Space telescope orbit and attitude simulation
The key objective of this study is the prediction of the number of satellite trails in future and present space telescopes in different configurations, represented by the Hubble Space Telescope (540 km), the terminator-aligned sun-synchronous orbit SPHEREx space telescope (700 km), Xuntian Space Telescope (450 km) and the proposed ESA mission ARRAKIHS (approximately 800 km). The main properties of the four telescopes are summarized in Extended Data Table 2. Xuntian and ARRAKIHS are missions still in development, and their configurations might change before launch. In particular, ARRAKIHS proposed orbit ranges from 650 km to 800 km (ref. 22). Because satellite contamination becomes less frequent at higher orbits, we chose a best-case scenario with an 800-km orbit.
The satellite trail simulation process is schematized in Extended Data Fig. 1. For each observatory, we assumed a survey plan that consisted of a series of pointings (right ascension and declination) taking place at an associated epoch (epoch at exposure start (t start ) and exposure end (t end ) with a certain exposure time (t exp = t end − t start )). The available regions on the sky depend on the telescope orbit (as defined by the two-line element) and epoch (that is, a telescope cannot observe a region blocked by Earth), as well as specific survey constraints (Sun avoidance, Earth limb and maximum zenith angles) for each telescope, as summarized below. For Hubble simulations, we randomly selected archival exposures (right ascension, declination, t start and t exp ) obtained with the wide-field channel of the Advanced Camera for Surveys during 2023–2024, assuming the closest orbit on time from its recorded history. The typical exposure time was \({t}_{\exp }={540}_{-200}^{+530}\,{\rm{s}}\).
To simulate the survey plan, orbital position and attitude of the SPHEREx, Xuntian and ARRAKIHS space telescopes, we chose random locations in the sky that were accessible with the adopted constraints of each telescope. For SPHEREx, we assumed a maximum zenital angle of 35°, a solar avoidance angle of 91° throughout the exposure and an exposure time of 112.5 s on h = 650 km terminator-aligned Sun-synchronous orbit37. Similarly, we chose h = 800 km terminator-aligned Sun-synchronous orbit for ARRAKIHS, with a fixed exposure time of 600 s (ref. 22) and 7.6° Earth-limb angle (as in Hubble). Finally, Xuntian was assigned the same orbit as the Tiangong Space Station (LEO; h = 450 km; inclination i = 41.47°), a 55° solar avoidance angle, 7.6° Earth-limb angle during the whole exposure and a random exposure time following the same distribution as the Hubble observational record, on the basis of their similar available time-per-orbit, altitude, aperture and spatial resolution.
Satellite constellation orbit
The orbital parameters for the satellite constellations were generated using the Planet4589 public database38, which provides data on the orbital altitude, number of shells, number of orbital planes and satellites per plane for each FCC/ITU-registered satellite constellation. In addition to the simulated satellite constellations on the basis of the orbits described in Extended Data Tables 1 and 3, we included a baseline of 8,544 existing large satellites, including all artificial satellites already orbiting Earth, excluding (1) those classified as part of constellations to avoid duplication; (2) CubeSats; (3) debris; or (4) objects known to be too small to be observed, such as Westford Needles. To analyse the effect of an increasing population of artificial satellite constellations, we randomly selected a varying number of satellites, starting from a baseline population of approximately 100 up to one million satellites. The simulated satellites were randomly selected from the pool described for each simulation, ensuring that we sampled the potential variability across scenarios.
On the basis of the orbital parameters and telescope survey plans, the Cartesian geocentric position \(({\overline{x}}_{t}=(x,{y},{z},{t}))\) of the telescope (observer) during the exposure was calculated (Extended Data Fig. 7). In parallel, the coordinates of the satellite constellation were estimated \(({\overline{x}}_{{\rm{s}}})\). The apparent locations on the sky (right ascension and declination) of Earth, Sun, Moon and the artificial satellite constellation were computed within the local reference frame of the telescope. The locations and extensions of Earth and the Moon were determined using their predicted ephemeris and physical properties, whereas the apparent locations of the artificial satellites were simulated as a function of time by propagating their orbits. Thanks to the described approach, we can determine which satellites are visible (not behind Earth); illuminated by the Sun, Moon or Earth; and/or inside the FOV of each telescope. The code is on the basis of Python/Skyfield39. The final product is a database (satellite trails) of the location of each satellite that crosses the FOV, including its brightness, apparent angular velocity, illumination and phase angles (for the Sun, Moon or Earthshine), distance to the observer and location in the sky as a function of time.
Satellite trail brightness
The surface brightness of satellite trails depends on several factors, including the (1) brightness of the light source; (2) bidirectional reflectance distribution function40 of the satellite and its distance to the observer; and (3) orientation of the reflecting surfaces to the light source41. For order-of-magnitude estimations, we implemented some simplifying assumptions.
A satellite located at a distance d sat (in metres) from a space telescope with a mirror diameter D mir crossing the FOV leaves a trail with a width θ sat (in steradians)27,42:
... continue reading