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I'm trying to make an application that calculates ISS flyovers.

I figured out how to actually get the flyover, but I am struggling with figuring out how to calculate the apparent magnitude of the space station during those flyovers. I've looked at Is there any way to calculate the visual magnitude of a satellite (ISS)? and Calculating the Phase Angle between the Sun / ISS and an observer on the earth.

I figured out how to calculate the solar phase angle, but I cannot figure out how to get the formula provided by Is there any way to calculate the visual magnitude of a satellite (ISS)? working. I have the phase angle in degrees and the distance to the satellite in km. This is the formula: 

Mag = Std. Mag - 15 + 5*LOG(Range) - 2.5*LOG(SIN(B) + (pi-B)*COS(B))

For the ISS I use -1.8 as the std.mag. https://stackoverflow.com/users/2949204/liam-kennedy provided this formula and seems to know how to get it working, but I can't for my life.

Note: I am doing this in C# and know my phase angle is correct, but even doing it with Python and pyephem I wasn't getting anything close to Heavens-Above's results. Setting B to 113, std.mag to -1.8, and range to 485 is giving me 11.25, yet on Heavens-Above with the exact same data they get -3.0.

Here is the code I am using

var B = phaseAngle;
var magnitude = intrinsicMagnitude - 15 + 5 * Math.Log(distanceToSatellite) - 2.5 * Math.Log(Math.Sin(B) + (Math.PI - B) * Math.Cos(B));

EDIT: I solved this problem here: https://astronomy.stackexchange.com/questions/28744/calculating-the-apparent-magnitude-of-a-satellite/28765#28765

Moderator please mark this solved.

Nick Brown
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  • It definitely is possible, i actually think the formula may be flawed. – Nick Brown Dec 17 '18 at 03:02
  • You need to account for the satellites solar panels and or antennas as they are very high percentage of the object surface and often are planar with a specific rotation. So you actually need to compute the reflection of such surface and sum the energies together. Both solar panels and antennas usually have a specified orientation (towards sun for max power input, towards earth to have best gain etc) so its deducible from satellite/sun/observer position. As you can see this can significantly alter the visual magnitude. If you account also for total reflection angles you can got the spikes – Spektre Dec 17 '18 at 08:56
  • For example Iridium satellites got those quite often and hence the predetermined antenna orientation its predictable ... So by using overall equation for homogenuous "spherical" surface you are making huge inaccuracies as satellites are anything but homogenuous nor spherical ... – Spektre Dec 17 '18 at 09:02
  • The intrinsic magnitude is the average brightness from 1000km away (this is accounted for in the equation). Im just trying to figure out how to make it like heavens-above.com. According to those threads i linked, it is able to do so, but i cant seem to figure out how to input the data properly. – Nick Brown Dec 17 '18 at 13:43
  • They have a simplified mesh and compute as I mention ... as average brightness (albedo) will not lead to valid results ... the solar pannels and antenna make a huge difference (objects that are normally ~ +11 mag with your equations and avg constants but -3.5 in real life once you hit the total reflection maximum... the main difference is that phase angles for the sun/panels/observer are very different from sun/satellite/observer angles ...) – Spektre Dec 17 '18 at 14:32

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I usually use the equation found at https://mostlymissiledefense.com/2012/08/21/space-surveillance-the-visual-brightenss-and-size-of-space-objects-august-21-2012/. Yours is similar. But the first thing I would check is your use of the LOG() function. LOG() calculates the natural log and I suspect what you wanted was the base 10 logarithm - e.g. LOG10().

Tom Johnson
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Both Math.Sin() and Math.Cos() take radians as their argument, not degrees — so you'll want to take your value 113 for B and do something like B * Math.PI / 180.0. In fact you'll want to do it all three places that B is used, since otherwise it won't make sense to compare its value to Math.PI.

Brandon Rhodes
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