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We would like to perform measurements of the brightness of Starlink satellites.

Is there any approved technique available ?

I see the name Mike McCants connected with magnitude values of satellites, but this guy can not be found yet on the internet.

We were thinking about astrometry of a guided satellite image vs. a star guided comparative starfield.

Thank you for any ideas.

Best

Rudolf

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I'm going to suggests some things you can try without using a guided image. If you really have the capability to accurately guide on a moving satellite, then you can skip much of the advice below and just use the equation.

It is going to be a challenge because the satellites are moving while the stars are fixed, so you can't compare exposure values per pixel of the satellites with that of stars if the exposure is long enough that the satellite trails or becomes elongated.

Try a wide or medium field camera and several short exposures and see if you can get an image where the satellite spot is the same size and shape as some nearby stars. As long as the spots are not overexposed, you can assume the values are approximately linear with brightness. You can use an image analysis program of your preference (one example is ImageJ but there are many out there). Draw a small region around each spot and integrate the intensity. Check that the maximum doesn't exceed the maximum value - no pixesl are overexposed. You can try drawing similar small regions in dark areas to estimate the background for subtraction.

If the shape of the satellite is elongated but well above background and not overexposed (same for the stars) then you can try using elongated regions to integrate, but be sure to use the same region shape for the stars, or if they are different, then at least make sure you use the same shape region for object measurement and background measurement before subtraction, in each case.

Once you have an integrated intensity of the satellite and a star, you can use the following:

$$ m_{sat} - m_{star} = 2.5 \log_{10} \left( \frac{star}{sat} \right) = 2.5 \log_{10}(I_{star}) - 2.5 \log_{10}(I_{sat})$$

$$ m_{sat} = 2.5 \log_{10}(I_{star}) - 2.5 \log_{10}(I_{sat}) + m_{star} $$

So for example if the integtated intensity of a dimmer, +1 magnitude star is 1,500 and of the satellite is 42,000, then the satellite is -2.6 magnitude.

Below is an example of integrating regions for a star and and a satellite trail.

enter image description here

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    $\begingroup$ Thank you very much for your detailed answer. This is definitely the direction I will go. The idea and formula concerning the integration of the sat trail is very helpful. My current setup with the CEM 60 mount only allows for frog leap tracking of satellites. Thanks again ! $\endgroup$
    – rbumm
    Sep 14, 2019 at 11:06
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    $\begingroup$ Hello again, I have maneged to set all up and measured data of a COSMOS satellite. When I try to integrate the lightness of trail vs. reference star I have used "integrated density" and get hugely different values of trail vs. star, despite the fact that the magnitude seems comparable. What do I do wrong ? Can I compensate for the area (trail area is bigger)?Thanks $\endgroup$
    – rbumm
    Sep 18, 2019 at 13:00
  • $\begingroup$ @rbumm Here's what I recommend; ask a new question and post an example of an image along with a short description of what you have tried. I think for this new question you might be better asking in Astronomy SE instead of here, since there are a lot of people there with experience processing astronomical images, including images of asteroids which can also leave trails. You can include a link to your first question here in the new question and that will help people with background. $\endgroup$
    – uhoh
    Sep 18, 2019 at 14:00
  • $\begingroup$ Good idea, will probably do that. AstroimageJ offers many functions and I am just diving into that software. $\endgroup$
    – rbumm
    Sep 20, 2019 at 10:11
  • $\begingroup$ @rbumm oh that's excellent! I had no Idea that there was an AstroimageJ cousin of ImageJ. Thanks for the info! By the way it's always okay to post an answer to your own question! $\endgroup$
    – uhoh
    Sep 20, 2019 at 10:14
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Slowly getting the facts together ... I was measuring Starlink 29 the other night with a Newton 8' f5 on an iOptron CEM60 mount. Used Skytrack (only availabe for iOptron) for sat tracking.

I plate solved the image in AstroimageJ and found four good stars nearby the satellite trail. The satellite was 12 deg above the horizon only.

Looked up the magnitutdes of the stars in Simbad (B V G J H M values) and compared the V values of two of the stars with the sat trail in AstroimageJ (fig 2)

This shows, that the sat magnitude was ~ 9.5-9.8 that evening.

Best regards

rudolf

enter image description here

enter image description here

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  • $\begingroup$ Wow, interesting results! A couple of quick questions; 1) for the fixed stars, you can integrate all of the photons in the small circular regions, but for the trail of the satellite, did you integrate over the whole trail, or are you just sampling a small fraction in that small circle in the middle of the trail? 2) did u check for certain that none of the star images were saturated (pixels reaching maximum ADC counts)? $\endgroup$
    – uhoh
    Oct 13, 2019 at 11:18
  • $\begingroup$ (1) in this first trial I used the aperture measurement tool of AstroimageJ, which compares two aperture circles and their corresponding background. Normally you would use this f.e. for measuring double stars. I do not know if I am correct here. If you think about it, the human eye would not sum up anything of a sat trail and compare the sat brightness with a very short "exposure" against a nearby star. (2) I always check that none of the stars nor the sat trail is saturated. $\endgroup$
    – rbumm
    Oct 14, 2019 at 13:19
  • $\begingroup$ What you mentioned about the human eye is correct, and so if you had analyzed a single frame of a video where both the satellite and the stars look like dots, that would be a correct analysis. But what you have here is an extended exposure, where the satellite photons are spread out over a much larger number of pixels than the star photons, which is not the same thing. You simply can't throw away most of the satellite's photons while counting all of the stars' photons and treat them as equivalent measurements. $\endgroup$
    – uhoh
    Oct 14, 2019 at 13:22
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    $\begingroup$ That is right and I noticed this fact when I recorded the last Starlink satellites yesterday with different exposure times. Thank you for your advice. I will have to compare the whole trail against the star. $\endgroup$
    – rbumm
    Oct 15, 2019 at 5:21
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After the discussion here I finally switched to measuring the integrated density of the complete sat trail, subtracted background noise and compared the result against the known star HD 211599 (mag 8.87). Here I also subtracted the background noise. The Excel formula is attached.

For Starlink 29 I calculated a magnitude of 7.59 near the horizon.

Nice :-)

enter image description here

enter image description here

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  • $\begingroup$ Don't forget the magnitude of the satellite varies with 1/range^2. For LEO satellites like Starlink the range varies a lot depending on their elevation. Standard satellite magnitudes are given at a range of 1000km so Starlink will be brighter than the standard value at the Zenith while OneWeb being higher will be dimmer. There is also evidence of variability with starlink depending on the Sun - Satellite - Observer angle and the satellite attitude. At present Starlink are refusing to publish their shape & reflectivity models and the attitude information. $\endgroup$
    – JohnM
    Jul 31, 2021 at 8:31

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