# The population of near-Earth asteroids larger than 1 km -- *March 7, 2018*

In a couple of recent papers, I have finally attacked the problem
of determining the orbital and size distribution of near-Earth asteroids (NEAs),
a subject that has attracted the attention of several distinguished groups of researchers over the years.
The problem is that of determining the characteristics of the full population of NEAs
from the fraction of NEAs that we have discovered so far.
The approach I adopted was to look at the observations of 9 of the most productive asteroid survey telescopes
collected over the past two decades,
to determine the thresholds of brightness and apparent velocity leading
to an asteroid detection,
with the results collected in
Tricarico (2016).
The second step was then to run computer simulations where approximately one million virtual asteroids
are monitored over the years, to determine whether or not they could have been
detected by asteroid surveys. This allows to determine the fraction of asteroids that go
undetected, and by comparing this to the catalog of know NEAs we can finally
estimate the orbital and size characteristics of the full NEA population,
with the results collected in
Tricarico (2017).

One of the main results of this work was a reduced estimated number of asteroids with an average diameter of 1 km or larger:
only approximately 920 ± 10.
This first figure (click for larger version) shows the evolution of the estimated number of NEAs larger than 1 km
over the years.
Results from the early 2000s were characterised by large uncertainties,
but many are actually in good agreement (within 1 sigma) with the estimated 920 ± 10,
highlighted by the gray strip.
Note that around 2002 it became clear that the reference absolute magnitude H associated to NEAs larger than 1 km
is H<17.75, compared to H<18 used up to 2002.
Recent works produced improved estimates centered near 1000,
and

Tricarico (2017)
appears to be the first to break that trend with an estimate of 920 ± 10.
Since then, the only other estimate in 2017 appears to confirm the drop
in the expected number of NEAs larger than 1 km.

In

Tricarico (2017)
I looked at the curve of total discoveries over time to obtain an alternative, independent and empiric estimate of
914

^{+19}_{-15} NEAs larger than 1 km,
in very good agreement with the 920 ± 10 from the full analysis.
Compared to the published version, this second figure includes the discoveries
for the years 2016 and 2017, while the fitting curve is unchanged from the published version.
The additional discoveries are within the predicted range and slightly above the nominal curve,
and an updated fit including all available data produces an empiric estimate of
919

^{+14}_{-12} NEAs larger than 1 km,
further improving the agreement with the 920 ± 10 from the full analysis.

In this last figure we look at the actual orbital distribution of the NEAs larger than 1 km.
The grey histograms are the discovered NEAs up to February 2018 included,
while the error bars are the expected distribution,
unchanged from

Tricarico (2017).
Since in the published version I included known NEAs only up to August 2014,
this updated figure allows to look at the model after a 3.5 years period.
The agreement appears to be still remarkably good,
and one can quickly alternate between the published version and the figure above to try to spot the differences.
Interestingly, the bins do not always grow, but can also slightly shrink over time:
as the orbits of newly discovered NEAs are refined thanks to additional observations, a NEA may move to a nearby bin,
or may leave the distribution if the updated orbit or absolute magnitude is no longer that of a NEA larger than 1 km.
This effect is particularly evident for the semi-major axis distribution,
where the population is spread over a larger number of bins,
leading to relatively larger statistical fluctuations,
compared to the distributions in eccentricity and inclination.

In conclusion,
the additional discoveries obtained since
Tricarico (2017)
indicate that the model is healthy and producing reliable predictions.
As of March 2018, approximately 96 ± 1 percent of the NEAs larger than 1 km have been discovered.
This research was supported by the NASA Near Earth Object Observations (NEOO) Program.