannister (4 April 2018)
2. ^ JPL Small-Body Database Browser for 2018 AG37
3. ^ JPL Small-Body Database Browser for 1999 DP8. Ephemeris table setting: #39. Range & range-rate = 6.8E+11 / AU / 3-sigma = 1500 AU
4. ^ JPL Small-Body Database Browser for C/2008 J4 (McNaught)
e = 0.9977 to 1.017
semi-major axis = −58
v=42.1219 1/50000 − 0.5/−58
5. ^ JPL Small-Body Database Browser for C/1999 U2 (SOHO)
6. ^ JPL Small-Body Database Browser for Comet Swift–Tuttle
7. ^ JPL Small-Body Database Browser for C/2001 OG108
(Close approach uncertainty: (MaxDist of 0.434) – (MinDist of 0.408) * 149597870.7 = 3.9 million km)