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In this paper, we learned that Hubble is the only telescope in the vicinity of Earth that can detect Ultima Thule directly. Hubble will eventually fail, and will be somewhat replaced by James Webb. James Webb will operate on a completely different frequency, however. Will James Webb be able to detect Ultima Thule, or objects like it?

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    $\begingroup$ It's an interesting problem! With an albedo of say 0.1, 10% of the sunlight that hits it reflected in the visible (roughly speaking) and 90% is re-radiated in thermal IR (though more widely) so you might think a dark asteroid is always brighter in thermal IR than reflected visible. The problem is that once you get past (very rough) 10 AU, the equilibrium temperature is so low that most of the "thermal" IR is much longer than 30 microns and so outside of the JWST range. So at very large distances, visible light wins. But for NEOs thermal IR wins like crazy. $\endgroup$ – uhoh Jan 7 at 16:03
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    $\begingroup$ No time to do the full calculation right now, might in a few days. See Planck distribution and approximate equilibrium temperature for the math. Cows are spheres and π = 1. $\endgroup$ – uhoh Jan 7 at 16:06
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The JWST sensitivity, per this URL, is as follows:

enter image description here

This page gives us this equation, which gives a resulting thermal equilibrium as follows: $280K [1-A]^{1/4}/a^{1/2}$

Assuming an albedo of 0.1, and a distance of 43 AU roughly, plugging those in gives us about 42 K. The two lobes have a diameter of 19 and 14 km each, so an area of about 283+154=437 km^2. At the distance of the Sun, that would give a solid angle of 1.5546356e-15 radians.

The black body radiation up to 30 um looks like this (Source)

enter image description here

Basically from these charts you can see that where JWST is less sensitive, 2014 MU69 is brighter. That means it is virtually impossible for it to detect from the thermal IR alone.

However, the sensitivity in the NIR is much better then Hubble, and a significant portion of the Sun's light comes in that spectrum. James Webb should easily be able to detect an object as dim as 2014 MU69. I can't find a direct comparison, but it should be quite visible still, better with JWST's larger mirror.

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