TITLE: Oort Cloud Detection
QUESTION [5 upvotes]: The hypothetical Oort cloud is an explaination for long period comets. It presumably is made up of icy bodies orbiting up to 50,000 AU from the Sun. If so, shouldn't the Spitzer IR telescope have  detected the radiation generated by solar energy from such a spherical cloud?

REPLY [2 votes]: Wikipedia puts the Spitzer Cold mission imaging capability in the band 3 -- 180 micrometers.
I calculate the blackbody temperature that would have a peak emission at the extreme of that band like this:
The frequency is
$$ \nu = \frac{3.0 \times 10^8 \text{ m/s}}{180 \times 10^{-6} \text{ m}} = 1.7 \times 10^{12} \text{ Hz} $$
And from that a corresponding temperature of
$$ T = \frac{1.7 \times 10^{12} \text{ Hz}}{59 \times 10^9 \text{ Hz}} = 28 \text{ K} $$
OK. What to compare that to?
Wolfram Alpha puts the surface temperature of Pluto at around $44\text{ K}$, so Spitzer Cold should have been able to image Pluto.
Unfortunately, Wolfram also puts the radius of Pluto's orbit at around 40 AU. The Oort cloud objects would somehow need to be 2/3 or Pluto's temperature to have been (just barely!) visible to Spitzer Cold. This is not my specialty, but I kinda doubt it.
{"set_name": "stack_exchange", "score": 5, "question_id": 8284}