It was not a homework question, and I do not know enough physics to be able to make it more descriptive/specific. Can you help?
Currently the conceptual basis of the question is wrong at a level that poses a real problem.
(And there are vocabulary issues that confuse things: say "thermal energy" not "heat energy", please. Heat is a property of interactions not of objects.)
You asked detectability as a function of something that is not directly (or even closely) related to detectability. To be sure, a good answer would start by setting you straight on that , but it still leaves the question of which of the several ways to proceed from where you started to a answerable question should be taken.
I was not among the close-voters, but I would have chosen "unclear what you're asking" if I had evaluated the question.
The main step to fix it would be to figure out what you really want to ask about. Possibilities include
- Temperature for blackbody objects (are you assuming a size?)
- Total radiated power assuming isotropic radiation
- Radiated intensity along our line of site (for non-isotropic cases)
I closed the question because you're just asking us to do a calculation for you. That kind of question is not what this site is for. Simply asking us to calculate something is one big marker for what we call "homework-like" questions, even though not all calculation requests are actually homework questions.
If you had shown some effort to do the calculation yourself and identified the step at which you got stuck, and asked about the reason you weren't able to proceed past that step rather than just asking us to do the calculation for you, then I would not have closed the question.
Granted, this wasn't the clearest case, but I stand by my belief that the question is not appropriate for the site as is. And none of the edits you've made (as I write this) change the body of the question, so there is no reason my decision would be any different for the current version of the question as opposed to its original form.