<p>Assume the object is small, spherical, and illuminated only by the Sun, and has some apparent motion. The object is either: <br></p>
<p>a) white - reflecting 100% perfectly diffusely (assume low temperature) <br></p>
<p>b) black - absorbing 100% and in uniform thermal equilibrium re-radiating infrared  <br></p>
<p>c) Arrokoth-like - having a similar albedo spectrum (reddish) and temperature (?).  <br>  (Is it possible/likely that JWST could find a new target for New Horizons to visit?) <br></p>
<p>d) Voyager-like - having ~5 kW of RTGs at ~570 K (<span class="math-container">$\lambda_{max} = 5 \mu m$</span>). <br>
(At what distance could JSWT still see Voyager?) <br></p>
<p>[Edit responding to @astrosnapper] <br>
It may be a rather artificial question, but assume we know closely where to look, e.g. the object is known to be in the field of view.</p>
<p>I'm adding a quick back-of-the-envelope calculation that answers the last question (JWST &amp; Voyager): <br></p>
<p>Sun's apparent <a href="https://en.wikipedia.org/wiki/Absolute_magnitude" rel="nofollow noreferrer">bolometric magnitude</a> is −26.832 corresponding to 3.0128×10^28 Watts of power. Voyager with 5 kW would have an apparent magnitude of <br> −26.832 - 2.5log10(5000/(3.0128×10^28)) = 35.1 at 1 AU. <br> JWST has a limiting magnitude of 34, So Voyager RTGs are not quite visible to JWST at 1 AU and obviously totally invisible at 155 AU :-(</p>

CC BY-SA 4.0
2022-01-15T00:59:04.743Z
Presumably you are referring to detecting known things (or at least very common things) ? Both JWST and HST have tiny fields of view, making them terrible for performing surveys for rare and faint objects because it's so expensive in terms of time. The HST search for a post-Pluto flyby target for New Horizons ([Stern et al 2018, Section 5](https://arxiv.org/pdf/1806.08393.pdf)) was only granted time after several years' search with 8m telescopes + wide field cameras and coming up empty (due to stellar crowding)
astrosnapper
CC BY-SA 4.0
2022-01-15T01:37:47.343Z
@astrosnapper Excellent point. I'll try to clarify/restrict the question
Roger Wood
CC BY-SA 4.0
2022-01-16T04:36:11.340Z
What's a) white and b) black and c) red all over? (A newspaper)
uhoh
CC BY-SA 4.0
2022-01-16T19:32:26.490Z
@uhoh hah! yes.  That would be interesting. I'm guessing a newspaper has an albedo of ~0.8 and is spectrally flat. but there's probably not very many in heliocentric orbit.
Roger Wood
CC BY-SA 4.0
2022-01-17T15:08:45.827Z
@uhoh  or a bleeding zebra.    But back to the question: what's the shortest focal range design for each of these 'scopes?
Carl Witthoft
CC BY-SA 4.0
2022-01-17T22:13:46.047Z
@CarlWitthoft a newspaper is "read" all over; it's a joke based on a homophone. The primary focal length of JWST and Hubble are in Wikipedia, but in each case some instruments  have optics that optimizes to a different focal length at a secondary focal plane.
uhoh
CC BY-SA 4.0
2022-01-18T12:37:24.427Z
@uhoh -- are you seriously trying to explain a stupid American joke to an American?  :-) .   The "zebra" followup is a meta-joke   almost as old as the original.
Carl Witthoft
CC BY-SA 4.0
2022-01-18T13:08:05.967Z
@CarlWitthoft I'm not sure; for me anything to do with humor is a challenge
uhoh
<solar-system><hubble-telescope><kuiper-belt><infrared><james-webb-space-telescope>
How do JWST and Hubble compare in detecting small bodies in the solar system that are a) white, b) black, c) Arrokoth-like, d) Voyager-like?
Roger Wood
# How do JWST and Hubble compare in detecting small bodies in the solar system that are a) white, b) black, c) Arrokoth-like, d) Voyager-like?

(Asked by: username_0 on 2022-01-14)

Assume the object is small, spherical, and illuminated only by the Sun, and has some apparent motion. The object is either:

a) white - reflecting 100% perfectly diffusely (assume low temperature)

b) black - absorbing 100% and in uniform thermal equilibrium re-radiating infrared

c) Arrokoth-like - having a similar albedo spectrum (reddish) and temperature (?).   
 (Is it possible/likely that JWST could find a new target for New Horizons to visit?)

d) Voyager-like - having ~5 kW of RTGs at ~570 K ($\lambda\_{max} = 5 \mu m$).   
(At what distance could JSWT still see Voyager?)

[Edit responding to @username_1]   
It may be a rather artificial question, but assume we know closely where to look, e.g. the object is known to be in the field of view.

I'm adding a quick back-of-the-envelope calculation that answers the last question (JWST & Voyager):

Sun's apparent [bolometric magnitude](https://en.wikipedia.org/wiki/Absolute_magnitude) is −26.832 corresponding to 3.0128×10^28 Watts of power. Voyager with 5 kW would have an apparent magnitude of   
 −26.832 - 2.5log10(5000/(3.0128×10^28)) = 35.1 at 1 AU.   
 JWST has a limiting magnitude of 34, So Voyager RTGs are not quite visible to JWST at 1 AU and obviously totally invisible at 155 AU :-(

**Tags:** solar-system, hubble-telescope, kuiper-belt, infrared, james-webb-space-telescope

> **Comments:**
> **username_1**: Presumably you are referring to detecting known things (or at least very common things) ? Both JWST and HST have tiny fields of view, making them terrible for performing surveys for rare and faint objects because it's so expensive in terms of time. The HST search for a post-Pluto flyby target for New Horizons ([Stern et al 2018, Section 5](https://arxiv.org/pdf/1806.08393.pdf)) was only granted time after several years' search with 8m telescopes + wide field cameras and coming up empty (due to stellar crowding)  
> **username_0**: @username_1 Excellent point. I'll try to clarify/restrict the question  
> **username_2**: What's a) white and b) black and c) red all over? (A newspaper)  
> **username_0**: @username_2 hah! yes.  That would be interesting. I'm guessing a newspaper has an albedo of ~0.8 and is spectrally flat. but there's probably not very many in heliocentric orbit.  
> **username_3**: @username_2  or a bleeding zebra.    But back to the question: what's the shortest focal range design for each of these 'scopes?  
> **username_2**: @CarlWitthoft a newspaper is "read" all over; it's a joke based on a homophone. The primary focal length of JWST and Hubble are in Wikipedia, but in each case some instruments  have optics that optimizes to a different focal length at a secondary focal plane.  
> **username_3**: @username_2 -- are you seriously trying to explain a stupid American joke to an American?  :-) .   The "zebra" followup is a meta-joke   almost as old as the original.  
> **username_2**: @CarlWitthoft I'm not sure; for me anything to do with humor is a challenge  

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## 0 answers

