Unintended electromagnetic radiation from Starlink satellites detected with LOFAR between 110 and 188 MHz

1 Introduction

Trendy radio astronomy has profited vastly from advances in know-how. Astronomical radio receivers these days are sometimes operated with giant fractional bandwidths (bandwidth Δν over observing frequency ν in extra of Δν/ν > 50%; e.g. Torne 2017; Hobbs et al. 2020), elevated sensitivity, and aperture (e.g. Jonas & MeerKAT Team 2016), in addition to wider fields of view (e.g. Johnston et al. 2007; van Haarlem et al. 2013). On the similar time, the numerical capabilities of digital again ends have enormously elevated owing to discipline programmable gate arrays (FPGAs) or graphics processing items (GPUs) that permit one to implement special-purpose algorithms in versatile {hardware} boosting the processing speeds. This enables one to document knowledge with unprecedented temporal and spectral decision, which advantages spectroscopy, pulsar, and really giant baseline interferometry (VLBI) observations alike.

Nonetheless, astronomy just isn’t alone in utilising the radio spectrum. There’s a big variety of purposes, resembling radio and TV broadcasts, high-speed wi-fi communications (e.g. cellphone networks and WiFi), or radars, which require entry to the spectrum. Any kind of radio communication and meant radio transmissions is regulated to keep away from a scenario the place totally different operators – when utilizing the identical or close by frequencies – create interference on one another’s programs. This regulation of the radio spectrum is dealt with on the nationwide degree by nationwide radio administrations; nevertheless, as radio waves don’t take care of nationwide borders, worldwide guidelines are required for harmonisation. The Radiocommunication sector of the Worldwide Telecommunication Union (ITU-R) is the highest degree organisation that takes care of this worldwide regulation. It’s a specialised company of the United Nations. The ITU-R (2020) publishes the Radio Laws (RR), which is a world treaty and member states are anticipated to rework the RR into nationwide regulation.

The ITU-R recognised radio astronomy as a service – the radio astronomy service (RAS) – already in 1959 and allotted bands within the radio spectrum to it. Sadly, the bands which can be allotted to the RAS are comparatively sparse and slender – for spectral-line observations, the vast majority of the reserved bands solely cowl the standard Milky Manner Doppler shifts. Additionally, the whole quantity of spectrum that’s allotted to the RAS just isn’t thought of to be adequate for contemporary radio astronomical analysis by most scientists. Beneath 4 GHz, solely 5% of the radio spectrum is allotted to radio astronomy at numerous ranges of safety. If solely major allocations (the very best degree of safety) are thought of, as little as 1.6% is allotted to the RAS. For extra particulars in regards to the regulatory course of, the radio astronomy service and its safety, we refer readers to the ITU Handbook on Radio Astronomy (ITU-R Working Get together 7D 2013), the CRAF Handbook for Radio Astronomy (Committee on Radio Astronomy Frequencies 2005), and the Handbook of Frequency Allocations and Spectrum Safety for Scientific Makes use of (National Academies of Sciences, Engineering, and Medicine 2015).

Not all radiation produced from digital units is topic to ITU-R rules. To a big extent, the RR solely cowl the so-called emissions, which consult with the radiation that’s straight associated to the intentional use of radio frequencies in a system (for the aim of communications, distant sensing, radionavigation, and so on.). This clearly consists of the needed alerts, but in addition undesirable emission: spectral sidelobes together with harmonics and intermodulation merchandise which can be an inevitable by-product of the era of the needed transmission. Undesirable emission is a consequence of the sign amplification or mixing, the chosen modulation scheme, and so on. Each the needed and undesirable emissions are regulated within the RR. However there’s one more supply of electromagnetic radiation current in any electrical machine (or system), which is expounded at its most basic degree to the acceleration and deceleration of costs in any electrical or digital circuits and never essentially associated to the era of needed radio alerts. Because the RR didn’t coin a regulatory time period for this, hereafter we consult with this as unintended electromagnetic radiation (UEMR); it’s value mentioning that in engineering this radiation might be known as electromagnetic interference (EMI). UEMR can seem, for instance, because the product of present loops in switching mode energy provides, communication alerts in unbalanced or mismatched transmission strains, quick switching alerts in printed circuits, and actuating electromechanical circuits, and so on. Principally any electrical circuit generates some degree of UEMR.

UEMR just isn’t explicitly regulated on the ITU-R degree, although different standardisation organisations have stuffed the hole. The Comité Worldwide Spécial des Perturbations Radioélectriques (CISPR¹), which is part of the Worldwide Electrotechnical Fee (IEC), units requirements for all types of terrestrial electrical and digital units with a purpose to management electromagnetic interference. Not like the RR, CISPR requirements refer not solely to radiocommunication programs however all types of digital units. Moreover, the requirements additionally cowl measurement procedures, that are used to find out the extent of UEMR produced by a tool below check.

Not like meant radio emission, UEMR just isn’t clearly specified by a centre frequency, output energy and bandwidth, but it has some traits value mentioning: (i) its radiated energy is often a number of orders of magnitude decrease than any intentional radiation; (ii) UEMR is normally not radiated via an antenna, however principally via cables and/or the mechanical construction of the system; due to this fact, its spatial radiation sample is normally unknown however more likely to be nearer to isotropic than that of a directional antenna system; and (iii) UEMR might have spectral contents which might be very variable relying on the kind of electrical alerts and design of the system.

Telescopes used for radio astronomy usually obtain UEMR from terrestrial sources situated close by (distances of kilometres) and predominantly although their sidelobes. There are various examples of radio telescopes coping with terrestrial UEMR, as is the case of wind farms affecting LOFAR observations² or emission from microwaves resembling astro-physical alerts (Petroff et al. 2015). Radio astronomers additionally put nice effort into shielding the required commentary gear (computer systems, receivers and so on.) to keep away from self-made UEMR to enter the info (Swart et al. 2022). Environmental interference (meant and unintended) to radio telescopes might be minimised by constructing them in designated radio quiet zones or RQZs (Rep. ITU-R RA.2259-1). Sadly, RQZs present no mitigation towards radio emission from Earth orbiting satellites, which radio telescopes can obtain via their major beam or close to sidelobes. Within the case of the Iridium satellite tv for pc constellation, undesirable radio emissions (i.e. not UEMR) interfered with astronomical observations of the 1612 MHz OH spectral line for greater than 20 years (e.g. Cohen 2004; ECC Report 171; ECC Report 247). Finding out reflections of terrestrial alerts from satellites, Prabu et al. (2020) reported attainable UEMR of two cubesats utilizing the MWA between 80 and 103 MHz.

The proliferation of the brand new and enormous satellite tv for pc constellations in low Earth orbit (LEO) – also known as mega-constellations – has brought on worries within the astronomical group owing to the satellites means to replicate daylight and to emit radio alerts (e.g. McDowell 2020; Hainaut & Williams 2020; Boley & Byers 2021). This led to the Satellite tv for pc Constellations workshops (SATCON1 and SATCON2; Walker et al. 2020b), the Darkish & Quiet Skies I and II workshops (Walker et al. 2020a, 2021) and the founding of the IAU Centre for the Safety of the Darkish and Quiet Skies from Satellite tv for pc Constellation Interference (IAU CPS), the members of which investigated and proceed to research the attainable affect of enormous LEO satellite tv for pc constellations on astronomy (see Rawls et al. 2020; Bassa et al. 2022; Di Vruno & Tornatore 2023). Owing to the rising complete variety of satellites in LEO, and therefore the rising likelihood {that a} satellite tv for pc seems throughout the discipline of view of a radio telescope, it is sensible to contemplate satellite tv for pc UEMR as a possible supply of interference sooner or later. The potential menace posed by satellite tv for pc UEMR from giant constellations was first thought of on the Darkish & Quiet Skies II workshop (Walker et al. 2021).

On this paper, we examine the potential affect of satellite tv for pc UEMR on radio astronomy via observations of the SpaceX Starlink satellite tv for pc constellation. On the time of the observations introduced right here, this constellation was the biggest in orbit with some 2100 satellites in orbit. This constellation gives broad-band web connectivity with radio emission used for downlinks allotted to the ten.7–12.7 GHz frequency band³. Compatibility with radio astronomy observations within the protected 10.6–10.7 GHz band has beforehand been studied by the Digital Communications Committee (ECC) of the European Convention of Postal and Telecommunications Companies (CEPT) in its ECC Report 271. As UEMR is predominantly anticipated at low frequencies (under ~ 1 GHz) (see Pulkkinen 2019), properly under the allotted radio transmission downlinks, we noticed satellites belonging to the Starlink constellation at frequencies between 110 and 188 MHz with the LOFAR radio telescope (van Haarlem et al. 2013).

This paper is organised as follows; Sect. 2 presents an outline of requirements and rules relevant to satellites and their subsystems, whereas Sect. 3 makes use of simulations to research the potential mixture affect of a number of satellite tv for pc constellations and its most radiated energy to adjust to the ITU-R threshold ranges in one of many protected radio astronomy bands. We describe the observations and their processing in Sect. 4 and talk about the evaluation of the detected alerts in Sect. 5. Lastly, Sect. 6 accommodates a abstract and conclusions.

2 UEMR of satellite tv for pc programs

There are some EMC requirements devoted to house missions, such because the NASA MFSC-SPEC-521 or the ESA ECSS-E-ST-20-7C, most of them based mostly on the US army commonplace MIL-STD-461. These EMC requirements outline, amongst different issues, the utmost degree of electromagnetic radiation that gear can generate. Most requirements for house are extra stringent than those used for business equipment resembling CISPR-32 (see Fig. 1) however that isn’t a tough requirement, as a satellite tv for pc doesn’t have to be appropriate with abnormal business gear.

As soon as fully assembled, a satellite tv for pc is normally characterised by a ‘system degree’ check that evaluates the general UEMR (amongst many different parameters) of it as an entire. These assessments can final for weeks, relying on the complexity of the satellite tv for pc, making it a really costly exercise. Because of this, system degree assessments are inclined to give attention to the minimal and obligatory checks for every parameter of a whole satellite tv for pc. A transparent instance of this may be seen in Blondeaux et al. (2016), the place UEMR just isn’t highlighted as an necessary step to characterise a satellite tv for pc constellation.

Whereas business requirements such because the IEC 61000 household, CISPR or the US Federal Communications Fee (FCC) half 15 (see Fig. 1), are harmonised and necessary to permit entry right into a sure market, there’s at present no worldwide company or house regulation that requires a spacecraft to conform to a sure EMC commonplace. Moreover, the details about which EMC commonplace is used for a particular programme, the thought of UEMR thresholds, or the true degree of emissions are not often made public. Few examples are within the public area resembling Yavaş & Akgül (2019) and Elkman et al. (2007). Casual communications with satellite tv for pc trade specialists indicated that the traditional observe for satellite tv for pc degree UEMR assessments is to set an emission threshold comparatively excessive (which speeds-up testing occasions) and solely apply stringent ranges (lengthy testing occasions) to slender frequency bands the place the satellite tv for pc or the rocket-launcher have receivers or delicate devices. In Yavaş & Akgül (2019), outcomes of a satellite tv for pc emission degree check are proven, the place the restrict threshold (marked as a strong pink line of their Fig. 7) is outlined at very excessive ranges of emission virtually for each frequency except for just a few communication bands.

Owing to this ignorance, we will suppose {that a} satellite tv for pc may emit comparatively robust UEMR alerts, outdoors of the bands of curiosity for the producer or operator, and nonetheless cross any such testing. This isn’t an unlikely scenario, since many subsystems can mixture their emissions or their interconnection can change the electromagnetic configuration of the satellite tv for pc and enhance the emissions in a sure frequency band. This will likely not have been a difficulty prior to now, with very small constellations or with single satellite tv for pc programs. Even when a satellite tv for pc had robust UEMR, it might require a really delicate receiver to detect it or in different phrases would require the satellite tv for pc to be in the principle lobe of a radio telescope for a substantial fraction of an commentary: a really uncommon situation till not too long ago.

With the appearance of the massive LEO satellite tv for pc constellations (resembling Starlink section 1 with 4408 satellites or OneWeb section 1 with 720 satellites⁴) the scenario adjustments. Firstly, the variety of LEO satellites results in a rise of the mixture sign, which could change into giant sufficient to trigger interference even via the sidelobes and will increase the likelihood of a detection in the principle lobes of the radio telescope. Secondly, the brand new satellites are manufactured in sequence, due to this fact it’s attainable that many satellites current related UEMR. These two results may make the scenario for radio astronomy difficult, even in radio bands reserved to radio astronomy.

Fig. 1 Radiated emission limits for a number of EMC requirements resembling business (CISPR, EN61000), army (MIL-STD-461), and house (MSFC and ECSS). Left axis exhibits electrical discipline measured at 10 m distance, proper axis exhibits equal spectral energy flux density (in Jy) assuming a supply at 1000 km distance.

3 Potential affect of satellite tv for pc EMR on RAS

To analyze the potential affect of satellite tv for pc EMR on radio astronomical observations, it’s attainable to utilize the established strategies that had been developed by ITU-R for normal compatibility calculations of needed and undesirable emissions. The ITU-R recommends to make use of the equal energy flux density (EPFD) methodology (see Rec. ITU-R S.1586-1; Rec. ITU-R M.1583-1). A satellite tv for pc constellation is simulated over a given time vary. The facility acquired from every satellite tv for pc might be calculated from the transmitted energy, considering transmitter and receiver antenna beneficial properties and path propagation losses (e.g. line of sight losses, atmospheric attenuation) earlier than it enters the radio astronomy receiver. The whole aggregated energy, which is the sum of all energy contributions, might be then decided. Below the belief of standardised traits of the receiving antenna, the acquired energy may also be transformed to the related energy flux density (PFD, referred to as complete or built-in flux density within the radio astronomy group), which permits to conveniently examine it to PFD threshold ranges which can be outlined in rules for the safety of a sufferer station. A bonus of this conversion is that it makes a greater comparability attainable between totally different receiving stations, which normally have totally different antenna patterns and beneficial properties. For instance, the RAS safety standards (Rec. ITU-R RA.769-2; in Tables 1 and 2) are offered for an isotropic receiver, though in actuality radio telescopes normally have very excessive ahead acquire.

3.1 Assessing the mixture affect of a satellite tv for pc constellation

Within the following, the EPFD methodology is used to find out the potential affect of UEMR from totally different satellite tv for pc constellations on radio astronomy observations. The EPFD methodology is extensively utilized in spectrum administration and is properly documented in ITU-R paperwork. For comfort, a extra detailed abstract is offered in Appendix A. Right here, the essential steps are defined in a simplified kind. To calculate the acquired energy for one explicit pointing path of the receiver antenna and a sure satellite tv for pc orbit configuration, the process is as follows.

In step one the satellite tv for pc positions (and transmitter antenna orientations) with respect to the observer are be decided for numerous time steps and for a given time period. The required time decision principally relies on the satellite tv for pc altitudes. For low-earth orbit (LEO) satellites the time decision must be 1 s or much less because the angular velocities are excessive. Then the hyperlink funds (path propagation losses in addition to transmitter and receiver antenna beneficial properties) between satellites and observer are computed. Because the satellites aren’t essentially in the principle beam of the radio telescope, the angular separation between the antenna pointing path and the geometrical place of the satellites must be accounted for, which adjustments the efficient receiver acquire. Likewise, the observer will normally not be located within the ahead path of the satellite tv for pc antenna. Trendy satellites are sometimes geared up with lively antennas that permit digital beam-forming in real-time, such that the successfully transmitted energy in direction of the observer can fluctuate strongly. It must be famous, nevertheless, that within the case of UEMR, given its nature, a excessive directivity just isn’t anticipated to be reached and an isotropic transmitting antenna sample is used hereafter as an approximation. After the hyperlink funds is calculated, all of the individually acquired powers (from every satellite tv for pc) are added, which yields the whole aggregated energy. Lastly the whole aggregated energy acquired on the radio telescope is in comparison with the permitted threshold ranges, for instance outlined in Rec. ITU-R RA.769-2. On this advice, the RAS safety ranges are specified for an integration time of 2000 s, thus it’s essential to simulate the orbits over this time span.

The calculation is carried out for a grid of sky cells (or telescope pointing instructions) having roughly equal strong angles. This enables to analyse the spatial distribution of the contributed energy ranges. To evaluate statistical scatter, the entire simulation is repeated a whole bunch or 1000’s of occasions for various beginning occasions and antenna pointings throughout the grid cells.

Typically, the facility flux density on the observer location (attributable to the satellites) is reworked into the so-called equal energy flux density (EPFD). That is the facility flux density, which might have to be current within the boresight of a radio telescope to create the identical energy because the aggregated energy from all satellites. Appendix A accommodates extra particulars on this.

3.2 EPFD and enormous satellite tv for pc constellations

The 150.05–153 MHz frequency band, which is allotted to the RAS, was chosen as it’s generally accepted that radiation attributable to digital circuits is principally concentrated under 1 GHz, and it falls throughout the observing band of LOFAR. The dangerous interference threshold on this band is −194 dB |W m⁻²] over a bandwidth of about 3 MHz, in line with Rec. ITU-R RA.769-2 (see their Table 1).

On condition that the truly radiated emissions from a single satellite tv for pc are unknown, we have now to imagine some worth. An electrical discipline power of 30 dB [µ V m⁻¹] is a typical radiation degree⁵ present in business requirements resembling CISPR-32 based mostly on a detector bandwidth of 120 kHz and measured at a distance of 10 m. This quantity is equal to a radiated spectral energy of −45.6 dB [m W MHz⁻¹]. We additionally assume in our simulations that this radiation is fixed in time and frequency throughout the studied band. In observe that is definitely not the case. UEMR options might be time-variable and may be narrow-band and in such a case a bandwidth correction issue would have to be utilized. We moreover work below the simplification that satellite tv for pc UEMR is isotropically radiated.

The RAS antenna sample and acquire used within the calculations relies on the kind of radio telescope. At these low frequencies, principally interferometric telescopes are used, resembling LOFAR and SKA1-Low. The precise antenna patterns of interferometers (after beam-forming and correlation) are advanced and aren’t completely described by the Rec. ITU-R RA.1631-0 mannequin. Subsequently, we carry out the EPFD assuming parabolic-dish antennas of diameter 25-m and 70-m, respectively, which roughly have the identical efficient antenna space as SKA1-Low tiles and LOFAR (worldwide) stations. In our simulations it’s assumed that the RAS station is situated on the geographical latitude of LOFAR, 53° N.

Utilizing these parameters and assumptions, EPFD calculations had been carried out for numerous present or at present in-deployment satellite tv for pc constellations: Spire⁶, Iridium NEXT⁷, OneWeb⁸, SpaceX/Starlink⁹, and SpaceX/Swarm¹⁰. This gives us a spread of constellation sizes from 66 satellites as much as 4408 (see Table 1) in numerous orbital configurations. For the satellite tv for pc place calculations we made use of the open-source Python package deal cysgp4¹¹ (Winkel 2023), which is obtainable below GPL-v3 license. It’s a wrapper across the sgp4lib¹² C++ implementation of the simplified perturbation mannequin SGP4 (see additionally Vallado et al. 2006). Moreover, the pycr af¹³ Python package deal (Winkel & Jessner 2Ol8a,b) was used, which gives implementations for numerous related ITU-R Suggestions. It’s also obtainable below GPL-v3 license.

3.3 Simulation outcomes

For every constellation in Table 1, 100 iterations (simulation runs) had been processed, which permits us to evaluate the statistical scatter of the outcomes. For example for the outcomes, Fig. 2 exhibits the cumulative distribution perform for EPFD values for the Iridium NEXT and Starlink constellations with the belief of UMR with an electrical discipline power of 30 dB [µ V m⁻¹] over the complete RAS bandwidth¹⁴ and a RAS antenna with a 70-m diameter situated a geographic latitude of 53° N. The sunshine inexperienced and blue curves within the determine present the outcomes for all sky cells in every particular person simulation run, whereas the darker curves signify the median of the person runs in every sky cell. Rec. ITU-R RA.1513-2 recommends that the whole knowledge loss attributable to a single interfering system mustn’t exceed 2%, which is indicated by the horizontal pink line (the 98% percentile) within the determine. The vertical pink line marks the Rec. ITU-R RA.769-2 threshold. The cumulative likelihood at which this threshold is exceeded can be utilized to find out the precise anticipated knowledge loss (about 10% for Iridium NEXT and 100% for Starlink with the assumptions used within the simulation). The intersection between the cumulative likelihood curve and the horizontal pink line of 98% percentile yields the so-called margin, that’s the distinction between the RAS threshold and the precise acquired energy flux density. Whether it is damaging, emissions from the respective satellite tv for pc constellation ought be under the assumed mannequin values by that quantity with a purpose to adjust to the thresholds within the RAS band. The inferred margins for all satellite tv for pc constellations are introduced in Fig. 3.

Primarily based on the margins, below the assumptions used within the simulation, it’s attainable to find out a most electrical discipline worth that every satellite tv for pc ought to adjust to to make sure that the acquired energy on the RAS station just isn’t in extra of the permitted RAS threshold ranges on the knowledge lack of 2%. These values are summarised in Table 1. It’s famous that the calculated values are decrease than business EMC commonplace thresholds such because the CISPR-32 Class B with 30 dB [µ V m⁻¹].

It’s also attainable to research the areas on the seen (topocentric) sky, which contribute most to the general acquired flux density, see Fig. 4, which exhibits the common EPFD per sky grid cell for the Iridium NEXT and Starlink constellations assuming a 70-m RAS antenna.

Fig. 2 Cumulative distribution capabilities for EPFD values owing to Iridium NEXT and Starlink, assuming an isotropic transmitter spectral energy of −45.6 dB (mW MHz−1) and a 70-m radio telescope situated a geographic latitude of 53° N.

Fig. 3 Calculated margins for all simulated satellite tv for pc constellations with the belief of a 30 dB [µ V m−1] UEMR with respect to the ITU-R thresholds in 150.05–153 MHz.

Fig. 4 EPFD acquired in every sky cell (common over 100 iterations) owing to Iridium NEXT and Starlink constellations in topocentric body (azimuth and elevation) as acquired by a 70-m RAS antenna.

4 Observations, knowledge calibration and sign detection

Primarily based on the outcomes obtained in Sect. 3, particularly those for giant satellite tv for pc constellations resembling Starlink, we carried out an commentary with the LOFAR telescope which not solely covers the frequency vary of curiosity however may also produce a number of beams concurrently rising the likelihood of detecting satellite tv for pc emissions inside a fairly quick marketing campaign. This part describes the commentary methodology, knowledge calibration and processing, and various kinds of detected alerts.

Fig. 5 Beam sample of the LOFAR commentary in equatorial coordinates (proper ascension and declination). The 91 tied-array beams are indicated with the smaller circles (24′ FWHM at 150 MHz), whereas the bigger dashed circle denotes the FWHM of a LOFAR core station (4°.7 at 150 MHz). Predictions of the movement of Starlink satellites with respect to the beam sample are indicated with the blue (at orbital altitude h = 358 km) and orange (at h = 550 km). The small and enormous black circles point out the ingress into and egress from the tied-array and station beams, respectively.

4.1 Observations

LOFAR, the Low Frequency Array (van Haarlem et al. 2013), is a community of telescopes with stations unfold over Europe and a dense core within the north of the Netherlands. We obtained a 1-h commentary focusing on principally SpaceX/Starlink satellites on 2022 April 1, beginning at 18:30:00 UTC. Radio alerts from the Excessive Band Antennas (HBA) of the central six LOFAR core stations, these on the Superterp, had been coherently beam-formed by the COBALT beam-former (Broekema et al. 2018) to kind 91 tied-array beams (TABs). The TABs had been distributed in 5 hexagonal rings overlaying the 4°.7 full width at half most (FWHM) station beam, every ring separated by 24′ from the subsequent; see Fig. 5. This separation was chosen such that the TABs overlap on the half-power level round 150 MHz, assuming round beams with a 24′ FWHM at 150 MHz. For every tied-array beam, (uncalibrated) Stokes I intensities within the type of dynamic spectra had been recorded between 110 and 188 MHz, with 10.48 ms time decision and 12.21 kHz frequency decision.

The TABs had been centred in direction of, and monitoring, α_J2000 = 08^h00^m00^s and δ_J2000 = +49°30′00″. This pointing path was chosen for its excessive Galactic latitude (b = 31° 1 at Galactic longitude l = 169°.4) and therefore low sky temperature (decreasing the general system temperature), in addition to the excessive elevation above the horizon of LOFAR (most elevation of 86°.5 at 18:54UTC), minimising the vary between Starlink satellites at their operational altitude of 550 km. Moreover, on the latitude of LOFAR (ϕ = 52°.92), the at present most populated Starlink shells (with orbital inclinations of 53°.0 and 53°.2) result in over-densities of satellites per unit space of sky close to LOFAR’s zenith (Bassa et al. 2022; Lawler et al. 2022), maximising the variety of Starlink satellites passing via the TABs.

We used public ephemerides¹⁵ of the Starlink satellites generated by SpaceX for the commentary planning and the processing of the info. The general public ephemerides present predictions for place and velocity of every Starlink satellite tv for pc with respect to an Earth-centred inertial coordinate body at 1 min time intervals, and embrace deliberate manoeuvres to regulate the satellite tv for pc orbit. From these ephemerides, the trajectory of every satellite tv for pc passing via the LOFAR beam sample in the course of the 1 h commentary was calculated, ensuing within the passes proven in Fig. 5. We additionally computed the time of ingress and egress of every satellite tv for pc via the station beam and the TABs. We word that particular person Star-link satellites are recognized to make small unplanned manoeuvres, which usually consequence within the satellite tv for pc passing early or late in comparison with predictions, with out considerably altering its trajectory on the sky. The ephemerides present {that a} complete of 68 particular person Starlink satellites handed via the LOFAR station beam in the course of the 1 h commentary, 22 of which had been on the operational altitude of h = 550 km. The opposite 46 Starlink satellites passing via the beam sample had been at an altitude of 350 km. These satellites belonged to a bunch of 48 satellites launched on 2022 March 9, 23 days earlier than our observations, and had been nonetheless elevating their orbits to operational altitudes. The Starlink satellites of this launch are of a more moderen model 1.5 kind¹⁶ in comparison with the Star-link satellites on the operational altitudes, which reportedly are model 1.0.

The properties of those satellites and their passes via the beam sample are offered in Table 2. Owing to the excessive elevation of the observations above the horizon, the distances to the Starlink satellites within the operational orbits at 550 km was round 555 km, whereas the orbit elevating group had been at distances of round 356 km. These distances are within the far discipline of the LOFAR Superterp, whose most baseline of ~300 m places the Fraun-hofer distance from 66 to 113 km for the noticed LOFAR band of 110 to 188 MHz. At these distances, the satellites crossed the 4°.7 FWHM of the station beam inside 6 and 4 s, respectively, whereas the 24′ TABs had been crossed inside 0.54 s for satellites at 550 km altitude, and 0.34 s for these at 350 km altitude (t_cross column of Table 2). Of the 68 satellite tv for pc passes, solely two didn’t cross via any of the TABs, whereas the vast majority of the others handed via a number of adjoining TABs, as indicated by the n_TAB column in Table 2. Lastly, we word that each one Starlink satellites passing via the beam sample throughout this commentary had been illuminated by the Solar, and that their photo voltaic panels may have been producing energy.

4.2 Knowledge calibration

To calibrate the recorded data-sets, we carried out each the frequency-dependent system acquire (band-pass) correction17 in addition to the depth calibration. For a single dish antenna, the on-source, off-source methodology represents a helpful technique to appropriate for the system acquire. In quite simple phrases, the recorded uncalibrated energy spectrum, P(t_i, f_j), at time, t_i and in frequency channel f_j is expounded to the precise antenna temperature, T_A, by way of the receiver system switch perform, G_bp(t_i, f_j). G_bp is a perform of frequency, nevertheless it additionally relies upon mildly on t_i owing to sluggish drifts of the receiver (amplifier) acquire. For the accuracy required for this venture, one can safely assume that G_bp is fixed with time over the comparatively quick commentary interval. Thus,

(1)

The concept of the on-source, off-source methodology is to divide two spectra to take away the frequency-dependent band-pass form (examine Winkel et al. 2012). This yields

(2)

Clearly, the beam-formed LOFAR knowledge just isn’t measured with solely a single antenna. However, the tactic outlined above can nonetheless be utilized in a really related method. The measured energy spectrum, P, is once more topic to a frequency dependent ‘system acquire’, which is now performing on an ‘efficient (ensemble) antenna temperature’ as an alternative of every factor’s antenna temperature. The on-source, off-source methodology will take away the imprint of this technique acquire from the info, however the ensuing amount just isn’t merely T_supply/T_sys as in Eq. (2) however a distinct amount.

For absolutely the flux calibration we used the strategy outlined in Kondratiev et al. (2016) which fashions the efficient space, beam form, system temperature and coherence of LOFAR. The radiometer equation (e.g. Dewey et al. 1985) relates the (energy) flux density root imply sq. (RMS) at TAB degree to those portions by

(3)

the place ΔT^station is the noise degree that may be achieved with a single station based mostly on the radiometer equation. It relies on the system temperature of a station, , the variety of polarisation channels, n_p = 2, that had been averaged, the mixing time, tob , and the bandwidth, Δν, which on this case is the width of a spectral channel. The amount is the sensitivity or acquire that interprets between the station degree system noise and the TAB flux density RMS. It’s decided by the efficient aperture space of a TAB, , and the Boltzmann fixed okay_B. The worth of relies on the beam-forming effectivity and the variety of contributing antennas. Kondratiev et al. (2016) derived an approximation method,

(4)

with the fraction of lively dipoles, η_lively = 0.95 (about 5% of the dipoles are sometimes not in operation), the variety of HBA sub-stations within the Superterp, N = 12, and the efficient aperture space, , of one in every of these sub-stations. van Haarlem et al. (2013) report on the values of for numerous frequencies. For the frequencies used on this paper, we interpolated these values linearly. van Haarlem et al. (2013) additionally estimated the system equal flux density (SEFD), which is the equal of the on the flux density scale. The SEFD is comparatively fixed within the frequency vary thought of within the following, with a worth of about 3 kJy. This may be transformed to the system temperature scale utilizing SEFD [Jy] = 2760 [K] [m²] (van Haarlem et al. 2013).

Primarily based on these equations and beforehand reported portions, the calibration parameters in Table 3 had been decided to be used within the subsequent sections. As a result of the station aperture, , seems in each phrases, and , is definitely impartial on . It has a worth of two.986 Jy for all frequencies in Table 3 (a flat SEFD was assumed). With a view to calibrate the spectra, it is just obligatory to find out the noise degree (in arbitrary items) and scale the info such that its RMS equals .

4.3 Sign detection

The band from 110 to 188 MHz into consideration is allotted to a number of radio companies resembling air visitors management (118–137, 138–144 MHz), beginner radio (144–146 MHz), emergency pagers (169–170 MHz), satellite tv for pc transmissions (137–138, 148–150 MHz) and digital audio broadcasting (174–230 MHz), with emergency pagers and digital audio broadcasting being the strongest sources of radio emission (Offringa et al. 2013). The vast majority of these emission sources are terrestrial and therefore are situated near, or on the horizon. As such, these alerts will probably be detected within the sidelobes of the LOFAR station beam and TABs, and therefore will seem on the similar time and with related sign power in all TABs. Quite the opposite, objects shifting via the sky will produce alerts within the dynamic spectra of the TABs at totally different occasions as they cross via the TABs. This not solely applies to the goal Starlink satellites, but in addition to different satellites in addition to plane.

Primarily based on these concerns, the data-set has been independently looked for alerts to keep away from biases. We first discovered a narrow-band sign at 175 MHz and broad-band options with various depth unfold throughout the band. Completely different knowledge processing methods had been utilized for this, which apparently had been appropriate to search out the 2 forms of alerts. After the primary detections had been made, it additionally turned clear that a few of the satellite tv for pc positions weren’t precisely predicted by the ephemerides. Nonetheless, these first discovering made it attainable to appropriate the positional knowledge, which triggered extra detections at additional frequencies. Within the following we offer a abstract of the method.

A lot of the brighter broad-band alerts had been already seen within the uncooked, uncalibrated dynamic spectra of the TABs after binning; see Fig. 6. Because the length of a cross via a TAB is of order 0.1 to 0.6 s, the dynamic spectra had been averaged to a time decision of 41.94 ms, maintaining the frequency decision fastened to 12.21 kHz. Subsequent, AOflagger (Offringa et al. 2012) was used with the usual LOFAR flagging technique to determine non-astrophysical alerts and create a masks for the dynamic spectrum of every TAB. We discovered that, on common, 23% of the dynamic spectrum is flagged, 6.25% of which is because of every sixteenth channel, which accommodates the DC element of 16 channel poly-phase filter-bank used to channelise the LOFAR 0.195 MHz sub-bands into 12.21 kHz channels.

For every Starlink satellite tv for pc passing via the LOFAR station beam, we began by extracting 20 s in time centred on the anticipated mid-point of the cross via the LOFAR station beam from every of the 91 TABs. For this we used the band-pass calibrated dynamic spectra. To minimise the affect of terrestrial alerts, which regularly seem related in all beams, we subtracted from the extracted dynamic spectrum of every TAB the imply of the dynamic spectra of all the opposite TABs. Lastly, once more for every satellite tv for pc cross, the ensuing dynamic spectra of these TABs via which the satellite tv for pc handed had been aligned in time based mostly on the anticipated passage time and averaged to extend the signal-to-noise of any satellite tv for pc emission. We word that with this strategy we particularly selected to not masks any knowledge that was flagged by AOflagger, this was to make sure that no emission from satellites can be faraway from the evaluation.

Inspection of those averages of TABs confirmed broad-band emission all through the noticed frequency vary, coinciding with the crossing occasions of Starlink satellites. Normalised, aligned, and averaged dynamic spectra for 2 satellites are proven in Fig. 7. The dynamic spectra have a time decision of 41 ms and the complete frequency decision of 12.21 kHz. Because of the normalisation with the dynamic spectra of the opposite TABs, brilliant alerts in these TABs might result in depressions in these plots. To forestall masking of alerts related to satellites, no masking has been utilized when normalising, aligning and averaging these spectra. Not all satellites reveal broad-band emission on the similar frequencies – the 2 most typical frequency ranges the place emission is detected are at 116–124 MHz and 157– 165 MHz. We focus our evaluation on these two frequency ranges, but in addition embrace the ITU-R RAS frequency band from 150.05 to 153 MHz.

In addition to broad-band emission, narrow-band emission was additionally detected in, and confined to, a number of particular person 12.21 kHz channels. The frequencies of those channels cowl 124.994 to 125.006 MHz, 134.991 to 135.004 MHz, 143.048 to 143.060 MHz, 149.994 to 150.006 MHz and 174.994 to 175.006 MHz. We embrace these alerts in our evaluation, and can consult with them because the narrow-band emission at 125, 135, 143.05, 150 and 175 MHz. As the utmost radial velocities of the Star-link satellites on this commentary are lower than |υ_r| < 1 km s⁻¹, any Doppler shifts at these frequencies are lower than ~ 600 Hz and therefore confined to particular person spectral channels.

As proven in Fig. 7, the sign power of those narrowband emission can fluctuate considerably between frequencies in addition to satellites. In some circumstances, the narrow-band options had been so brilliant, that the satellite tv for pc was detected passing via the sidelobes of particular person TABs. Moreover, in lots of circumstances, particularly at 125 MHz, the narrow-band alerts had been superposed with terrestrial alerts. That is additionally why the info processing technique needed to be modified with a purpose to extract the narrow-band alerts correctly. As an alternative of subtracting the common of all beams from every spectrogram we subtracted a spectral baseline in a small window round every narrow-band peak.

Lastly, in some, however not all, of the decrease altitude Starlink satellites, a comb of slender (inside a 12.21 kHz channel) peaks was seen within the frequency vary above 155 MHz. The dynamic spectra of satellite tv for pc 51998 proven in Fig. 7 exhibits this comb for frequencies between 170 and 176 MHz. Energy spectra of the emission between 157 to 165 MHz exhibits that these peaks are spaced at 50 kHz offsets and is detectable in 17 of the 46 satellites at decrease altitudes, however not one of the larger altitude satellites. The satellites the place this comb was detected are marked in Table 2.

For all satellites which had been detected via both broadband or narrow-band emission, we decided the time offset between the noticed and the anticipated passage time via the TABs by becoming a Gaussian profile to the temporal emission profiles. These time offsets are listed in Table 2. We discovered that the time offsets are lower than 1 s for all however 4 satellites, and excluding these yields a median time offset of . The 4 satellites with the biggest time offsets handed via the beam sample by as a lot as 6.4 s earlier, and others 1.3 s late in comparison with predictions. We moreover discovered that the temporal width of the Gaussian matches matches these from predictions, the place the satellites at 350 km orbital altitudes moved via the beam quicker than these at 550 km. Subsequently, all these offsets had been used to change the satellite tv for pc ephemerides and additional analyses had been based mostly on the corrected positions.

To visualise the emission as a satellite tv for pc passes via the LOFAR TAB beam sample, Figs. 8–10 present the temporal profiles of satellite tv for pc passes compared to the situation of the satellite tv for pc because it passes via the beam sample. The case of satellite tv for pc 47373 proven in Fig. 8 is one in every of instance for a really brilliant occasion, the place the narrow-band emission at 175 MHz was robust sufficient to be detected in all TABs for the complete length that the satellite tv for pc handed via the 4º.7 FWHM station beam. In different circumstances, resembling for the cross of satellite tv for pc 45705 (Fig. 9) the behaviour was ‘regular’, nevertheless, and a sign was solely detected within the beams overlaying the satellite tv for pc sky observe. For completeness, additionally an instance for the broad-band emission between 116 to 124 MHz is displayed in Fig. 10 for the cross of satellites 51978. As anticipated, the strongest detections coincide with the anticipated time that the satellites handed via the person TABs, confirming that the sign was coming from the path of the satellites.

Subsequent, we used the intensity-calibrated spectra to estimate the facility flux densities (PFD) for every one of many detected alerts. Because the satellites normally didn’t cross any of the beam centres precisely, we decided the PFD as a perform of the angular separation between the satellite tv for pc positions with respect to every of the TAB centres; see Fig. 11 for 2 instance satellites. Primarily based on a Gaussian least-squares match to the info factors, the height PFD could possibly be estimated. These PFD measurements are offered in Table 2. Moreover, a visible overview is offered in Fig. 12. It’s noteworthy that for the occasions with very excessive depth (above about 100 Jy) the Gaussian match was made tough due to the cross-talk induced by the LOFAR beam-former (e.g. Fig. 11 left panel). Subsequently, the width parameter of the Gaussian match curve was constrained to values under . Likewise, for all matches the zero degree offset was constrained to values near zero. Additionally, the scatter within the flux density values was moderately giant, such that the accuracy of the S_v values in Table 2 shouldn’t be overestimated.

Fig. 6 Dynamic spectrum of tied-array beam 18, displaying broad-band radio emission of three Starlink satellites (NORAD IDs 51993, 51988 and 51986) coincident with the predictions from satellite tv for pc ephemerides. For NORAD ID 51993, the emission is seen from 115 to 130 MHz, whereas objects 51988 and 51986 are extra apparent from 140 to 175 MHz. The dynamic spectrum has been averaged by an element 4 in time to a time decision of 41 ms, and an element 16 in frequency to a frequency decision of 0.195 MHz. To indicate the temporal and spectral construction of the satellite tv for pc emission, in addition to that of different anthropogenic alerts, the uncooked, uncalibrated dynamic spectrum is proven, with out masking of anthropogenic alerts. The bars on the prime of the dynamic spectrum point out the anticipated time ranges the place the indicated satellite tv for pc handed via the LOFAR station beam (in gray), and the particular tied-array beam (in pink). Within the case of object 51988, the emission is about 0.33 s delayed in comparison with the prediction. The histogram on the best exhibits the fraction of the dynamic spectra that might have been masked in frequency by OAflagger (Offringa et al. 2012).

Fig. 7 Spectral and temporal properties of the passes of satellites 45186 (common of 11 TABs) and 51998 (common of 10 TABs). For every satellite tv for pc cross, normalised, aligned and averaged dynamic spectra are proven over the complete noticed bandwidth and inside 2.5 s on the anticipated passage time. Time sequence at narrow-band frequencies of 125, 135, 143.05, 150, and 175 MHz are proven within the prime insets, in addition to for broad-band frequency ranges (116 to 124, 150.05 to 153, and 157-165 MHz). The color of every time sequence matches the marked frequencies and frequency ranges in the identical colors to the perimeters of the dynamic spectra. For each satellites a mix of broad-band and narrow-band emission is seen. Within the case of satellite tv for pc 45186, broad-band emission is generally confined to the frequencies under 155 MHz, however narrow-band emission at 125, 135, 150, and 175 MHz is detected, with sidelobes being seen at 175 MHz. Some construction within the broad-band emission is apparent between 120 and 122 MHz. For satellite tv for pc 51998, broad-band emission is obvious in any respect frequencies not affected by terrestrial alerts, whereas narrow-band emission is absent, aside from 143.05 MHz. Between 170 and 176 MHz, a comb of narrow-band, usually spaced peaks, is superposed on the broad-band emission. The temporal profiles present time offsets of the noticed satellite tv for pc cross with respect to predictions (+0.09 s for 45186, −0.07 s for 51998).

Fig. 8 Visualisation of the detected sign from satellite tv for pc 47373 because it crossed the sector of view of the LOFAR tied array beam sample. Every circle marks one of many beams. The inlays present the 175 MHz sign (spectral PFD) as a perform of time spanning about ~20 s centred across the occasion time (roughly 35 s after commentary begin). The grey-shaded areas mark the whole time interval over which the satellite tv for pc was within the discipline of view, the pink shaded areas consult with the time when the satellite tv for pc was within the corresponding beam space.

Fig. 10 As Fig. 8 however for satellite tv for pc 51978 visualising a broad-band sign in 116-124 MHz.

Fig. 11 Measured spectral energy flux densities for satellites 47373 and 45705 as a perform of angular separation from beam centres. Completely different colors and symbols mark totally different beams. The black strong line represents a least-squares match (Gaussian perform) to the info factors. This enables to estimate the precise spectral PFD of the satellite tv for pc, which is about 460 Jy (47373) and 25 Jy (45705), respectively, averaged over one spectral channel of 12.2 kHz at 175 MHz.

Fig. 12 Radio emission detected from Starlink satellites in the course of the LOFAR commentary. Passes of Starlink satellites via the LOFAR beam sample are marked in time with strong vertical strains for satellites at h = 550 km, and dotted strains for these at h = 350 km. The colored horizontal strains and bands point out the frequencies of frequency ranges during which fluxes had been measured, with the circles indicating the corresponding flux density measurements.

5 Evaluation of the detected occasions

5.1 Sign properties

Utilizing the flux density measurements of satellite tv for pc occasions on the narrow- and broad-band frequencies as listed in Table 2 we will infer some properties of the detected alerts.

We discovered that the narrow-band emission at 125, 135, 150, and 175 MHz is simply detected for the Starlink satellites at their operational altitude of h = 550 km, and never seen in any of the Starlink satellites within the decrease orbit at altitudes of h = 350 km. As the upper altitude satellites are extra distant (d ~ 555 km) in comparison with the decrease altitude satellites (d ~ 356 km), any emission of equal depth ought to trigger a detection within the acquired knowledge about (555 km/356 km)² ~ 2.4 occasions brighter for the satellites at decrease altitudes. Whereas the person satellites confirmed some variation within the sign strengths, it’s deemed extraordinarily unlikely that the entire decrease altitude satellites would by probability have very low emission. Therefore, it naturally seems that there’s an intrinsic distinction between the satellites in larger altitude and decrease altitude orbits with respect to the narrow-band options.

This isn’t the case for the broad-band emission, which was detected for almost all of satellites, no matter their orbital altitude. We discovered that the median PFD of the low altitude satellites is an element 2.0 and a pair of.3 larger than that of the excessive altitude satellites for frequency ranges of 116 to 124 MHz and 150.05 to 153 MHz, respectively. As that is near the anticipated issue of two.4, this means that the era of this emission is impartial on altitude. Curiously, the broad-band emission between 157 and 165 MHz is an element 15 larger within the low altitude satellites, suggesting an intrinsic distinction on this frequency vary.

The incidence of the alerts for particular person satellites at totally different frequencies is correlated. For 18 out of 19 circumstances during which narrow-band emission at 125 MHz was detected, emission was additionally current at 135 MHz, albeit considerably fainter. An identical relation exists between the emission at 125 MHz and 175 MHz, although the emission at 175 MHz seems to be extra variable and might be brighter than at 125 MHz. The sign at 175 MHz was detected in 14 circumstances. The narrow-band emission at 150 MHz was solely seen for these satellites that had been very brilliant at 175 MHz (and cross the station beam) and was detected in six circumstances.

Because the decrease altitude satellites had been nonetheless within the orbit-raising section, the 125 and 175 MHz may be related to the common operation (e.g. communication-link transmissions) of the satellites. Additionally, each frequencies are odd multiples of 25 MHz – a frequency typically used for native oscillators – and could possibly be harmonics, which normally seem stronger at both odd and even multiples of the basic mode. This might additionally clarify, why the 150 MHz sign is simply current for the brightest of the 175 MHz detections (as 150 MHz is a fair a number of of 25 MHz). Usually, sq. wave-like alerts are anticipated to supply odd harmonics. It’s unclear, how the 135 MHz characteristic would match into this. It may be owing to some intermodulation product of the detected narrow-band options with another sign, however we weren’t capable of finding additional proof for this.

We attribute the narrow-band emission detected at a frequency of 143.05 MHz to the GRAVES house surveillance radar (Michal et al. 2005). The GRAVES transmitter is situated 30 km east of Dijon, France and is thought to transmit steady wave alerts at 143.050 MHz for bi-static Doppler monitoring of satellites. The transmitter illuminates a 180° vary in azimuth (east to west via south) and a 30° vary in elevation (Jouade & Barka 2019). Although the radiated energy of the transmitter just isn’t publicly recognized, radar reflections from meteors are usually detected by radio amateurs utilizing modest gear, even for meteors situated properly outdoors of the nominal illumination sample of the GRAVES transmitter (e.g. Fleet 2015). The Starlink satellites that we noticed had been additionally situated far outdoors of the (recognized) GRAVES illumination space, implying that even within the far sidelobes of the GRAVES radar the successfully transmitted energy is substantial.

One other attention-grabbing discovering is that the majority high-altitude satellites don’t present GRAVES reflections, though LOFAR ought to have the sensitivity to detect them. The 2 satellites that had been detected at 143.05 MHz had been even brighter than the low-altitude satellite tv for pc reflections (when they need to be weaker owing to longer propagation paths). This means that the main points of the propagation are topic to a number of results, the magnitude of which can’t simply be decided with out extra info. One side is definitely the orientation of the satellite tv for pc relative to the LOFAR station. It’s recognized that Starlink makes use of the ‘open-book’ mode throughout orbit elevating, the place the photo voltaic array is aligned parallel to the satellite tv for pc physique to cut back atmospheric drag, whereas the operational satellites are in ‘shark-fin’ configuration, the place the photo voltaic array is situated principally behind the satellite tv for pc as seen from Earth. Moreover, the precise path geometry is anticipated to vary between decrease and better orbit altitudes, in addition to the side-lobe acquire of GRAVES in direction of totally different elevations.

5.2 Evaluation of transmitted energy ranges

(5)

assuming solely line-of-sight propagation loss and neglecting different results, resembling atmospheric attenuation. The ensuing minimal and most spectral EIRP values for every band are compiled in Table 4, offering outcomes for low- and high-altitude satellites individually.

The transmitted EIRPs may also be transformed to electrical discipline strengths to make comparability with EMC requirements easier; examine Sect. 3.2. The corresponding values are additionally offered within the desk. For the narrow-band alerts at 125, 135, 143, 150, and 175 MHz, respectively, electrical discipline strengths within the vary of 24 to 49 dB [µ V m⁻¹] are decided, normalised to what a median detector with bandwidth of 120 kHz at a distance of 10 m would measure. The everyday values for the broad-band alerts are between 21 and 39 dB [µ V m⁻¹], once more for a 120 kHz detector bandwidth.

These values might be in contrast with the outcomes of the EPFD simulations in Sect. 3.3, specifically with Table 1. Within the EPFD simulations it was nevertheless assumed {that a} sign had a relentless electrical discipline power over the complete allotted RAS band 150.05–153 MHz. All electrical discipline values have additionally been transformed to a measurement bandwidth of two.95 MHz which totally covers the RAS band for the comfort of comparability. They’re offered within the right-most column of Table 4. It’s famous that for narrow-band alerts the values are the identical for each detector bandwidths (120 kHz and a pair of.95 MHz), as a result of the whole built-in energy is similar, whereas for a broad-band sign the whole energy will increase, the extra bandwidth is taken into account. The vary of discipline strengths for the measurement bandwidth of two.95 MHz is thus 24 to 49 dB [µ V m⁻¹] (narrow-band) and 35 to 52 dB [µ V m⁻¹] (broad-band)

For the detected Starlink satellites, Table 1 cites most E-field values of 25.6 and 23.8 dB [µ V m⁻¹] given a measurement bandwidth of two.95 MHz for the (efficient) antenna diameters of 25 and 70 m, respectively. Therefore, even the weak detections exceed the advised restrict, whereas the brightest detections are greater than 20 dB above the restrict.

It must be emphasised, although, that our observations signify solely a snapshot, measuring a small sub-set of all satellites and that the detected alerts aren’t equally brilliant and a few satellites didn’t even reveal UEMR at sure frequencies. However, the general variety of detections signifies that satellite-borne UEMR from giant satellite tv for pc constellations may certainly be a difficulty for RAS operations.

5.3 Intrinsic emission or reflection?

5.3.1 Geometrical concerns

In Fig. 13, the trail geometry is analysed for the high- and low-altitude satellites. It’s assumed that the satellite tv for pc seems at an elevation angle of 85 deg from the LOFAR observer. Primarily based on the azimuthal angle of the satellite tv for pc (with respect to LOFAR) one can assemble a geodesic¹⁸ beginning on the LOFAR observer out to a sure distance. Alongside this path, one can put a hypothetical transmitter and decide below which elevation angle the identical satellite tv for pc would seem within the transmitter body (topocentric). Likewise, the geodesic distance (i.e. the projection on the bottom) between transmitter and satellite tv for pc might be inferred. The latter two portions are proven in Fig. 13 as pink and blue curves, respectively. At about 2000 km distance, the low-altitude satellite tv for pc can be set under the horizon.

Fig. 13 Geometry of the satellite tv for pc reflection state of affairs.

5.3.2 Hyperlink budgets

(6)

Within the line-of-sight case (which isn’t related right here), one would discover19

(7)

(8)

and we will specific this in the same method as Eq. (6):

(9)

Figure 14 shows the trail propagation losses of the satellite tv for pc reflection state of affairs vs. the direct terrestrial (trans-horizon) path loss. It must be famous that for the terrestrial path, neither the terrain (resembling hills) nor litter was accounted for. Each can add substantial extra path propagation losses of 20 dB and extra, every. Within the reflection case, the LOFAR TAB factors on the satellite tv for pc, such that the complete principal beam acquire applies (43 dBi at 175 MHz). Once more, with out additional information it’s assumed that the transmitter acquire in direction of the satellite tv for pc is 0 dBi. Below these assumptions, the propagation path over the reflection off the satellite tv for pc can be extra environment friendly past about 900 km in comparison with the terrestrial propagation. At this distance the satellite tv for pc would seem at roughly 20–25° elevation within the transmitter body. If the transmitter sign can be focused in direction of the satellite tv for pc, then the antenna acquire, can be a lot larger than the assumed 0 dBi, which might additional lower the gap at which the reflection state of affairs is extra environment friendly. Likewise, diffraction at terrain or litter losses would additionally enhance the terrestrial path loss and make the reflection state of affairs extra environment friendly.

Fig. 14 Path propagation losses of the satellite tv for pc reflection state of affairs vs. the direct terrestrial (trans-horizon) path loss. The pink line signifies the gap (~ 620 km of the GRAVES radar from the LOFAR observer.

5.3.3 Estimating the transmitter energy (reflection state of affairs)

Primarily based on the reflected-case path propagation loss in Fig. 14 and the utmost acquired narrow-band energy of

(10)

the transmitter energy (EIRP in direction of satellite tv for pc) would have to be between 81 and 92 dB [W] or 73 and 88 dB [W] for high- or low-altitude satellites, respectively, relying on the gap between radar transmitter and satellite tv for pc. It is a big quantity and would require a LOFAR-size transmitter with a carried out energy within the kilo-Watts regime (concentrated inside a bandwidth of solely 12.2 kHz)20. Within the case of the GRAVES frequency, it’s certainly very probably that the detected sign is in truth originating from the GRAVES radar and mirrored off the satellites. GRAVES in all probability has adequate transmit energy to elucidate the acquired alerts. In actual fact, there are quite a few reviews by amateurs who obtain GRAVES alerts that had been mirrored by meteors with small receiving antennas. The space between GRAVES within the jap a part of France and the LOFAR superterp is about 620 km. That is giant sufficient to make the reflection path extra environment friendly than the direct terrestrial path, as for LOFAR the native litter setting will play a job and there’s additionally comparatively hilly terrain alongside the propagation path in France and Belgium that might enhance the diffraction losses.

No different radar facility is thought that operates on the detected frequencies. Whereas for these circumstances, the radar state of affairs can’t be totally excluded, we discover it unlikely. The truth that the 125 and 175 MHz alerts had been solely noticed for the upper orbit satellites is one other side that might be onerous to elucidate inside a radar state of affairs. And a strong radar that might function broad-band between about 110 and 170 MHz would in all probability be well-known as it might intervene with many purposes in a big space across the transmitter.

6 Abstract and conclusions

As a result of the detected alerts in our 1-h commentary signify solely a snapshot and a small fraction of the Starlink constellation, one can at present not estimate precisely if and the way a lot a complete satellite tv for pc constellation, Starlink or different, would exceed safety thresholds in RAS frequency bands. Nonetheless, the detected intensities are orders of magnitude above the extent that every particular person satellite tv for pc can be allowed to have with a purpose to adjust to the Rec. ITU-R RA.769-2 thresholds (if all satellites had been equally brilliant as defined in Sect. 3). Subsequently, we’re of the opinion that satellite tv for pc operators and regulation authorities ought to take into account satellite tv for pc UEMR and mirrored alerts as one other side of the regulatory course of.

Moreover, a dialogue between the satellite tv for pc operators and the (radio) astronomical group can be welcome to know how {the electrical} properties and operational procedures of the satellites have an effect on radio astronomy, and the way these can be utilized to mitigate their affect. Hopefully, this dialogue can construct on the co-operation that SpaceX/Starlink has with optical astronomy (see dialogue in Green et al. 2022), particularly since radio observations could also be affected repeatedly, not primarily throughout twilight as is the case with optical/infrared astronomy. This might comply with the instance that was set with the latest coordination settlement between the US Nationwide Science Basis (NSF) and SpaceX. A lot of the authors of this work are lively members within the IAU CPS, the place this dialogue can happen.

It can’t be overstated, that any lack of observing time can straight be translated right into a financial lack of the substantial investments which went into creating, working and utilizing radio astronomy services (e.g. Barentine et al. 2023). Nonetheless, the a lot graver consequence is the lack of the output of this comparably small funding – basic analysis is a big sector of bodily science, which normally pays out solely in a matter of a long time. Whereas a few of the present satellite tv for pc constellations have the means to guard radio astronomy websites from meant radio transmissions by steering their radio beams away, this type of lively mitigation won’t be attainable for UEMR. Therefore, this is a matter in want of shut consideration by satellite tv for pc operators, regulators and the astronomical group. Tens of 1000’s of low-Earth orbit satellites are within the making and with out correct consideration, these may probably produce a man-made sphere of ‘radio gentle’ that leaks into astronomical observations, rendering some astronomical observations unimaginable.

Acknowledgements

This paper relies (partially) on knowledge obtained with the Worldwide LOFAR Telescope (ILT) below venture code DDT16_003. LOFAR (van Haarlem et al. 2013) is the Low Frequency Array designed and constructed by ASTRON. It has observing, knowledge processing, and knowledge storage services in a number of nations, which can be owned by numerous events (every with their very own funding sources), and which can be collectively operated by the ILT basis below a joint scientific coverage. The ILT assets have benefitted from the next latest main funding sources: CNRS-INSU, Observatoire de Paris and Université d’Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science Basis Eire (SFI), Division of Enterprise, Enterprise and Innovation (DBEI), Eire; NWO, The Netherlands; The Science and Expertise Services Council, UK; Ministry of Science and Increased Training, Poland. The venture resulting in this publication has acquired funding from the European Union’s Horizon 2020 analysis and innovation programme below grant settlement No 101004719. The authors thank the help of the IAU Centre for the Safety of the Darkish and Quiet Sky from Satellite tv for pc Constellation Interference (IAU CPS). The IAU CPS is a digital centre of the Worldwide Astronomical Union arrange in partnership with the SKAO and the NSF’s NOIRLab. The Centre coordinates collaborative and multidisciplinary worldwide efforts from establishments and people working throughout a number of geographic areas, seeks to boost consciousness, and mitigate the damaging affect of satellite tv for pc constellations on ground-based optical, infrared and radio astronomy observations in addition to on humanity’s enjoyment of the night time sky. Conversations about UEMR began again in 2020 on the Darkish and Quiet Skies 2 workshop and this paper is a results of these conversations and research. We thank Willem Baan and Uwe Bach for proof-reading our preliminary draft and offering precious suggestions. This paper made intensive use of the Python scientific stack, and we want to thank the builders of NumPy (van der Walt et al. 2011), matplotlib (Hunter 2007), SciPy (Jones et al. 2001), Astropy (Astropy Collaboration 2013, 2022), and Cython (Behnel et al. 2011).

Appendix A The Equal-Energy Flux Density methodology (EPFD)

(A.1)

The angles (φ_i, ϑ_i) describe the place of satellite tv for pc i within the observer body (e.g. azimuth and elevation), whereas () is the place of the observer within the satellite tv for pc antenna body. The space between every of the satellites and the observer is denoted as di. Moreover, P_tx is the transmitted energy in ahead path, G_tx,rx are the efficient transmitter and receiver antenna beneficial properties. The trail attenuation/path propagation loss is subsumed into L_i(φ_i, ϑ_i, d_i).21 If solely line-of-sight loss can be accounted for (which is roughly appropriate at low frequencies), L_i turns into

(A.2)

(A.3)

(A.4)

(A.5)

References

All Tables

All Figures

	Fig. 1 Radiated emission limits for a number of EMC requirements resembling business (CISPR, EN61000), army (MIL-STD-461), and house (MSFC and ECSS). Left axis exhibits electrical discipline measured at 10 m distance, proper axis exhibits equal spectral energy flux density (in Jy) assuming a supply at 1000 km distance.
In the text

	Fig. 2 Cumulative distribution capabilities for EPFD values owing to Iridium NEXT and Starlink, assuming an isotropic transmitter spectral energy of −45.6 dB (mW MHz−1) and a 70-m radio telescope situated a geographic latitude of 53° N.
In the text

	Fig. 3 Calculated margins for all simulated satellite tv for pc constellations with the belief of a 30 dB [µ V m−1] UEMR with respect to the ITU-R thresholds in 150.05–153 MHz.
In the text

	Fig. 4 EPFD acquired in every sky cell (common over 100 iterations) owing to Iridium NEXT and Starlink constellations in topocentric body (azimuth and elevation) as acquired by a 70-m RAS antenna.
In the text

Fig. 5 Beam sample of the LOFAR commentary in equatorial coordinates (proper ascension and declination). The 91 tied-array beams are indicated with the smaller circles (24′ FWHM at 150 MHz), whereas the bigger dashed circle denotes the FWHM of a LOFAR core station (4°.7 at 150 MHz). Predictions of the movement of Starlink satellites with respect to the beam sample are indicated with the blue (at orbital altitude h = 358 km) and orange (at h = 550 km). The small and enormous black circles point out the ingress into and egress from the tied-array and station beams, respectively.

In the text

Fig. 6 Dynamic spectrum of tied-array beam 18, displaying broad-band radio emission of three Starlink satellites (NORAD IDs 51993, 51988 and 51986) coincident with the predictions from satellite tv for pc ephemerides. For NORAD ID 51993, the emission is seen from 115 to 130 MHz, whereas objects 51988 and 51986 are extra apparent from 140 to 175 MHz. The dynamic spectrum has been averaged by an element 4 in time to a time decision of 41 ms, and an element 16 in frequency to a frequency decision of 0.195 MHz. To indicate the temporal and spectral construction of the satellite tv for pc emission, in addition to that of different anthropogenic alerts, the uncooked, uncalibrated dynamic spectrum is proven, with out masking of anthropogenic alerts. The bars on the prime of the dynamic spectrum point out the anticipated time ranges the place the indicated satellite tv for pc handed via the LOFAR station beam (in gray), and the particular tied-array beam (in pink). Within the case of object 51988, the emission is about 0.33 s delayed in comparison with the prediction. The histogram on the best exhibits the fraction of the dynamic spectra that might have been masked in frequency by OAflagger (Offringa et al. 2012).

In the text

Fig. 7 Spectral and temporal properties of the passes of satellites 45186 (common of 11 TABs) and 51998 (common of 10 TABs). For every satellite tv for pc cross, normalised, aligned and averaged dynamic spectra are proven over the complete noticed bandwidth and inside 2.5 s on the anticipated passage time. Time sequence at narrow-band frequencies of 125, 135, 143.05, 150, and 175 MHz are proven within the prime insets, in addition to for broad-band frequency ranges (116 to 124, 150.05 to 153, and 157-165 MHz). The color of every time sequence matches the marked frequencies and frequency ranges in the identical colors to the perimeters of the dynamic spectra. For each satellites a mix of broad-band and narrow-band emission is seen. Within the case of satellite tv for pc 45186, broad-band emission is generally confined to the frequencies under 155 MHz, however narrow-band emission at 125, 135, 150, and 175 MHz is detected, with sidelobes being seen at 175 MHz. Some construction within the broad-band emission is apparent between 120 and 122 MHz. For satellite tv for pc 51998, broad-band emission is obvious in any respect frequencies not affected by terrestrial alerts, whereas narrow-band emission is absent, aside from 143.05 MHz. Between 170 and 176 MHz, a comb of narrow-band, usually spaced peaks, is superposed on the broad-band emission. The temporal profiles present time offsets of the noticed satellite tv for pc cross with respect to predictions (+0.09 s for 45186, −0.07 s for 51998).

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Fig. 8 Visualisation of the detected sign from satellite tv for pc 47373 because it crossed the sector of view of the LOFAR tied array beam sample. Every circle marks one of many beams. The inlays present the 175 MHz sign (spectral PFD) as a perform of time spanning about ~20 s centred across the occasion time (roughly 35 s after commentary begin). The grey-shaded areas mark the whole time interval over which the satellite tv for pc was within the discipline of view, the pink shaded areas consult with the time when the satellite tv for pc was within the corresponding beam space.

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Fig. 11 Measured spectral energy flux densities for satellites 47373 and 45705 as a perform of angular separation from beam centres. Completely different colors and symbols mark totally different beams. The black strong line represents a least-squares match (Gaussian perform) to the info factors. This enables to estimate the precise spectral PFD of the satellite tv for pc, which is about 460 Jy (47373) and 25 Jy (45705), respectively, averaged over one spectral channel of 12.2 kHz at 175 MHz.

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Fig. 12 Radio emission detected from Starlink satellites in the course of the LOFAR commentary. Passes of Starlink satellites via the LOFAR beam sample are marked in time with strong vertical strains for satellites at h = 550 km, and dotted strains for these at h = 350 km. The colored horizontal strains and bands point out the frequencies of frequency ranges during which fluxes had been measured, with the circles indicating the corresponding flux density measurements.

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	Fig. 14 Path propagation losses of the satellite tv for pc reflection state of affairs vs. the direct terrestrial (trans-horizon) path loss. The pink line signifies the gap (~ 620 km of the GRAVES radar from the LOFAR observer.
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