Here's a difficult astronomical question for me...

[seawasp]

Say that one has various objects in Earth orbit. ("One has various objects in Earth orbit!", yes, yes, thank you verymuch)

Let's say that I can determine dimensions and albedos for these objects, which may range from several meters across down to centimeters.

How can I tell how bright these targets will look to an observer at a given distance? I.e., whether they look like really bright pinpoints, like regular first-magnitude stars, or are invisible to the naked eye? I've been doing some wild guesses and BOTE calculations but I have no idea if I'm even getting close. Let's say the distances of interest are 10km, 100km, 1,000km, and 10k km. And that we're In SPAAACE and thus not having to worry about air, fog, etc. getting in the way.

I did some searches and found all sorts of people who want to use this information, and a lot that assume I know it, but nothing that said "Take your satellite dimensions, overall albedo, and distance, and plug in here to get the apparent visual magnitude."

Comments

[kengr]

I can't find my copy of the various Astronomy on your Calculator/PC books I have. I'm pretty sure there are calcs for that sort of thing in there.

[kira-snugz.livejournal.com]

i have no clue. but if you have a local planitarium.... they should know the maths.

good luck!

[sub-musashi.livejournal.com]

How are they lit? Assuming that they are just lit by the sun, here's a qualitative walkthrough:
-start w solar luminosity. Figure out how much of the sun's light is intercepted by your object (what portion of a sphere at the object's distance is taken up by the object's size)
- multiply that amount of light by the albedo
- find the distance from the object to the observer. Spread out that light on a sphere of a radius equal to that distance. You should get a number in W/m^2.
- convert that number to magnitude (googling should turn that up without much trouble)
- Note that this assumes your observer is getting the "full phase" of the object. If your observer is at an angle, they will see less of the lit face and it will be dimmer.

Let me know if this makes sense.

[mrmeval.livejournal.com]

Know of an app for that? :) How about a program that does 'good enough'?

[sub-musashi.livejournal.com]

Alas I don't - I learned how to do those calcs with pen on paper. But the math isn't very hard (just algebra and geometry) - someone more facile with programming than myself should be able to whip up a quick program. I'm happy to put the formulae together if someone wants to do the programming.

[mrmeval.livejournal.com]

I'm math intolerant. I had a teacher beat that into me. :/

[k-kinnison.livejournal.com]

if you know the dimensions and albedo you know the objects absolute Magnitude. from there it should be a simple calculation of calculation the apparent magnitude of a NEO (near earth object)

http://en.wikipedia.org/wiki/Absolute_magnitude#Solar_System_bodies_.28H.29

http://spaceguard.iasf-roma.inaf.it/NScience/neo/neo-what/ast-charact.htm

http://spaceguard.iasf-roma.inaf.it/NScience/neo/neo-what/ast-magnitude.htm

That should help a bit.

[xpioti.livejournal.com]

If you don't get an answer, I can pass your question along to my uncle. He probably can answer it.

[wizwom.livejournal.com]

Well, the technical bit is:
1300 W/m^2 in Earth orbit when fully lit.
* albedo {amount of incident light reflected}
/ (4 * pi * r ^ 2) {Area of sphere}

that gives incident energy in Watts at where you are.
You could convert that to photons at an average wavelength of ~500nm

A dark-adjusted eye can detect a single photon, if it happens on it.