Guest Post: Modelling of Starlink trail brightness and comparison to observations

(The following post is a Guest Post written by Richard Cole)

Observers have been reporting ‘missing passes’ of Starlink trains since the Starlink L1.1 launch, the first of the operational spacecraft. A missing pass is where an examination of the NORAD or SpaceX orbital elements, or a prediction from one of the Starlink websites, would indicate that multiple spacecraft should be expected to be visible but none appear on time.

An observer in Argentina noted missing passes to their south in late February, local summer. Initially, I thought that perhaps the spacecraft had been temporarily placed into the operational low brightness mode (that brightness having been seen on the prototypes after deployment in mid-2019) but this did not match other observers seeing the same spacecraft at normal brightness at similar times. This phenomenon affected spacecraft in the holding orbit at 350-380km, not the operational spacecraft at 550km.

Recently, the images of the spacecraft on-orbit by Ralf Vandebergh and Szabolc Nagy showed its large solar panel of the solar array was facing the Earth when the spacecraft were overhead and explained the normally high brightness of the spacecraft as seen from the ground. The longer dimension of the panel was observed to be parallel to the velocity vector of the orbit, i.e. the orbit path.

SpaceX had referred in communications to a low-drag mode which was consistent with the observed appearance. This raised the question of how this mode of operation would deal with acquiring enough solar power. Would the panel always face upwards to the zenith, or would the spacecraft be rolled around the velocity vector to get more sunlight onto the panel?

During April 2020 more observers saw missing passes. I had personally tweeted a prediction for a late evening pass of the Starlink L1.5 train to the north of my site in southern UK on April 20th, but the spacecraft were only magnitude 6, needing binoculars to be seen at all. Observers in northern UK reported they had visually seen spacecraft on that pass. It was clear that the spacecraft were indeed being rolled around the velocity vector and by such an angle they were nearly directly facing the Sun, now towards the north in Spring, and observers to the south were just seeing the shadowed back of the panel.

Since it was clear that further analysis was needed to accurately predict visible passes, early on April 21st I created a simple model of the spacecraft panel pointing axis assuming the panel long axis was the velocity vector and the spacecraft was being rolled so that the Sun was in a plane normal to the panel and through the long axis (figure 1). Usually the panel cannot directly face the Sun, but is at some offset angle, in azimuth and elevation.

Figure 1: Spacecraft Roll-Angle concept.  Click diagram to enlarge

This concept allows calculation of the angle between the direction the panel is pointing and the observed Starlink direction for a particular observer on the ground, for the same time. This ‘panel view angle’ will be different for each possible observer of the same spacecraft at the same time, some will see a large part of the sunlit side of the panel, some will see only a little of the same side and some will see only the back of the panel away from Sun, which is dark.

The model gave panel view angles consistent with recorded occasions of observed train non-appearances.

Marco Langbroek’s excellent observation and images of the L1.5 train from Leiden on 2020 April 21 (the same day as the first version of the model was written, as it turned out) provided a useful test of the model. Further, more recent information from SpaceX has confirmed this behaviour and suggested that the actual roll-angle used on-board many not be exactly as calculated above.

In the image below (figure 2) I plot the calculated glancing angles to the sunlit side of the solar panel (so a glancing angle of zero means the view angle of the panel is to the edge of the panel, an angle of 90 would be face on). I have done this for two altitudes (elevations) in Marco's image, 50° and 70°. The roll-angle was as calculated above.

Figure 2: Marco Langbroek's image of Starlink 5 passes, with the calculated panel glancing angles overlaid. Click to enlarge

The trend of a reducing glancing angle with Starlink brightness is correct, so as the Starlinks passed further north (to the right of the image) of Marco at Leiden, less and less of the panel sunlit surface was visible until nothing could be seen. There was one predicted Starlink that passed on the right of the image (further north) but is only detectable by image analysis, it can’t be seen in the original camera image because very little of the sunlit side was facing the camera:

Figure 3: the extra and faint track of a predicted Starlink satellite in the image. Click to enlarge

I was observing the same pass from southern UK a few minutes earlier than Marco and saw the same behaviour of reducing Starlink brightness as each Starlink passed further to the north. I was very pleased to see he had recorded it in his image.

However, the fit is not perfect so I tried changing the roll-angle by a small amount from that calculated. The fit was best for a deviation of nine degrees from the model, that is the actual roll-angle was nine degrees less that the simple model predicts and the panel is pointing slightly higher in the sky. This gave a better fit:

Figure 4: the same image with the changed panel glancing angles overlaid, using an offset of nine degrees in the solar panel pointing direction. Click to enlarge

SpaceX is now promising to change the roll-angle model used on-board to minimise the Starlink brightness as seen from the ground. The panel will be rotated, at periods when the Starlink can be seen from the ground, so the sun falls on the edge of the panel, not on its face as in figure 1. This is a small portion of each orbit and as Starlinks at low altitude are not using their communication equipment, they will need less power to keep functioning.

Richard Cole
Twitter: @richard_e_cole