Starlink satellite simulations

O.Hainaut - ESO - 2020-03-15, upd. 05-05

The following simulations evaluate the visibility of ~12000 Starlink satellites on the sub-constellations listed in the table below (which is a slight simplification of the announced actual orbital distribution). This constellation is the original one. In Apr.2020, Starlink announced a plan to to deploy the satellites originally planned at altitudes 1100-1300km on lower orbits in the 540-570 range. The simulations are performed using the original constellation. A comparison with the new constellation is given below.

Altitude [km]Inclination [deg]PlanesSatellites
346 53 42 2547
341 48 42 2478
336 42 42 2493
550 53 72 1584
1110 54 32 1600
1130 74 16 400
1275 81 10 375
1325 70 12 450
Table 1: Original Starlink constellation.

The simulations are based on the calculation of the positions of each satellite for various observatories, seasons and time of night. For a probabilistic evaluation of the effect of satellite constellations on astronomical observations, pls refer to Hainaut & Williams (2020 - arXiv:2003.01992).

The planes in a sub-constellation are regularly spaced, and the satellites are positioned at regular intervals on their orbit. As an example, here is a view of the first sub-constellation with the planes marked, and all the sub-constellations together (the Earth --outlined in cyan-- is inclined 40deg in this view).

The position of each satellite is computed for the time of observation, resulting in a distribution map as below. The orange dots mark illuminated satellites, the blacks dots satellites in the shadow of the Earth. The big yellow dot is the sub-solar point, and the red dot marks the observatory.
The position of the satellites with respect to the observatory is represented below. The black circle is the silhouette of the Earth, with the observatory as a black dot at the top. In the first row, satellites in range of the observatory are in blue (about 5% of the whole constellation, while those below the horizon are in red). In the bottom row, illuminated satellites aer in yellow, and those in the shadow of the Earth in black.

The magnitude of each satellite is computed accounting for the distance to the observatory, the atmospheric extinction (0.125 mag/airmass), and the solar phase angle (assuming a geometric diffusion on a sphere, which is pessimistic). See Hainaut & Williams (2020 - arXiv:2003.01992) for details. The magnitudes are scaled to V=6 at 550km at zenith, a value between the measurements for a normal satellite (r=5.3) and a darksat (r=6.2, Tregloan-Reed et al 2020, arXiv:2003.07251).

In the plots below,

The plots are generated for solstices and equinox, for an equatorial observatory (0deg latitude), Paranal (25deg lat. S) and Brussels (50deg lat. N.).

The summary plots show the number of satellites as a function of local time. The black curve is the number of satellites in the sky, cyan the number of illuminated satellites (of any magnitude), orange those brighter than mag 6, the red line those brighter than mag 5. The 3 plots show the number of satellites in the whole sky, above 10deg of elevation (for visual observations and astrophotography), and above 30deg (for telescopic observations).

Latitude = 0deg: Equator

Equinox

Sun elevation:-6deg-12deg-18deg-30degMidnight

Solstice

Sun elevation:-6deg-12deg-18deg-30degMidnight

Latitude = 25deg: Paranal

Winter

Sun elevation:-6deg-12deg-18deg-30degMidnight

Equinox

Sun elevation: -6deg-12deg-18deg-30degMidnight

Summer

Sun elevation: -6deg-12deg-18deg-30degMidnight

Latitude = 50deg: Brussels

Winter

Sun elevation: -6deg-12deg-18deg-30degMidnight

Equinox

Sun elevation: -6deg-12deg-18deg-30degMidnight

Summer

Sun elevation: -6deg-12deg-18deg-30degMidnight
-n/a-

Comparison between the original and new Starlink constellations

In April 2020, Starlink requested permission to deploy the ~2800 satellites originally foreseen for altitudes above 1000km to the 540 to 570 range. The following plots show a comparison between the original and new configurations. The main changes are the following:
OriginalNew