# Visibility Predictions for Near-Future Satellite Megaconstellations:
Latitudes near 50∘ will Experience the Worst Light Pollution

Samantha M. Lawler Campion College and the Department of Physics, University
of Regina  Aaron C. Boley Department of Physics and Astronomy, University of
British Columbia  Hanno Rein Department of Physical and Environmental
Sciences, University of Toronto at Scarborough

###### Abstract

Megaconstellations of thousands to tens of thousands of artificial satellites
(satcons) are rapidly being developed and launched. These satcons will have
negative consequences for observational astronomy research, and are poised to
drastically interfere with naked-eye stargazing worldwide should mitigation
efforts be unsuccessful. Here we provide predictions for the optical
brightnesses and on-sky distributions of several satcons, including Starlink,
OneWeb, Kuiper, and StarNet/GW, for a total of 65,000 satellites on their
filed or predicted orbits. We develop a simple model of satellite
reflectivity, which is calibrated using published Starlink observations. We
use this model to estimate the visible magnitudes and on-sky distributions for
these satellites as seen from different places on Earth, in different seasons,
and different times of night. For latitudes near 50∘ North and South, satcon
satellites make up a few percent of all visible point sources all night long
near the summer solstice, as well as near sunrise and sunset on the equinoxes.
Altering the satellites’ altitudes only changes the specific impacts of the
problem. Without drastic reduction of the reflectivities, or significantly
fewer total satellites in orbit, satcons will greatly change the night sky
worldwide.

††software: This research was made possible by the open-source projects
REBOUND (Rein & Liu, 2012), WHFast (Rein & Tamayo, 2015), Jupyter (Kluyver et
al., 2016), iPython (Pérez & Granger, 2007), and matplotlib (Hunter, 2007;
Droettboom et al., 2016).

##  1 Introduction

The placement of tens of thousands of communications satellites into low-Earth
orbit (LEO) raises multiple concerns for users of the night sky. These
concerns include the impact of satellites on astronomical observations, with
implications for space exploration and fundamental science, as well as impacts
on stargazing for recreation or traditional cultural practices. The sheer
number of proposed satellites, along with their orbits, will alter the sky far
beyond pre-2019 levels. In light of these changes, astronomers are undertaking
multiple national and international policy initiatives regarding protections
for the night sky (e.g., the SATCON1 report111Full report available here:
https://aas.org/sites/default/files/2020-08/SATCON1-Report.pdf, the
International Astronomical Union Dark and Quiet Skies Report222Full report
available here: https://www.iau.org/static/publications/dqskies-
book-29-12-20.pdf, and Boley et al. 2021a). There have also been a number of
efforts to characterize the observed brightness distribution of satellites in
orbit, as well as the brightness distribution of proposed satellite
megaconstellations (satcons).

McDowell (2020) explores the impact of 12,000 Starlink satellites based on one
of Starlink’s earlier proposed orbital distributions. This work shows that
relatively high concentrations of satellites will be in the sky for mid-
latitude locations due to the orbital inclinations of the satellites. Hainaut
& Williams (2020) modelled a wide range of proposed satcons with 26,000
satellites as seen in different wavelengths. They focused on fairly low
latitudes, where many “big-glass” observatories are located. A general finding
is that wide-field surveys will be most strongly affected by satellite light
pollution.

Tyson et al. (2020) focuses on the effects of satcons on the upcoming Vera C.
Rubin Observatory’s Legacy Survey of Space and Time (LSST), finding that if
satellites are brighter than $V\simeq 7$, they will produce cross-talk within
the CCD chips and make observations unreliable across several chips, not just
within a streak of pixels. It is clear from these previous simulations that
satcons have the potential to cause major disruptions to observational
astronomy.

Predicting satellite brightnesses prior to launch is difficult. A complete
model would require extremely detailed information about the shapes and
materials in satellites, and launching companies do not provide this
information publicly, in general. However, as more satellites are launched,
observations are being collected to characterize the brightnesses, and this
information can be used to characterize generalized reflection models to
approximate future satellite brightnesses, or to assess satellite impacts in a
statistical sense. In particular, Horiuchi et al. (2020) and Tregloan-Reed et
al. (2021) characterize Starlink’s initial voluntary mitigation attempt
(“Darksat”), and Mallama (2021a, b) and Boley et al. (2021b) have measured the
brightness of original Starlink satellites and their second-generation
mitigation attempt of “Visorsats”. The SATCON1 report also contains a large
number of recent Starlink observations. All of these observations show that
astronomers are rightly concerned about the future of the night sky: the
satellites currently in orbit are bright. Many are naked-eye visible when
sunlit, and their brightness is currently unregulated.

In this work, we model brightnesses and the on-sky distribution for a possible
future with 65,000 satellites on realistic orbits based on credible filings
from satellite operators. While we do not know the actual fraction of the
proposed satellites that will be launched, the ongoing emergence of new
operators, sometimes backed by states, suggests that models exploring tens of
thousands of satellites are reasonable. We first build a realistic orbital
model to find which satellites will be sunlit and potentially visible from
different places on Earth, at different times of night, and different seasons
(Section 2). We then use an assumed satellite reflection model calibrated to
recent observations of Starlink satellites (Section 3.1) to build all-sky
visibility predictions (Section 3.2), finding that latitudes near 50∘N and S
will be the regions most strongly affected by satellite light pollution. We
briefly explore the effects of satellite altitude (Section 3.3), finding that
there is no “best” satellite altitude; rather, it is a choice between
different impacts. We then discuss in more detail some of the negative effects
this will have on observational astronomy (Section 4). Our satellite modelling
code is publicly available so that others may make predictions for their own
night sky, and modify it to use with future satellite configurations.

##  2 Orbit Model and Sunlit Satellite Distribution

We compiled a list of proposed orbits from filings submitted to the U.S.
Federal Communications Commission for Starlink, OneWeb, and Kuiper. The
information for StarNet/GW is taken from filings at the International
Telecommunications Union (ITU). The FCC and ITU filings contain information on
the orbital inclination and orbit altitudes, but not necessarily on the
details of how satellites are distributed throughout their orbits. To build
our model, we dispersed the satellites so that they would have a smooth
distribution without significant clumping or precisely regular spacing. Two
approaches were undertaken in the development of the simulation tools.

The first, which we call ‘even-spacing’, is as follows: (1) If the filing
contains a set number of planes and satellites per inclination plane, then the
planes’ nodes are evenly distributed from 0 to 360∘ and the satellites in each
plane are evenly distributed in mean anomaly, plus a small random offset to
avoid excessive clumping due to perfectly regular spacing. (2) If the filing
places all satellites onto their own planes or if the plane distribution is
ambiguous, then we evenly space the orbital nodes for each satellite and set
the satellites’ mean anomalies to ensure a relatively smooth and non-clumping
distribution. This is achieved by creating an array of evenly spaced mean
anomalies between 0 and $2\pi$ for all satellites ($N_{\rm Sat}$) in a given
orbital shell and then assigning each satellite the array value that is
$\sqrt{N_{\rm Sat}}$ away from the previous satellite’s value. This is used
for Figure 1.

However, due to the large number of satellites being considered, a second
approach is also employed for the webapp (see Section 3.2) and related
figures. Namely, a quasi-random distribution is used by evenly spacing the
orbital nodes of all the planes or, if specific planes are not given, the
nodes of all satellites in a shell, and then selecting a satellite mean
anomaly from a uniform random distribution on the interval $[0,2\pi)$. We
refer to the this method as the ‘quasi-random’ initialization. Randomizing the
satellites in mean anomaly is not an unrealistic approximation. Starlink in
particular has already announced their intentions to use autonomous collision
avoidance by its satellites. In general we expect the distributions to be
continuously changing, and fortunately, the overall results are independent of
the exact initialization procedure used. Most figures here use this quasi-
random distribution.

The altitudes and inclinations of the four different satcons used here are
given in Table 1. For simplicity, we list the total number of satellites at a
given inclination rather than the breakdown per plane. Additional details are
in the publicly available code (Section 3.2).

Table 1: Megaconstellation orbital parameters

operator | $N_{\rm Sat}$ | inclination [∘] | Altitude [km]
---|---|---|---
StarlinkaaAssumes Starlink Gen1 (FCC, 2016, 2017, 2020a) and Gen2 (FCC, 2020b) operate together. | 7178 | 30 | 328
(USA) | 7178 | 40 | 334
| 7178 | 53 | 345
| 2000 | 96.9 | 360
| 1998 | 75 | 373
| 4000 | 53 | 499
| 144 | 148 | 604
| 324 | 115.7 | 614
| 2547 | 53 | 346
| 2478 | 48 | 341
| 2493 | 42 | 336
| 1600 | 53 | 550
| 1584 | 53.2 | 540
| 720 | 70 | 570
| 348 | 97.6 | 560
| 172 | 97.6 | 560
OneWebbbIncludes Phases 1 and 2 (FCC, 2021). | 720 | 87.9 | 1200
(UK) | 1764 | 87.9 | 1200
| 2304 | 40 | 1200
| 2304 | 55 | 1200
StarNet/GWccBased on consolidation of ITU filings (Press, 2021). | 480 | 85 | 590
(China) | 2000 | 50 | 600
| 3600 | 55 | 508
| 1728 | 30 | 1145
| 1728 | 40 | 1145
| 1728 | 50 | 1145
| 1728 | 60 | 1145
KuiperddBased on FCC (2019). | 1156 | 51.9 | 630
(USA) | 1296 | 42 | 610
| 784 | 33 | 509

Note. — Orbits and numbers for Starlink, OneWeb, and Kuiper are listed as
filed and amended with the FCC. StarNet/GW is based on ITU filings.

Figure 1 shows a snapshot of the positions of these 65,000 satellites over the
world, and over a small region of the globe (centred on North America), to
give a more intuitive sense of what the distribution of this extremely large
number of satellites looks like.

Several conspicuous features form, including regions where the satellites have
higher densities. These are the orbital caustics, caused by the satellites
following their inclined orbits and passing through the turnaround points in
latitude. Multiple caustics are visible in Figure 1, for example over southern
Canada, the middle latitudes of the United States, and northern Mexico. The
locations of these caustics, resulting from a satellite operator’s choice in
the inclination distribution, has an important consequence for the number of
satellites in the sky at different latitudes.

Figure 1: A snapshot of the positions of satellites in our model, over the
entire globe (left) using a Mercator projection and the slice over North
America (right) using a Lambert conformal map projection. Note that there are
obvious bands of higher on-sky density where large numbers of satellites have
the same inclination and, as seen in latitude, librate at those parallels. The
satellites here use the even-spacing initialization.

###  2.1 Sunlit satellite distribution

Now that we have a distribution of satellites in space, we need to determine
the number of those satellites that are sunlit for a given observer at a given
Solar hour and time of year. To proceed, we use an initial coordinate system
that places Earth’s equator in the X-Y plane and the spin direction aligned in
the Z direction. The satellites’ Cartesian positions are then determined in
this coordinate system from their orbital elements.

The observer’s Cartesian coordinates on the Earth’s surface are determined
next, based on the desired latitude and solar hour of interest. We set
midnight for an observer to be when they are on the +X axis.

With the position of the observer now set relative to the satellites, we
rotate all satellites and the observer about the $Y$ axis by an angle
consistent with the Sun’s declination for the desired time of year, creating a
new coordinate system $\rm X^{\prime},~{}Y=Y^{\prime},~{}Z^{\prime}$. The Sun
is on the $\rm-X^{\prime}$ axis. To simplify the calculations, we take a
satellite to be sunlit if its $\rm Y^{\prime}-Z^{\prime}$ projection is
greater than the radius of the Earth or if it is in the domain $\rm
X^{\prime}<0$. In other words, we do not include atmospheric refraction (if it
was included, it would cause a slightly larger number of satellites to be
partially sunlit on the edge of Earth’s shadow).

Figure 2: The instantaneous number of sunlit satellites above the horizon at
different latitudes and different times of night: left panels are heatmaps
with daylight (sunrise to sunset) indicated by the grey shaded region; right
panels show curves for four different latitudes (shown by lines in the left
planels). The four latitudes highlighted are for the approximate latitude of
several observatories in Canada (black solid line), the latitude of
observatories on the Canary Islands (blue dashed line), the latitude of
observatories on Maunakea in Hawaii (green dash-dotted line), and the
approximate latitude of several observatories in Chile (purple dotted line).

Figure 3: The instantaneous number of sunlit satellites more than 30∘ above
the horizon at different latitudes and different times of night: left panels
are heatmaps; right panels show curves for four different latitudes (shown by
lines in the left plots). Same symbols as Figure 2.

Finally, we determine whether a given sunlit satellite is visible to the
observer in question, and if so, make cuts based on the satellite’s elevation
for that observer. We proceed as follows: Let the vector to the observer be
denoted ${\bf r}_{\rm obs}$ and the vector to a given satellite be ${\bf
r}_{\rm sat}$, each with an origin at the geocentre. The vector from the
observer to the satellite is thus ${\bf s}={\bf r}_{\rm sat}-{\bf r}_{\rm
obs}$. The resulting zenith angle of the satellite for the observer is
$\cos\theta_{z}={\bf s}\cdot{\bf r}_{\rm sat}/\left(\big{|}s\big{|}\big{|}{\bf
r}_{\rm sat}\big{|}\right)$.

Figure 2 shows the on-sky density of sunlit satellites at different latitudes,
different times of night, and different times of year. Many of the hundreds or
even thousands of sunlit satellites in Figure 2 are close to the horizon, at
higher airmasses than would be used for research observing. But there are
still hundreds of sunlit satellites more than 30∘ above the horizon (Figure
3), where they could interfere with research astronomy.

In the right panels of Figures 2 and 3, we highlight the number of sunlit
satellites over the course of a night from four different observatory
latitudes: observatories in Canada, which are all situated close to 50∘ N,
observatories on the Canary Islands at 28∘ N, observatories in Hawaii at 20∘
N, and observatories in Chile which are all close to 30∘ S.

The first feature that is immediately obvious is that latitudes near 40∘ N and
S have the most sunlit satellites, consistent with that found by, e.g.,
McDowell (2020). This is not surprising given the distribution of satellites
in Figure 1. But due to Earth’s shadow, there is a period of few-to-no sunlit
satellites for $\sim$5-6 hours around midnight during the winter at these
latitudes. However, during summer, there are more than a thousand sunlit
satellites above the horizon all night long (see 50∘N curves and yellow-filled
contours in Figure 2, which represents $\sim$3000 sunlit satellites). Closer
to the equator, where many research observatories are located, the seasonal
variation is not so extreme, and there is a period of about 3 hours in the
winter and near the equinoxes with few-to-no sunlit satellites. But there are
still hundreds of sunlit satellites all night at these latitudes in each
hemisphere’s summer.

The distribution of sunlit satellites more than 30∘ above the horizon is
similar (Figure 3). Mid-latitudes have a $\sim$5-6 hour period of no
satellites centred around midnight in their winter and equinoxes. But in the
summer, even from these mid-latitudes, there are dozens of sunlit satellites
$>$30∘ above the horizon. This is more extreme at latitudes near 50∘: there is
no drop in the number of sunlit satellites $>$30∘ above the horizon, even at
midnight, at 50∘N or S latitude in their respective summers.

##  3 Satellite Visibilities

Just because a satellite is sunlit does not necessarily mean that it will be
visible by eye or even in a telescope. However, many of the satellites that
are currently being launched did not account for light pollution during the
design phases, resulting in satellites that are quite bright at operational
altitude. While satellite reflectivity is now being considered by some
operators, brightness reduction efforts thus far have been limited to
retrofits of existing designs. Moreover, there are no regulations concerning
how bright a satellite can be – astronomers are currently dependent on good-
faith cooperation with the satellite operators, with the actual brightness and
variability of satellites ultimately not known until they are deployed and
observed.

###  3.1 Satellite Reflection Models

A satellite’s brightness depends on its non-trivial bidirectional reflectance
distribution function (BRDF), which takes into account the detailed shape of
the satellite and its materials. The brightness at any given moment may depend
sensitively on the satellite’s exact orientation in space with respect to the
incoming light and the observer. Satellites are known to vary in brightness as
they move across the sky, continuously changing their orientation with respect
to the observer. This evolving perspective can lead to sudden, and in the case
of flares, dramatic changes in brightness. This brightness variability can be
observed, in principle, even for a single satellite traversing the field of
view of a telescope.

Satellite variability and flares have long been observed by astronomers, both
by purposefully observing satellites and by the accidental passage of
satellites through research images (e.g., Hainaut & Williams, 2020; Mallama,
2021a); naked-eye observations by many stargazers around the world also note
this behaviour.333This includes the authors of this paper.

In practice, the detailed BRDF is typically unknown and simplifying
assumptions must be employed. Such assumptions will not capture sudden
satellite variability, but can still be useful enough to simulate the overall
trends and distributions of satellite brightness.

We use a diffuse Lambertian sphere reflection model (e.g., Pradhan et al.,
2019) to estimate the distribution of visible magnitudes of these sunlit
satellites:

$m_{v}=m_{\rm
Sun}-2.5\log\left(\frac{2}{3\pi^{2}}A\rho[(\pi-\phi)\cos\phi+\sin\phi]\right)+5\log
R$ (1)

where $m_{\rm Sun}$ is the apparent magnitude of the Sun (-26.77 in $V$-band,
-26.47 in $g^{\prime}$-band for AB magnitudes; Willmer, 2018), $A$ is the
cross-sectional area of the satellite, $\rho$ is the Bond albedo, $\phi$ is
the Solar phase angle between the observer and the satellite, and $R$ is the
distance between the observer and the satellite. We do not know the reflecting
area or albedo of future satellites, and cross-sectional area will vary
depending on viewing phase and satellite attitude. To further simplify our
reflectance model, $\rho$ and $A$ are combined into one albedo-area variable,
the effective area $\zeta=\rho A$.

To calibrate our model, we compared our model satellite brightness
distribution with the observed distribution of Starlink satellites magnitudes
from Boley et al. (2021b), which used the Plaskett Telescope at the Dominion
Astrophysical Observatory in Victoria, BC (latitude 48.5 ∘N) to observe a set
of Starlink satellites. While OneWeb satellites have so far proved fainter
than Starlinks, they have approximately the same absolute magnitude (Mallama,
2021a). Since Kuiper and Starnet/GW do not yet have any satellites in orbit, a
set of Starlink observations is a reasonable starting point for our model
calibration. We set up the model using the same general observing directional
biases, matching the season, time of night of the observing run, and the
latitude, and we only used Starlink satellite orbits near 550 km altitude,
since that is the most prominent orbital shell occupied as of the time of
observations (see Table 1). Such Starlink satellites have orbital inclinations
of about $53^{\circ}$, meaning their orbits can pass through the sky at low
zenith angles at the latitude of the Plaskett Telescope.

As discussed in Boley et al. (2021b), we first attempted to use only the
Visorsat Starlinks in our calibration, in hopes that these brightness
mitigations would be used on all future satellites. But upon further
investigation, we found that although all Starlinks since the 7 August 2020
launch are reportedly equipped with visors444see, e.g.,
https://directory.eoportal.org/web/eoportal/satellite-missions/s/starlink,
there is no available information on how many of those satellites actually
have the visors successfully deployed. The variation in brightness observed in
Boley et al. (2021b) leads us to speculate that there may be inconsistencies
among the visors, or that their effectiveness is very sensitive to the precise
orientation between the satellite, Sun, and observer. We note that the latter
case is hinted at by observations in Mallama (2021b).

Figure 4: Histograms of $g^{\prime}$ magnitudes for observations of Starlink
satellites (blue hatched) compared with our satellite model output (grey). The
observations (Boley et al., 2021b) were obtained in July 2021 from the
Plaskett 1.8 m telescope at the Dominion Astrophysical Observatory (latitude
48.5∘N). The satellites were observed between $\pm 1.5$ hr of midnight. The
Sun’s declination at the time of the observations was about 21∘. Only Starlink
satellites near the 550 km orbital shell were targeted. This figure
demonstrates that using an effective surface area of $\zeta$ = 0.8 m2 is a
reasonable choice for our model, with the important caveat that this is
applicable to a mixture of Starlink satellites: future satellites may have a
very different actual brightness distribution depending on the size, shape,
and materials used.

With the above in mind, we fit our model to the entire distribution of
observed Starlink satellites, both listed Visorsats and original-design
Starlinks, which is shown in Figure 4. This may be a more realistic
distribution of satellite brightnesses, since it includes both satellites with
mitigation (Visorsats) and those without (original Starlinks). ]We also note
that initial observations of Visorsats and original Starlinks by amateur
astronomers (e.g., McDowell, 2020) showed a wide range of brightnesses for
both satellite types. Without regulatory obligations to make their satellites
fainter, or widely adopted and followed industry standards, there will likely
be a large range of reflectivities in future satellites.

The modelled albedo-area variable was changed until the resulting model
distribution of Starlink satellites matched the observed distribution from
Boley et al. (2021b), under similar observing directional and time biases
(Figure 4). We also added a small scatter in brightness (Gaussian noise with
$\sigma=0.5$ magnitudes) to simulate the scatter observed in Boley et al.
(2021b). This best fit corresponds to a satellite effective area $\zeta\approx
0.8~{}\rm m^{2}$, which could realistically be matched by a reflecting
satellite area of 4 m2 with an albedo of 0.2, as an example.

The Plaskett measurements compare favourably with measurements from Mallama
(2021a), but taken from 48.5∘N rather than 39∘-44∘N, where satellites will
remain bright throughout the night for the time of year of the observations
(Section 3.2). The median observed $g^{\prime}$-magnitude in the Boley et al.
(2021b) sample, which includes Starlink satellites with and without visors, is
$g^{\prime}=5.7$, compared with a median of 5.9 measured by Mallama (2021a),
which used an observing filter within 0.1 mags of $V$-band. For the Sun,
$g^{\prime}-V=0.3$, so $V\approx 5.9$ corresponds to $g^{\prime}\approx 6.2$.
However, the observational biases between the samples are expected to be
different. The results presented by a follow-up study (Mallama, 2021b) find a
median $V$ of about 6.8 for Visorsats, after they have been adjusted to a
range of 1000 km. Correcting this to 550 km, yields a 550 km “absolute”
$V$-magnitude of $H_{V}\approx 5.5$ or $H_{g’}\approx 5.8$. This compares
favourably to the Visorsat-only subsample from Boley et al. (2021b) which
measured $H_{g’}=5.7$ (coincidentally the same value as the apparent
magnitudes of their full sample).

We reiterate that there are many reflection effects that we are ignoring in
our satellite brightness model, and that the brightness distribution is
sensitively dependent on effective cross-sectional area and exact observing
geometry. But based on comparison between this model and published
observations of one satcon (Starlink), we find that the overall scale of the
satellite brightness is well-represented.

###  3.2 Visible magnitude predictions

We now apply this model calibration to the satellite distributions to
calculate their apparent magnitudes as seen in the sky at different latitudes,
different times of year, and different times of night, with the caveats
discussed above. We also include realistic atmospheric extinction in this
model (Kasten & Young, 1989), which is significant for the lowest elevation
satellites. We calculate the visual magnitudes for all sunlit satellites in
each field of view, but we pay particular attention to three magnitude cuts:
those with $g<5$, which are visible from a typical suburban environment; those
with $g<6.5$, which are naked-eye visible from a truly dark sky; and those
with $g<7$, which are bright enough to cause serious data loss for LSST (Tyson
et al., 2020) and other research facilities.

The source code needed to reproduce all of these brightness simulation figures
is available at https://github.com/hannorein/megaconstellations/. Furthermore,
we provide an easy-to use web interface to make predictions at custom
observatory locations, times of night, and different seasons at
http://megaconstellations.hanno-rein.de.

Figure 5: All-sky snapshots of the predicted satellite distribution and
brightnesses as viewed from Hawaii (latitude 20∘ N, will be the same
distribution at 20∘S, but flipped N-S on the sky). Colour shows $g$-band
magnitude. Moving left to right across the grid: Winter solstice, equinox,
summer solstice. Top to bottom across the grid: Nautical dusk, midnight,
nautical dawn. For each snapshot, Ntot is the total number of sunlit
satellites in the sky from this location at this time of day and year, and
Nvis is the number of satellites that are naked-eye visible (approximately
$g<6.5$) from this location at this time of day and year. Note that these
numbers are not exact and are expected to vary by $\sqrt{N}$ due to
randomization of satellite distribution within their orbital shells. The
satellite distribution is faint and close to the horizon or not illuminated at
all for most of the night, except for near dusk and dawn, when the brightest
satellites will be close to the zenith, with hundreds being naked-eye visible.

Figure 6: Same plots as Figure 5, but viewed from a latitude of 50∘ N (e.g.,
many Canadian observatories). In the summertime, the number of sunlit and
visible satellites (hundreds) only drops by a small fraction over the course
of the night.

Figure 7: Same plots as Figure 5, but viewed from the Equator (latitude 0∘).
There are no sunlit satellites at midnight in any season.

Figure 8: Similar to Figure 5, but viewed from the North Pole (latitude 90∘N).
Because of extreme seasonal illumination, satellites would not actually be
visible close to the summer solstice due to 24-hour daylight, or close to the
equinox because of 24-hour near-daylight, but the dozens of satellites
brighter than $g<6.5$ will be visible 24 hours per day during the winter. For
comparison, we show midnight on the Winter Solstice (24 hours of full
darkness), at a Solar declination of -18∘ (24 hours of astronomical twilight),
and at a Solar declination of -12∘ (24 hours of nautical twilight). Note that
from the North Pole, all directions are south.

Figures 5-8 show the calculated all-sky satellite distributions and
brightnesses for a selection of seasons and times of night for different
latitudes on Earth. These are also available in the form of time-lapse movies
at http://uregina.ca/~slb861/satcon.html. The results are further summarized
in Table 2, where the number of satellites above each magnitude cut is
compared to the number of visible stars in the observer’s sky. At latitudes
near 50∘N and S, where the light pollution is the worst, up to 8% of all point
sources in the sky are satellites at certain times of night. Because the
satellite orbits are symmetric about Earth’s equator, the simulations can be
applied to either hemisphere for the corresponding season. For example, the
all-sky view for Hawaii (20∘ N) on the June Solstice is equally applicable to
São Paolo, Brazil (20∘ S) on the December Solstice, but the all-sky image must
be flipped north-south. The number of sunlit and visible satellites is given
for each sky-field. These numbers are slightly randomized due to the pseudo-
random satellite distribution and the small random scatter added in to the
satellite brightnesses.

Table 2: Satellite magnitudes

Latitude | Season | time | $g<5$ |  | $g<6.5$ |  | $g<7$ |
---|---|---|---|---|---|---|---|---
|  |  | number | % sats | number | % sats | number | % sats
60∘N/S | summer | midnight | 19 | 2% | 292 | 6% | 480 | 6%
| equinox | midnight | 0 | 0% | 9 | 0% | 16 | 0%
|  | nautical dusk/dawn | 9 | 1% | 137 | 3% | 244 | 3%
50∘N/S | summer | midnight | 48 | 6% | 259 | 6% | 386 | 5%
|  | nautical dusk/dawn | 60 | 7% | 317 | 7% | 487 | 6%
| equinox | midnight | 0 | 0% | 0 | 0% | 0 | 0%
|  | nautical dusk/dawn | 72 | 8% | 311 | 7% | 438 | 5%
40∘N/S | summer | midnight | 0 | 0% | 34 | 1% | 71 | 1%
|  | nautical dusk/dawn | 79 | 9% | 327 | 7% | 487 | 6%
| equinox | midnight | 0 | 0% | 0 | 0% | 0 | 0%
|  | nautical dusk/dawn | 76 | 9% | 322 | 7% | 493 | 6%
30∘N/S | summer | midnight | 0 | 0% | 1 | 0% | 4 | 0%
|  | nautical dusk/dawn | 78 | 9% | 299 | 6% | 450 | 6%
| equinox | midnight | 0 | 0% | 0 | 0% | 0 | 0%
|  | nautical dusk/dawn | 78 | 9% | 310 | 7% | 480 | 6%
20∘N/S | summer | midnight | 0 | 0% | 0 | 0% | 0 | 0%
|  | nautical dusk/dawn | 60 | 7% | 246 | 5% | 375 | 5%
| equinox | midnight | 0 | 0% | 0 | 0% | 0 | 0%
|  | nautical dusk/dawn | 56 | 7% | 259 | 6% | 403 | 5%
Background stars | 804 |  | 4395 |  | 7702 |

Note. — “% sats” means the percentage of point sources in the sky at that are
satellites, not stars, at each magnitude cut, for top-of-the-atmosphere
magnitudes (i.e., no extinction).

There are notable patterns in the on-sky satellite brightness distributions.
As expected, satellites get fainter close to the horizon, and are brightest as
they pass overhead - this is due to a combination of effects: the phase angle,
satellite range (distance between the satellite and the observer), and the
satellite’s instantaneous airmass. The satellite will be closest to the
observer when it passes through the zenith. As the satellite moves toward the
Sun from the zenith, its range increases and its phase angle also increases,
causing the satellite to become faint quickly under the diffuse sphere model,
although the results of Mallama (2021b) show that this behaviour can be
complex. Moreover, as the satellite moves away from the zenith and away from
the Sun, the range is increasing (causing dimming) while the phase angle is
decreasing (causing brightening), two competing effects that make overall on-
sky brightness patterns difficult to predict.

The shadow of the Earth is apparent in many of the all-sky images, and is what
blocks the closest overhead satellites from being sunlit close to the equator.
In latitudes closer to the poles, because of geometry, the Earth’s shadow does
not block the satellites near the zenith, resulting in bright satellites being
visible throughout the night.

In the locations close to the equator ($0^{\circ}$, Figure 7, and Hawaii at
20∘ N, Figure 5), only faint satellites are visible, primarily close to the
horizon. From Hawaii, and to a greater extent from the Vera Rubin Telescope
site in Chile (30∘ S), there are a handful of bright satellites crossing the
zenith close to sunrise and sunset in the summer. This could restrict the
portions of the sky that are available for scientific studies in the
summertime, when the weather is generally better. This effect of satcons on
research astronomy can also be seen in Table 2, where satellites make up only
a tiny fraction of all points sources in the sky at midnight in the range of
$g$-magnitudes tested at 20-30∘ latitudes.

At higher latitudes of 50∘ N (Figure 6), where many Canadian and European
observing facilities are located, as well as a large fraction of the
population of Canada, Europe, and northern-tier US states, the problem of
light pollution from satellites is much more severe seasonally (and is equally
severe at 50∘ S). In the winter, only a handful of satellites are visible late
into the night and are faint, while near the equinox, satellites are visible
at midnight, but they are all faint. However, near the summer solstice, there
are many bright satellites crossing the zenith all night long. The shadow of
the Earth blocks many of the would-be brightly-lit satellites close to the
equinox, but this does not occur closer to the summer solstice. Table 2
quantifies this: at 50∘N or S latitude, near the summer solstice, satellites
will make up 6-7% of all visible point sources in the night sky at $g<5$,
$g<6.5$, and $g<7$ within a couple hours of sunrise or sunset; Restated: as
seen by the naked eye, about one in every 14 stars in the sky will actually be
a satellite. Close to midnight, this fraction drops slightly to 5-6%, but as
shown in Figure 6, the brightest satellites ($g$-magnitudes near 5-5.5) remain
close to the zenith at all hours of the night.

It is nearly as severe of an effect at 40∘N or S: 6-9% of point sources in the
sky are going to be satellites for these magnitude cuts within a couple hours
of sunrise and sunset near the summer solstice. At 40∘N or S, the brightness
of satellites drops off more steeply toward midnight and toward the equinox as
compared with 50∘N or S, so many fewer satellites are visible at midnight.

At even more northerly/southerly latitudes of 60∘N or S, the fraction of
satellites is 2-6% all night long near the summer solstice. The fraction drops
quickly close to the equinox. Of course, close to the summer solstice at these
high latitudes, there is very little darkness, so the summer light pollution
by satellites might be much less noticeable than at latitudes of 50∘ or even
40∘.

As a check of our calculations, and the most extreme case, we also include the
view from the North Pole (Figure 8, equally applicable to the South Pole).
Interestingly, there are never any satellites directly overhead: this is
because satellites are not inclined by exactly 90∘. Of course, the visibility
pattern will be quite different at the North Pole than at other latitudes: the
Summer Solstice satellites will not be visible at all due to 24-hour daylight,
while the Winter Solstice satellites will be visible all day and night due to
24-hour darkness. Close to the Winter Solstice, only the highest altitude
satellites close to the zenith will be illuminated and visible (presumably
24-hours per day). For comparison, we also modelled the sky view at midnight,
with the Sun at a declination of -18∘ (October 24), when there is 24 hours of
astronomical twilight, and at -12∘ (November 12), when there is 24 hours of
nautical twilight. As the Sun creeps to higher declinations, the bright
satellites appear further and further south in the polar sky. While there
aren’t any observing facilities at the North Pole, there are high-latitude
facilities, and these predictions are equally applicable to Antarctic
astronomical facilities.

These calculations highlight the unequally distributed light pollution that
will result from satcons at different places on Earth: according to our
simulations, 50∘N and S latitudes will experience some of the worst effects of
light pollution compared to anywhere else on Earth.

###  3.3 The Effects of Altitude

Figure 9:  65,000 satellites on the same orbits as Table 1, but all at an
altitude of 1200 km (first and third columns) or 550 km (second and fourth
columns), as viewed on the summer solstice. Models are shown at nautical dusk
(first and second columns) and at midnight (third and fourth columns). Rows
show the models at different latitudes. This plot highlights the fact that
there is no “best” altitude for satellites, it is a trade-off of different
problems for different locations on Earth.

One recommendation from the SATCON1 report is that satellites should orbit at
lower altitudes. While this makes them brighter, it also causes them to move
through a given telescope field of view more quickly, smearing the reflected
sunlight across more pixels in a shorter amount of time, decreasing the damage
to science images. Our models here show that while this strategy works well
for lower latitudes, where many research telescopes are located, it will lead
to many bright satellites visible all night long at higher latitudes during
times close to the summer solstice.

To more thoroughly explore the effects of satellite altitude, we build two toy
models. Each toy model uses the same number of satellites and the orbits from
Table 1, but all of the satellites have been moved to an orbital altitude of
550 km in one model and 1200 km in the other. Figure 9 shows these two
satellite altitude toy models on the summer solstice, at nautical dusk and at
midnight, and at many different latitudes, illustrating the patterns in light
pollution across the Earth caused by satellites at different altitudes.

The number of sunlit satellites in the sky is much larger for the 1200 km
model than the 550 km model, at all latitudes. The satellites in the 1200 km
model are also on average much fainter, with significantly fewer satellites
that are visible to the naked eye for all latitudes and at all times of night.
However, while there are fewer bright satellites in the higher altitude model,
the rate of motion across the sky is slower, making each satellite visible in
a given telescope’s field of view for a longer period of time, as noted above.
With this in mind, satcon operators will require more satellites at lower
altitudes than at higher altitudes to provide comparable beam coverage, all
other things being equal. This is not captured in this toy model, which uses
the same number of satellites for the two altitude cases. Thus, the total
number of satellites in the sky might not vary too much according to the
chosen altitude, depending on the satcon designs. These trade-offs need to be
handled with a high degree of care and continuously re-evaluated.

Another issue to consider is that while satellites are overall brighter in
lower orbits, the number of sunlit and visible satellites drops very quickly
after nautical dusk for the lower latitudes, giving a period of very few
sunlit satellites for most of the night. However, this fast drop-off in low-
orbit visible satellites does not happen at higher latitudes. For example, at
50∘ N, there continues to be hundreds of naked-eye visible satellites all
night long near the summer solstice. The higher orbit satellite model also
produces many naked-eye visible satellites at high latitudes all night long in
the summer, but not as many as the lower orbits.

There is no perfect solution - higher altitude orbits may be better overall
for naked-eye stargazers, but lower orbits are thought, based on the astronomy
community’s current understanding of satcon operation plans, to be better for
large research facilities, which tend to be at lower latitudes.

##  4 Discussion: Some Effects on Astronomy

With hundreds or even thousands of sunlit satellites moving across the night
sky at a time, research astronomy will be affected. Other works discuss a
broad range of negative effects (such as pollution and collision risks) that
satcons will have, for example, on the sustainable development of space (e.g.
Boley & Byers, 2021), but here we focus specifically on the effects on
research astronomy. Following Hainaut & Williams (2020), we highlight in this
section a few of the prominent negative effects, but this is by no means an
exhaustive list.

###  4.1 Bright streaks in research images and astrophotography

The most obvious effect of satellites on optical research astronomy is the
contamination of research images by bright satellite trails, appearing as
lines cutting across the entire field of view of research or astrophotography
images555Many astronomers have already experienced this, and it is documented
widely.. Research astronomers are developing algorithms to process these
streaks, such as automatically identifying, characterizing, and removing them
from images (see e.g., the SATCON2 Report). Such algorithms will help to
mitigate some forms of data loss from science images and allow further image
processing, but they cannot recover lost data.

If satellite trails are too bright, they can create cross-talk between CCD
chips in large telescope, most well-documented for the LSST telescope (Tyson
et al., 2020). If satellite operators can reduce brightnesses below $g$
magnitude $\sim$7, then such cross-talks might be significantly reduced for
some detectors, although this needs to be continuously evaluated. Further, if
operators meet this brightness limit, it will fulfill the task of keeping most
satellites below naked-eye visibility. SpaceX has stated that this is the goal
for their Starlink satellites – a goal that has not yet been achieved (e.g.
Boley et al., 2021b; Mallama, 2021a).

The level of disruption to research astronomy will most strongly depend on
satellite brightnesses and rates of motion. Consider Figure 3, which shows 400
satellites above 30∘ elevation for at least a portion of each night. This
corresponds to a sky area of $\pi$ sr. The expectation that the satellite will
pass through the FOV is then estimated as

$E=RwtN/\Omega_{\rm sky},$ (2)

where $R$ is the typical sky motion of a satellite, $w$ is the characteristic
width of the detector (taken to be $1^{\circ}$, typical for a wide-field
camera), $t$ is the exposure time, and $N$ is the number of satellites in the
sky area $\Omega_{\rm sky}$. For $R\approx 2000$ $\arcsec$/s (typical for a
satellite at $\sim$500km orbital altitude) and an exposure time of $t=10$ s,
we find $E\approx 0.22$. Assuming Poisson statistics, the probability of one
or more satellites passing through the FOV of the sq. degree telescope is
about 20% under the models explored here. For a 3 minute exposure, as is
common for deep Kuiper Belt surveys (e.g., Bannister et al., 2018), a typical
exposure will include 4 satellite trails, depending on satellite brightness.
While most parts of the world will have some period of time each night with
few-to-no sunlit satellites, telescopes at high latitudes will experience this
rate of satellite contamination all summer.

This calculation assumes that the satellites are independent of each other,
when actually, their motions across the sky are highly correlated. Our rough
calculations here agree with the much more thorough analysis of the number of
satellites per telescope field and the fraction of lost exposures for
different telescope facilities that is presented in Williams et al. (2021).

###  4.2 Severe effects on radio astronomy

This paper is focused on optical light pollution, but we note that radio
astronomy has the potential to be strongly affected by the abundance of
transmitting satellites, particularly if the electronics that are used allow
for out-of-band emission or overtones falling into bands otherwise protected
for astronomy (as happened with the Iridium satcon, see e.g., Council, 2010).
Additional spectrum is further being sought after, and the use of frequencies
that are typically used in terrestrial applications might be explored for on-
orbit infrastructure, further restricting the frequencies available for
scientific research.

The SATCON2 report, available to the public in October 2021666available at
https://doi.org/10.5281/zenodo.5608820, contains recommendations for how
satcon operators can mitigate damage to radio astronomy.

###  4.3 False positives in occultation studies

Even when satellites are not sunlit, they can still potentially interfere with
astronomical observations. They are too fast to cause a measurable change in,
for example, an exoplanet transit observation. But occultation experiments
like TAOS, which is using high cadence observations with the goal of detecting
occultations of stars by small bodies in the solar system (Zhang et al.,
2013), could potentially experience a new source of noise.

A satellite occultation of a star lasts between about a tenth of to a full
millisecond (Hainaut & Williams, 2020), as LEO satellite on-sky motions are of
the order 2000 $\rm{}^{\prime\prime}/s$, as noted above. While this timescale
is much shorter than what is expected for an occultation by a small body in
the outer solar system, an observing cadence of a few frames per second would
cause this short dip to be confused with the $\sim$0.1 sec dip in brightness
caused by a real occultation (Schlichting et al., 2012; Lehner et al., 2019).
With 65,000 satellites, satellite occultations could become frequent enough,
depending on a telescope’s field of view, to produce a false-positive signal
as high as is expected for distant solar system small bodies.

To approximately calculate this, consider the same setup as in Section 4.1,
with 400 satellites passing through a sky area of $\pi$ sr at any moment. At a
range of 1000 km, a plausible angular size of a satellite is about
$0.^{\prime\prime}5$. Taking the satellite’s sky motion to be 2000
${}^{\prime\prime}/\rm s$, then the satellite population would sweep out an
area equivalent to that entire section of the sky with a frequency of about
$0.3\rm~{}d^{-1}$. During that time, if we are monitoring an average of 10,000
stars (as TAOS II plans to do; Lehner et al., 2019) in each field, then for 8
hr nights, we would expect around 1000 satellite occultation events per night,
on average. This is much higher than the expected occultation frequency of
stars by small trans-Neptunian objects (TNOs; $<10^{-3}$ per star per year),
and may become a limiting source of noise for this type of astronomy research.

###  4.4 Cumulative Effects: Total Sky Brightness

As a result of adding more point sources, the total brightness of the night
sky will increase. For an estimate, we calculate a summed flux density using
$V$ band magnitudes of all stars in the Hipparcos catalogue with $V<10$,
converting to Janskys using the AB magnitude zero point, i.e.,
$m=-2.5\log_{10}(f_{\nu}/3631\rm Jy)$. Averaging over the entire sky gives a
surface brightness of 13.7 Jy/sq. deg. We then repeat this calculation for our
satellite models (using $V$ band estimates), including only the illuminated
satellites and their corresponding brightness. For a latitude of 50∘ on the
summer solstice at nautical twilight, satellite night sky brightness is about
0.5 Jy/sq. deg., about 4% of the starlight contribution.

This simplistic calculation ignores any reflection by diffuse particles or by
the atmosphere. Diffuse emission caused by sunlight reflecting off the huge
number of tiny pieces of debris in orbit (“space junk”) has already been
calculated to increase the overall brightness of the sky by 10% above pre-
industrial levels (Kocifaj et al., 2021). The placement of such large amounts
of infrastructure in space raises the issue of the further generation of space
debris, particularly if there is an on-orbit accident such as a collision or
explosion, compounding the brightness problem.

##  5 Conclusions

We acknowledge the broader engagement by SpaceX other satcon operators, such
as OneWeb and Amazon (as in SATCON2), in entering discussions with astronomers
concerning this issue. SpaceX has stated that they will engineer their
Starlink satellites to be fainter than visual magnitude 7. We applaud their
efforts, but note that they have yet to achieve this goal. Mallama (2021a)
presents observations showing that about 70% of Visorsat Starlinks are
brighter $V<7$ as observed from 39-44∘. Boley et al. (2021b) presents
observations from 48.5∘ N, which show about 80% of Starlinks are brighter than
$g<7$, supporting the results of our modelling: the 550 km Starlink satellites
are bright and visible throughout the night during the summer at moderate to
high latitudes.

Orbital altitudes of satellites are important, but there is no perfect
strategy that will help all latitudes equally. The current recommendation from
the SATCON1 report is for satcon operators to use orbital altitudes of 600 km
or less, and many of the operators have filed for orbits that primarily meet
this requirement. Such cooperation is good. But as the modelling presented
here shows, this altitude will not prevent satellites from being bright during
the little but precious night available to researchers and sky-watchers during
summer at latitudes above approximately 45∘N and S.

The stated point of many of these new and future communications satcons is to
bring high-speed internet to the world, benefiting many potential rural and
remote users, especially isolated communities. There are nonetheless important
questions concerning the accessibility of such services (e.g., Rawls et al.,
2020), particularly given the global impacts that bright orbital
infrastructure could have, without mitigation. Such impacts are felt
regardless of the degree of use or even access to the services, similar to
classical pollution problems. Furthermore, orbital light pollution is
inherently transboundary in that a state authorizing a satcon distributes that
pollution worldwide, which has so far been done without broad consultation.
The simulations presented here show how the effects of satcons are a long-term
change to the night sky worldwide, which is a shared resource enjoyed and used
by humanity (see e.g., Boley et al., 2021a, for further discussion).

There is simply no way to have tens of thousands of satellites in Low Earth
Orbit and avoid consequences for astronomy. But with strong, international
cooperation and appropriate regulation of satellite numbers, reflectivities,
and satellite broadcasting, we can perhaps reach a compromise that allows much
of research astronomy and traditional naked-eye stargazing to continue with
minor losses.

The authors wish to acknowledge the land on which they live and carry out
their research: Canadian Treaty 4 land, which is the territories of the
nêhiyawak, Anihšināpēk, Dakota, Lakota, and Nakoda, and the homeland of the
Métis/Michif Nation; the traditional, ancestral, and unceded territory of the
Musqueam people, which has always been a place of learning for the Musqueam,
who for millennia have passed on their culture, history, and traditions from
one generation to the next on this site; the traditional land of the Huron-
Wendat, the Seneca, and the Mississaugas of the Credit, which today is still a
meeting place and the home to many Indigenous people from across Turtle
Island. This research has been supported in part by NSERC Discovery Grants
RGPIN-2020-04111 (SML), RGPIN-2020-04635 (ACB) and RGPIN-2020-04513 (HR), as
well as the Canada Research Chairs program.

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