Earth's blind spot: A closer look at observational biases for Earth coorbital asteroids
Authors: Christou Apostolos , Nedelchev Boris , Borisov Galin , Dell’Oro Aldo , Cellino Alberto 
Published: July 2021

Asteroids with an average heliocentric distance of 1 au present special challenges to surveys. Because of the very slow Earth-relative net motion from one orbital revolution to the next, they can remain far from our planet and close to the Sun's location in the sky (Fig 1). For this reason, the likelihood of discovering objects for this type should be generally lower than for other near-Earth asteroids (NEAs). Observational incompleteness for these Earth coorbitals was quantified by Tricarico (2017) and is now readily apparent in the NEA inventory as a deficit of asteroids with a semimajor axis of 1 au (Fig 2).Figure 1: Illustration of Earth-relative motion of an asteroid with a = 1.001 au and initially 180o away in orbital mean longitude. The asteroid is initially located behind the sun as seen from Earth and drifts towards the Earth&#8217;s location at a rate of 0.5o/year. After 180 yr, solar elongation has increased from 0 to 45o.Figure 2: Number of NEAs in the NEODYS database (https://newton.spacedys.com/neodys/) on 16 May 2021 as a function of semimajor axis counted with a bin size of 0.02 au. Only asteroids with 1-sigma semimajor axis uncertainty of 0.001 au or better were included. The error bars correspond to Poisson counting statistics for each bin. Note the lack of asteroids with a semimajor axis of 1 au.We have constructed a simple survey simulator to understand how this bias behaves for different asteroid orbits. The relative longitude &#955; - &#955;Earth between the Earth and the asteroid is a key parameter determining whether an asteroid is discovered or not, affecting even bright asteroids that should otherwise be easy to discover even far from the Earth. Figure 3 shows the observational completeness for H=14 (D=4 km for pv=0.25) asteroids on a 40-yr synthetic survey down to a limiting magnitude of V=20.7 and a solar elongation cutoff of 70o. At a=1 au - the exact co-orbital condition - the asteroid is stationary as seen from the Earth and completeness is determined solely by the fraction of the orbit that resides within the solar elongation limit. Orbits away from 1 au gradually drift away from the anti-solar point and eventually exit the ``blind spot&#8217;&#8217; caused by the solar elongation limit, allowing their detection.&#160;An important implication is that the gap in Fig 2 could contain undiscovered km-sized or larger asteroids which may be potentially hazardous (PHAs). To eliminate or significantly reduce the gap in a few decades or sooner, it would be necessary either to operate a survey with a much reduced solar elongation limit or move the detector away from the Earth.Figure 3: Observational completeness for asteroids with semimajor axis within 0.01 au of Earth&#8217;s for a synthetic 40-year survey with a solar elongation cutoff of 70o and a limiting magnitude V=20.7. The asteroid parameters were H=14, e=0.1 and I=5o. Completeness takes values from 0 to 1 and is linearly proportional to greyscale intensity. The region of near-zero completeness centred at a = 1.000 au and &#916;&#955; = 180o is caused by the asteroid not exceeding the elongation cutoff for the duration of the survey.At the meeting we will show model results to demonstrate how the observational completeness for co-orbital asteroids depends on the elements of the orbit: eccentricity, inclination, periapsis and node. An estimate for the number of as-yet-undiscovered co-orbital asteroids as a function of size will also be provided. In addition, we will be applying the simulator to known asteroids presently observed in different libration modes of the 1:1 resonance: Trojans (2010 TK7; Connors et al, 2011), horseshoes (419624 2010 SO16; Christou &amp; Asher, 2011) and quasi-satellites (469219 Kamo&#699;oalewa; Chodas, 2016) and aim to report the results at the conference.Acknowledgements: This work was supported via grant ST/R000573/1 from the UK Science and Technology Facilities Council (STFC).&#160;References: Chodas, P., 2016, The orbit and future motion of Earth quasi-satellite 2016 HO3, DPS meeting #48, id.311.04.Christou, A. A., Asher, D. J., 2011, A long-lived horseshoe companion to the Earth, MNRAS, 414, 2965-2969.Connors, M., Wiegert, P., Veillet, Ch., 2011, Earth&#8217;s Trojan asteroid, Nature, 475, 481-483. Tricarico, P., 2017, The near-Earth asteroid population from two decades of observations, Icarus, 284, 416-423.