SPHEREx confirms predictions for artificial satellite trail pollution in Low Earth Orbit

SPHEREx confirms predictions for artificial satellite trail pollution in Low Earth Orbit Author: Alejandro S. Borlaff - NASA Ames Research Center Space Science and Astrobiology Division. April 2026. In this article we measure the number of artificial satellite trails appearing in a series of astronomical images obtained by the NASA SPHEREx space telescope, a near-infrared low Earth orbit observatory dedicated to the creation of an all-sky survey of 450 million galaxies. The following notebook produces the main plots generated in the article, which compare the satellite trail simulations based on Borlaff, Marcum and Howell (2025, Nature) with the observations of satellite trails from this article. For publication in the Astronomical Journal. Data and code available on Zenodo. https://doi.org/10.5281/zenodo.17957748 Dependencies:Python==3.10rosalia-wfi: https://pypi.org/project/rosalia-wfi/bootmedian: https://pypi.org/project/Bootmedian/ipykernel: conda install -n empty ipykernel --update-deps --force-reinstallpandas: https://pandas.pydata.org/numpy: https://numpy.org/astropy: https://www.astropy.org/ Description: SPHEREx_trails_database.csv--------------------------------------------------------This table contains a series of identified satellite trails in real SPHEREx images, obtained between May 2025 and September 2025. The properties listed contain: ra: Average right ascension of the identified trail (degrees)dec: Average declination of the identified trail (degrees)pa: Position angle of the trail in equatorial coordinates (degrees, PA = 0 is North, + counter-clockwise).OBSID: SPHEREx Observation IDMJDOBS: Modified Julian Date of the observation.XPOSURE: [s] Exposure (integration) time SGT_LAT_MIDPT: / [deg] Ground track latitude at midpoint SGT_LON_MIDPT: / [deg] Ground track longitude at midpoint SGT_MIN_GCD2SAA: / [deg] Closest ground track dist to SAA SPS_ELON: [deg] Ecliptic longitude of planned telescope boresight SPS_ELAT: [deg] Ecliptic latitude of planned telescope boresight SPS_EPA: [deg] PA of FP y axis at planned boresight, E of ecl N SPHEREx_ / HST_per_trail_database.csv--------------------------------------------------------This table contains the properties of the simulated satellite trails in SPHEREx and HST images: track_id: ID of the simulationtelescope: Simulated telescope mirror_radius: Radius of the telescope (m) pixscale: Pixel scale of the detector (arcsec/pixel)nsats: Number of satellites in the simulation. ra_obs: Right ascension of the observation (degrees). dec_obs: Declination of the observation (degrees).ra_earth: Average right ascension of the Earth from the observatory (degrees). dec_earth: Average declination of the Earth from the observatory (degrees). ra_sun: Average right ascension of the Sun from the observatory (degrees). dec_sun: Average declination of the Sun from the observatory (degrees).ra_moon: Average right ascension of the Moon from the observatory (degrees). dec_moon: Average declination of the Moon from the observatory (degrees).altitude_telescope: Altitude of the telescope over the surface of the Earth (km). angular_radius_earth: Apparent angular radius on the Earth from the telescope (degrees).sep_obs_earth: Angular separation between the pointing and the Earth (degrees). limb_angle: Angular distance between the limb of the Earth and the pointing (degrees).expstart: Modified Julian Date of the start of the exposure. expend: Modified Julian Date of the end of the exposure. phase_sat_sun: Apparent solar illumination phase of the satellite from the telescope. phase_sat_moon: Apparent lunar illumination phase of the satellite from the telescope. phase_sat_earth: Apparent Earthshine illumination phase of the satellite from the telescope. exptime: Exposure time (s)exposure_name: Name of the exposure. trail_epoch: Epoch of the satellite trail. trail_time: Approximate time between satellite trail start and end (s). sunlit_in_FOV: Is the satellite illuminated by the Sun? (bool).moonlit_in_FOV: Is the satellite illuminated by the Moon? (bool).dsat: Distance from the telescope to the satellite (m).omega_sat: Angular velocity of the satellite in the field of view (arcsec/s). altitude_satellites: Altitude of the satellite (m).pa_trail: Position angle of the satellite trail (degrees, positive East of North)earthshine_sun_ratio: Ratio of the reflected Earthshine to the Solar radiation. moon_phase: Solar phase of the Moon at the exposure epoch. mu: Estimate surface brightness of the satellite trail (AB mag/arcsec2). bool_detected: Is the satellite detectable? (bool) SPHEREx_ / HST_per_sim_db.csv--------------------------------------------------------This table contains the properties per simulation of the trails in SPHEREx and HST images: trail_list: Name of the simulation file. crossing_trails: Number of detectable satellite trails in the simulated exposure. exptime: Exposure time (s). nsats_per_sim: Population of satellites in the simulation. limb_angle_per_exp: Earth limb angle of the exposure (degrees)ntrails: Total number of satellites in the image (detectable and undetectable). ntrails_sunlit: Number of satellites illuminated by the Sun in the image. ntrails_moonlit: Number of satellites illuminated by the Moon in the image. spherex_per_bin_db.csv / hst_per_bin_db.csv-------------------------------------------------------- This table contain the average number of satellite trails detected by SPHEREx and HST as a function of the total population of satellites in orbit. Columns: Number of satellites in orbit. Rows: 1 - Mean number of satellite trails per exposure.2/3 - 1 sigma confidence intervals for 1. 4/5 - 2 sigma confidence intervals for 1. 6/7 - 3 sigma confidence intervals for 1. kruk_borlaff_26_db.csv--------------------------------------------------------This table contains the number of satellite trails [col: "hst_san_ntrails"] as a function of the number of satellites in orbit [col: "nsats"]. The estimation is based on the Equation 1 from The impact of satellite trails on Hubble Space Telescope observations (Krul+23) [https://www.nature.com/articles/s41550-023-01903-3] applied to the satellite layer population described in Planet4589 [https://planet4589.org/space/con/conlist.html].SPHEREx验证近地轨道中人工卫星轨迹污染的相关预测 作者：亚历杭德罗·S·博尔拉夫（Alejandro S. Borlaff）——美国国家航空航天局（NASA）艾姆斯研究中心，空间科学与天体生物学分部，2026年4月。 本文针对NASA SPHEREx空间望远镜所获取的一系列天文图像中的人工卫星轨迹数量展开测量。SPHEREx是一台近红外近地轨道天文台，旨在完成包含4.5亿个星系的全天空巡天项目。 本配套Jupyter笔记本可复现本文中生成的核心绘图，用于对比基于Borlaff、Marcum与Howell（2025年，《自然》）的卫星轨迹模拟结果与本文的卫星轨迹观测数据。 本文拟发表于《天文学期刊》（Astronomical Journal）。 数据集与代码已上传至Zenodo平台，DOI：10.5281/zenodo.17957748。 #### 依赖项 Python==3.10 rosalia-wfi：https://pypi.org/project/rosalia-wfi/ bootmedian：https://pypi.org/project/Bootmedian/ ipykernel：可通过`conda install -n empty ipykernel --update-deps --force-reinstall`命令安装 pandas：https://pandas.pydata.org/ numpy：https://numpy.org/ astropy：https://www.astropy.org/ --- ### SPHEREx_trails_database.csv 该表格收录了2025年5月至2025年9月间获取的真实SPHEREx图像中已识别的多个人工卫星轨迹。表格包含以下属性字段： - `ra`：已识别轨迹的平均赤经（单位：度） - `dec`：已识别轨迹的平均赤纬（单位：度） - `pa`：赤道坐标系下轨迹的位置角（单位：度，位置角PA=0指向北，正值为逆时针方向） - `OBSID`：SPHEREx观测编号 - `MJDOBS`：观测的修正儒略日期 - `XPOSURE`：[秒] 曝光（积分）时长 - `SGT_LAT_MIDPT`：[度] 轨道星下点中点处的纬度 - `SGT_LON_MIDPT`：[度] 轨道星下点中点处的经度 - `SGT_MIN_GCD2SAA`：[度] 星下点到南大西洋异常区（South Atlantic Anomaly, SAA）的最短地面距离 - `SPS_ELON`：[度] 望远镜预定视轴的黄道经度 - `SPS_ELAT`：[度] 望远镜预定视轴的黄道纬度 - `SPS_EPA`：[度] 预定视轴处焦平面（Focal Plane, FP）y轴的位置角，以黄道北东侧为基准 --- ### SPHEREx与哈勃空间望远镜（Hubble Space Telescope, HST）单轨迹数据库（SPHEREx_ / HST_per_trail_database.csv） 该表格收录了SPHEREx与HST图像中模拟人工卫星轨迹的各项属性： - `track_id`：模拟任务编号 - `telescope`：模拟使用的望远镜 - `mirror_radius`：望远镜主镜半径（单位：米） - `pixscale`：探测器像素比例尺（单位：角秒/像素） - `nsats`：模拟任务中的卫星总数 - `ra_obs`：观测指向的赤经（单位：度） - `dec_obs`：观测指向的赤纬（单位：度） - `ra_earth`：观测站视角下地球的平均赤经（单位：度） - `dec_earth`：观测站视角下地球的平均赤纬（单位：度） - `ra_sun`：观测站视角下太阳的平均赤经（单位：度） - `dec_sun`：观测站视角下太阳的平均赤纬（单位：度） - `ra_moon`：观测站视角下月球的平均赤经（单位：度） - `dec_moon`：观测站视角下月球的平均赤纬（单位：度） - `altitude_telescope`：望远镜相对于地球表面的轨道高度（单位：千米） - `angular_radius_earth`：望远镜视角下地球的视在角半径（单位：度） - `sep_obs_earth`：观测指向与地球的角距离（单位：度） - `limb_angle`：观测指向与地球边缘的角距离（单位：度） - `expstart`：曝光开始时刻的修正儒略日期 - `expend`：曝光结束时刻的修正儒略日期 - `phase_sat_sun`：望远镜视角下卫星的太阳照射相位角 - `phase_sat_moon`：望远镜视角下卫星的月球照射相位角 - `phase_sat_earth`：望远镜视角下卫星的地球反照照射相位角 - `exptime`：曝光时长（单位：秒） - `exposure_name`：曝光任务名称 - `trail_epoch`：卫星轨迹对应的历元 - `trail_time`：卫星轨迹从起始到结束的近似时长（单位：秒） - `sunlit_in_FOV`：卫星是否处于太阳照射的视场（Field of View, FOV）内？（布尔型） - `moonlit_in_FOV`：卫星是否处于月球照射的视场内？（布尔型） - `dsat`：望远镜与卫星之间的距离（单位：米） - `omega_sat`：卫星在视场内的角速度（单位：角秒/秒） - `altitude_satellites`：卫星轨道高度（单位：米） - `pa_trail`：卫星轨迹的位置角（单位：度，正值指向北偏东方向） - `earthshine_sun_ratio`：卫星轨迹的地球反照辐射与太阳辐射的比值 - `moon_phase`：曝光时刻月球的太阳相位角 - `mu`：卫星轨迹的表面亮度估计值（单位：AB星等/角秒²） - `bool_detected`：卫星是否可被探测到？（布尔型） --- ### SPHEREx与HST单模拟任务数据库（SPHEREx_ / HST_per_sim_db.csv） 该表格收录了SPHEREx与HST图像中单次模拟任务对应的轨迹属性： - `trail_list`：模拟任务文件名称 - `crossing_trails`：模拟曝光中可被探测到的卫星轨迹总数 - `exptime`：曝光时长（单位：秒） - `nsats_per_sim`：模拟任务中的卫星种群规模 - `limb_angle_per_exp`：单次曝光对应的地球边缘角（单位：度） - `ntrails`：图像中卫星总数量（包含可探测与不可探测） - `ntrails_sunlit`：图像中处于太阳照射范围内的卫星数量 - `ntrails_moonlit`：图像中处于月球照射范围内的卫星数量 --- ### spherex_per_bin_db.csv 与 hst_per_bin_db.csv 这两个表格分别收录了SPHEREx与HST探测到的卫星轨迹平均数量随轨道卫星总种群规模变化的关系数据： - 列：轨道卫星总数量 - 行： 1. 单次曝光中探测到的卫星轨迹平均数 2/3. 第1行数据对应的1σ置信区间 4/5. 第1行数据对应的2σ置信区间 6/7. 第1行数据对应的3σ置信区间 --- ### kruk_borlaff_26_db.csv 该表格收录了卫星轨迹数量（列名：`hst_san_ntrails`）随轨道卫星数量（列名：`nsats`）变化的关系数据。该估算基于《卫星轨迹对哈勃空间望远镜观测的影响》（Krul等，2023）中的公式1，将其应用于Planet4589平台描述的卫星层种群模型。相关文献链接：https://www.nature.com/articles/s41550-023-01903-3，卫星层种群数据来源：https://planet4589.org/space/con/conlist.html。