Radar observations can be used to obtain accurate orbital elements for near-Earth objects (NEOs) as a result of the very accurate range and range rate measureables. These observations allow the prediction of NEO orbits further into the future and also provide more information about the properties of the NEO population. This study evaluates the observability of NEOs with the EISCAT 3D 233 MHz 5 MW high-power, large-aperture radar, which is currently under construction. Three different populations are considered, namely NEOs passing by the Earth with a size distribution extrapolated from fireball statistics, catalogued NEOs detected with ground-based optical telescopes and temporarily captured NEOs, i.e. mini-moons. Two types of observation schemes are evaluated, namely the serendipitous discovery of unknown NEOs passing the radar beam and the post-discovery tracking of NEOs using a priori orbital elements. The results indicate that 60–1200 objects per year, with diameters

All current radar observations of near-Earth objects (NEOs), namely asteroids and comets with perihelion distance

The amount of radar observations of NEOs is limited by resources, i.e. there are significantly more observing opportunities during close approaches than there is radar time available on the Arecibo (2.36 GHz, 900 kW) and Goldstone DSS-14 (8.56 GHz, 450 kW) radars, which are the two radars that perform most of the tracking of asteroids on a routine basis. In order to increase the number of radar measurements of NEOs, it is desirable to extend routine NEO observations to smaller radars, such as the existing EISCAT radars or the upcoming EISCAT 3D radar (233 MHz, 5 MW), henceforth abbreviated to E3D, which is to be located in Fenno-Scandinavian Arctic. While these radars may not be capable of observing objects nearly as far away as Arecibo or Goldstone or generating high-quality range–Doppler images, these radars are able to produce high-quality ranging.

Smaller radars can be used for nearly continuous observations, and it is possible that they can even contribute to the discovery of NEOs.

As a result of the enhanced survey capability with optical telescopes, the discovery rate of NEOs has greatly increased during the last two decades, from 228 NEOs discovered in 1999 to 2436 discovered in 2019. Recent discoveries include significantly more small objects that have close approach distances within 1 LD compared to discoveries made 20 years ago. It is these objects that are often within the reach of smaller radars. The EISCAT UHF system has in fact already been successfully used to track the asteroid 2012 DA

Range–Doppler intensity radar image of asteroid 2012 DA

When NEOs make a close approach to Earth, they enter a region where the Earth's gravity dominates. Most of the time, objects will make one single pass and then leave this region again. In some rare cases, the objects are temporarily captured by the Earth–Moon system

The EISCAT radars have already been used for around 20 years to observe the statistical distribution of space debris without prior knowledge of the orbital elements

The space debris application is very closely related to NEO observations as they both entail the discovery and tracking of a population of hard radar targets. Both populations follow a power law distribution in size, i.e. exponential cumulative growth in number as size decreases. There are, however, several differences. The number density of NEOs close enough to the Earth to be detectable with radar is significantly lower. While observability of NEOs using Arecibo and Goldstone has recently been investigated

E3D is the next-generation international atmosphere and geospace research radar in northern Scandinavia. It is currently under construction and is expected to be operational by the end of 2021. E3D will be the first multi-static, phased array, incoherent scatter radar in the world. It will provide essential data to a wide range of scientific areas within geospace science

The E3D system will initially consist of three sites, namely in Skibotn in Norway, near Kiruna in Sweden, and near Karesuvanto in Finland. Each of these sites will consist of about 10

In this work, we investigate two possible use cases for E3D for observing NEOs, namely the (1) discovery of NEOs and (2) post-discovery tracking of NEOs with known a priori orbital elements. The first case resembles that of space debris observations, where objects randomly crossing the radar beam are detected and, based on their orbital elements, are classified as either orbital space debris or natural objects. The second case is the more conventional radar ranging of NEOs based on a priori information about the orbital elements which yields a more accurate orbit solution. This is described in detail in Sect.

We estimate the detectability using three different approaches, roughly categorised as first order, second order, and third order. The first-order model uses a power law population density based on fireball statistics

Fireball observation statistics can be used to estimate the influx of small NEOs colliding with the Earth. By making the assumption that the flux of NEOs passing nearby the Earth is the same, it is possible to make a rough estimate of the number of objects that cross the E3D radar beam. A synthesis of NEO fluxes estimated by various authors is given by

This population model is convenient as it will allow us to theoretically investigate the number of objects detectable by a radar without resorting to large-scale simulations.

The Jet Propulsion Laboratory (JPL) CNEOS maintains a database of NEO close approaches. This database contains objects that have close encounters with the Earth and provides information, such as the date and distance for the closest approaches

In addition to the closest approach distance, the database provides an estimate of the diameter of each object estimated from the absolute magnitude. The diameter is used to estimate the signal-to-noise ratio (SNR) obtainable for radar observations and both planned and serendipitous discovery observations near the closest approach.

In Fig.

The CNEOS catalogue offers a way to judge what a realistic number of tracking opportunities will be for E3D. Because the orbital elements are not known for most smaller NEOs, the primary source for tracking opportunities is newly discovered objects, which are added to the database near closest approach. Approximately 50 % of the objects are discovered before the closest approach and 50 % afterwards, primarily as the objects are approaching from the direction of the Sun and are not observable in the day-lit hemisphere using telescopic surveys. The number of annual detections has been steadily increasing, and we expect significantly more tracking opportunities within the next few years given the constantly improving sky surveys and the start of new surveys, such as the Rubin Observatory Legacy Survey of Space and Time

Only two mini-moons have been discovered so far, and we therefore have to rely on theoretical predictions of their orbits and sizes rather than a model that is based on direct observational data. The theoretical models are based on a numerical analysis of the NEO capture probability, estimation of the average capture duration, and the estimated flux of NEOs into the capturable volume of phase space. Whereas

Here we use the newer mini-moon model by

Orbital elements of the synthetic mini-moons in the heliocentric J2000 frame. This is the initial distribution for the mini-moon simulations. We have not illustrated the longitude of the ascending node as this will be closely related to the temporal distribution of objects.

We need to convert absolute magnitudes to diameters to find the radar SNR in subsequent calculations. Using the relationship between the absolute magnitude

We also need an estimate of the NEO rotation rate because it affects the SNR of a radar measurement (Sect.

When observing NEOs with radar, the most important factor is radar detectability, which depends on the SNR. SNR is determined by the following factors specific to an object, namely diameter, range, Doppler width, and radar albedo, and factors specific to the radar system, namely antenna size, transmit power, wavelength, and receiver system noise temperature. The following model for radar detectability presented here is similar to the one given by

The measured Doppler bandwidth is a combination of relative translation and rotation of the observing frame and the intrinsic rotation of the observed object around its own axis. However, in all cases considered by this study, the effect of a moving observation frame is negligible. As such, the Doppler width

The radar echo power originating from a space object, assuming the same antenna is used to transmit and receive, can be obtained using the radar equation as follows:

The radar cross section of NEOs can be estimated using the radar cross section of a dielectric sphere, which is either in the Rayleigh or geometric scattering regime (e.g.

To determine if the measurement is statistically significant or not, a criterion can be set on the relative standard error

The above considerations for the detectability of a space object assume that there is a good prior estimate of the orbital elements, which allows radial trajectory corrections to be made when performing the coherent and incoherent averaging. If the objective is to discover an object without prior knowledge of the orbit, one must perform a large-scale grid search in the radial component of the trajectory space during detection. In this case, it is significantly harder to incoherently average the object for long periods of time while matching the radial component of the trajectory with a matched filter; the search space would simply be too large. For space debris targets, we estimate the longest coherent integration feasible at the moment to be about

Assuming that we cannot perform incoherent averaging without a priori knowledge of the orbital elements, the SNR will then be as follows:

The E3D Stage 1 is expected to be commissioned by the end of 2021. It will then consist of one transmit and receive site in Skibotn, Norway, (69.340

The transmitter in Skibotn will initially have a peak power of 5 MW, later to be upgraded to 10 MW. For this study, we have assumed a transmit power of 5 MW. The transmit duty cycle of the radar is

The other key radar performance parameters for the Stage 1 build-up of E3D are as follows: peak radar gain of 43 dB (

Using Eq. (

As E3D will have a lower sensitivity and very short transmit beam on/off switching time compared to conventional planetary radars, it may be possible to use it as a search instrument, as it is possible to observe nearby objects, and the beam has a large collecting volume. The ability to use the phased array antenna to point anywhere quickly with a 120

A full FOV scan can be performed relatively quickly. The beam broadens as the radar points to lower elevations making the scan pattern non-trivial to calculate. At the zenith the beam width of E3D is about 0.9

An example full FOV radar scan pattern for E3D including the beam broadening effect. The coordinate axis are the normalised wave vector ground projection

Most

Cross-sectional area of NEOs hitting Earth is indicated by

Using the fireball flux reported by

The cumulative flux of objects larger than diameter

The maximum coherent integration time is

The cumulative number of radar detections of objects with

It is worth noting that the above-mentioned numbers are very rough estimates based on the above simplistic “shotgun” model. However, the results are very promising because the magnitude of the number of serendipitous radar detections of NEOs is an order of magnitude between 10 and 1000, which is significantly larger than 0. It is therefore plausible that NEOs in the size range

Assuming that objects are in the geometric scattering regime and that the radar antenna aperture is circular, the search-collecting area for a radar is as follows:

By applying the methods described in Sect.

In order to estimate SNR, we require the distance between the radar and the object, the object's diameter, and the rotation rate of the object. The CNEOS database contains the minimum and maximum diameter estimates derived from object absolute magnitude. We use the mean of these two diameter estimates. The HORIZONS ephemeris provides distance and elevation angle during times of observation. Rotation rates are not well known and neither system provides this property for our population of objects.

Objects detectable using E3D during a 1 year interval.

A summary of the characteristics of the objects that can be tracked or detected during the studied 1 year interval is shown in Table

The observable objects were relatively close to the radar, with the shortest range being 0.08 LD and the furthest range being 1.6 LD. The diameters of the observable objects ranged between 2.0 and 94 m. The highest SNR h

All observable NEOs were above the 30

Only a fraction of all objects are discovered and are entered into the CNEOS database. We can assume that there are significantly more objects that could be large enough and have approaches close enough so that E3D would discover them with an all-sky scan. It should be noted that 2012 DA

Orbital elements of CNEOS database for the period 13 March 2019 to 13 March 2020, with objects having close approaches to the Earth and being simultaneously observable from the E3D facility, marked with red crosses.

Although we have a very limited sample of the total NEO population, it appears that our measurements are not biased towards measuring a specific subset of NEOs with close Earth approaches (Fig.

In order to determine the feasibility of tracking NEO close approaches using the existing EISCAT facilities, we made a similar search for objects observable using the EISCAT UHF radar, which has an antenna gain of

The results indicate that it would be feasible to perform routine NEO post-discovery tracking observations using both the upcoming E3D radar and the existing EISCAT UHF radar. This observing programme would nicely complement the capabilities of existing planetary radars, which cannot observe targets that are nearby, due to the long transmit/receiver switching time. Of the

To accurately determine the observability of a population, one needs to construct a chain that considers the following:

Model of the measurement system (E3D)

Model of the population (mini-moons)

Temporal propagation of the population (solar system dynamics)

The observation itself (a detection window and SNR).

A recent effort to determine the capability of E3D with regards to space debris measurement and cataloguing produced a simulation software called SORTS

SORTS propagates each object of a given population and searches for time intervals where the object is within the FOV of E3D. We consider the effective FOV of E3D to be a 120

The only remaining component of the simulation is an interface with a suitable propagation software (item 3). SORTS already includes propagation software but only for objects in stable Earth orbit, i.e. objects that do not transition to hyperbolic orbits in the Earth-centred inertial frame. We have thus chosen to use the Python implementation of the REBOUND propagator

The REBOUND code is freely available at

The integration was configured to use a time step of 60 s. This step size allows for decent resolution when searching for viable observation windows by the radar system. The initial state for REBOUND was inputted in the J2000 heliocentric ecliptic inertial frame; thus the output was also given in this frame. A standard routine was used to transform to the Earth-centred, Earth-fixed J2000 mean Equator and equinox frame. In this frame the E3D system is fixed in space and observation windows are readily calculated.

All 20 265 synthetic mini-moons were integrated for 10 years past their initial epochs. As previously mentioned, we chose to assume that the objects could have one of four different rotation rates, namely 1000, 5000, 10 000, or 86 400 revolutions per day. As such, four different SNRs were calculated for each point in time. It was also assumed that signal integration could not last longer than 1 h, i.e.

Orbital element distribution of mini-moons that can be tracked by E3D. This is not the detected orbital element distribution but rather what part of the initial distribution is observable. This illustration should be compared to the initial distribution in Fig.

Distribution of ranges and sizes of possible observation windows. Also included is the distribution of peak SNR for these observation windows.

If we assume that we have a prior orbit for these objects, the detections are in essence follow-up tracking measurements, and we can consider the tracking SNRs for observability. The a priori orbit does not have to be of good quality; it need only be sufficiently accurate to restrict the search region in the sky. For these tracking measurements, a total of 1999 out of the 20 265 objects (9.9 %) had at least one possible measurement window, assuming the 1000 revolutions per day rotation rate. This number dropped to 7.9 %, 7.2 %, and 5.2 % for 5000, 10 000, or 86 400 revolutions per day respectively.

Without a prior orbit, we have to consider the SNR for serendipitous discovery. Only a total of 116 objects had an observation with 10 dB SNR or more. The rotation rate does not affect this SNR in this case, as the noise bandwidth is determined by the coherent integration time. We assume that the coherent integration time is limited to 0.2 s due to the computational feasibility of performing a massive grid search for all possible radial trajectories that matches the trajectory of the target. This results in an effective noise bandwidth of

Yearly count of possible observation windows of mini-moons, assuming a rotation rate of 1000 revolutions per day and that a prior orbit is available.

The zenith angle distribution of all possible observation windows, assuming a rotation rate of 1000 revolutions per day and that a prior orbit is available.

The length of each possible observation window that would provide a SNR above 10 dB assuming a rotation rate of 1000 revolutions per day and that a prior orbit is available.

The distribution of sizes, ranges, and SNRs of observable objects are illustrated in Fig.

The expected annual detection rate is illustrated in Fig.

The initial orbital element distribution of the observable objects is illustrated in Fig.

In Fig.

Summary counts of the mini-moon observability simulations spanning 19 years and propagated for 10 years. The number of observable objects is representative of the expected total number of real mini-moons that can be tracked by E3D in future if prior orbital elements are known. Each object can have more than one possible observation window and, on average, each object has approximately 1.5 tracking opportunities. The number of discoverable objects indicates how many serendipitous mini-moon detections can be made if an E3D scan hits the object with an integration time of 0.2 s. Only a few objects have multiple discovery opportunities.

Summary statistics of the observability study can be found in Table

The number of discoverable objects in Table

As discussed in Sect.

Conducting routine NEO follow-up observations using E3D would allow for refined orbits and radar measurements of hundreds of mini-moons every year. Assuming a rotation rate of 1000 revolutions per day and using the observation window length for each possible tracking window, as illustrated in Fig.

Distribution of ranges and sizes of possible discovery windows. Also included is the distribution of peak SNR for these discoveries.

For convenience, we have summarised the statistics from all three methods that were used to determine the observability of NEOs with E3D in Table

Summary statistics from all three methods used to determine the observability of NEOs with E3D.

The fireball observations described in Sect.

Based on the CNEOS catalogue, we have found that E3D can be used to observe

The difference in examined populations between the methods suggests that if routine NEO observations are implemented at E3D, the simulation described in Sect.

It was shown in

Our results indicate that E3D can provide valuable and unique follow-up measurements of mini-moons and NEOs with close approaches. It also shows that, even though discovering mini-moons is sparse, discovery and scanning for the combined population of mini-moons and generic NEOs may be very cost effective as this is inherently dual usage with space debris observations. That is, the same radar pulses and survey patterns can be used for discovering objects from all of the above-mentioned populations. Even the discovery of a single new mini-moon would be significant since, to date, only two have been discovered.

The scientific gain from tracking operations at E3D can be summarised as being efficient, high-quality orbit determination and, if the target is sufficiently larger than the wavelength, novel data on surface properties and rotation rates. There are currently not many methods that can discover smaller NEOs unless they collide with the Earth's atmosphere, as shown by the low number of discovered mini-moons. As such, the scientific gain from discovery operations is in essence the discovery itself, i.e. the observation capability of a population otherwise not observable. If the objects are larger, they can be detected with higher probability using optical methods. In these cases, radar observations are still valuable for the same reasons as tracking operations are.

The feasibility of a follow-up observation programme can be tested in practice by using known space debris objects with large distances. For example, large objects with Molniya orbits are good candidates for testing the detection capabilities of faraway objects over long integration times.

It is also valuable to note that E3D will observe over 1000 meteors per hour

Our results indicate that it is plausible that E3D can be used to discover NEOs with diameters

The study of the mini-moon subset of the NEO population indicates that a significant fraction of objects could be tracked, with 80–160 observing opportunities per year, assuming that the objects have been previously discovered. There is currently only one mini-moon in the Earth's orbit, but it is no longer observable using EISCAT UHF or E3D due to the long range when the object is in the radar field of view. However, there will be more opportunities in future for such observations as new mini-moons are discovered

Our study shows that establishing a post-discovery NEO tracking programme that uses close-approach predictions is feasible. Such an initiative could already be commenced with the existing EISCAT UHF radar, which is only slightly less sensitive than the upcoming E3D radar for this purpose. We estimate that roughly 0.5 % to 1 % of the 2000 objects discovered annually could be tracked using the EISCAT UHF or E3D radars, based on close approaches in 2019. The need for radar resources is minimal, with only a few 4–8 h observing windows each month. However, the observations would need to be scheduled on short notice, using an automated alert system that notifies of upcoming observing possibilities

The underlying research data came from two sources, namely the CNEOS database and a mini-moon model provided by Mikael Granvik, which is not publicly available. The CNEOS database is available online at

DK performed the numerical simulations of mini-moon observations by E3D in Sect.

Juha Vierinen is on the editorial board of the journal.

This article is part of the “Special Issue on the joint 19th International EISCAT Symposium and 46th Annual European Meeting on Atmospheric Studies by Optical Methods”. It is a result of the 19th International EISCAT Symposium 2019 and 46th Annual European Meeting on Atmospheric Studies by Optical Methods, Oulu, Finland, 19–23 August 2019.

This paper was edited by Petr Pisoft and reviewed by Peter Brown and one anonymous referee.