Section 7: Altitude and surface brightness effects
The effects of a satellite constellation on astronomy depend on the satellite's altitude both directly and through changes in surface brightness of the streaks.
Direct effects of altitude:
- Higher satellites are visible from a wider area on the ground, so more illuminated satellites are visible to the observer and there are more streaks on a given image.
- Higher satellites are illuminated for longer after ground sunset, so more illuminated satellites are visible to the observer and there are more streaks on a given image.
- Higher satellites have lower angular velocity with respect to a ground observer, which leads to more streaks on a given image.
- Higher satellites are fainter. This could lead to fewer detected satellites, but for typical megaconstellation satellites they are still bright enough to be easily detected by typical astronomical observations. However, satellites above 600 km are unlikely to be naked-eye objects.
Surface brightness effects:
- Higher satellites are more in focus and subtend a smaller angular size at the telescope, increasing the surface brightness per pixel
of the trail.
- The slower angular velocity increases the surface brightness per pixel.
The surface brightness of a streak is important because:
- Very high surface brightness streaks cause severe electronic crosstalk in detectors, making entire frames unusable (as shown by Tony Tyson and his group at Rubin Observatory).
- Very low surface brightness streaks will not be detectable against detector background - they could still provide an unmodelled spatially variable contribution to that background, throwing off calibrations in various ways.
Below I simulate a constellation of 10,000 satellites at various altitudes. In each case the inclination is 53 degrees and there are 32 orbital planes; the calculation is done for midsummer at latitude 30 south.
The plot shows the number of illuminated satellites above 20 degees elevation versus time of night. You can see from the figure that with the same number of satellites, higher altitude constellations are more visible.
