<p>A <a href="https://en.wikipedia.org/wiki/Brown_dwarf" rel="nofollow noreferrer">brown dwarf</a> is a <a href="https://en.wikipedia.org/wiki/Deuterium_fusion" rel="nofollow noreferrer">deuterium-fusing</a> substellar object, and, in the cases of the larger ones, a <a href="https://en.wikipedia.org/wiki/Lithium_burning" rel="nofollow noreferrer">lithium-fusing</a> one. They often emit electromagnetic radiation in frequencies that humans cannot see. However, the larger ones tend to emit visible light, if not much of it.</p>
<p>In this scenario, there's an Earth-sized body whose center is 2,000,000 kilometers from the center of a brown dwarf. Assume that the Earth-sized body is functionally identical to Earth in every way except for a lack of cloud cover.</p>
<p><strong>How luminous does the brown dwarf need to be in order to illuminate the Earth-sized body with 0.5 <a href="https://en.wikipedia.org/wiki/Lux#Illuminance" rel="nofollow noreferrer">lux</a>/0.5 <a href="https://en.wikipedia.org/wiki/Lumen_(unit)" rel="nofollow noreferrer">lumens</a> per square meter of visible light at <a href="https://en.wikipedia.org/wiki/Noon#Solar_noon" rel="nofollow noreferrer">high noon</a>?</strong> Assume that the Earth-sized body has an atmosphere identical to Earth's, except without cloud cover capable of reflecting said visible light.</p>
<p>Note that I'm not referring to <a href="https://en.wikipedia.org/wiki/Radiant_flux" rel="nofollow noreferrer">radiant flux</a> per unit area here here; radiant flux per unit area is the total of <em>all</em> electromagnetic striking a certain area, whereas <em>I'm</em> referring to <a href="https://en.wikipedia.org/wiki/Luminous_flux" rel="nofollow noreferrer"><em>luminous</em> flux</a> - that is, the amount of <em>visible light</em> striking a certain area. Certainly, there'll more energy striking the Earth-sized body then what's visible, but, in this question, I'm only referring to visible light.</p>

CC BY-SA 4.0
2022-01-30T17:32:39.247Z
Why does it have to be an Earth-sized planet? The rest of the question is ill-defined since the luminosity and temperature of a brown dwarf depend hugely on their age and mass.
ProfRob
CC BY-SA 4.0
2022-01-30T20:18:29.893Z
@ProfRob Not sure, actually, but I figured that it would just make it easier for the person answering the question. As for the age and mass, I plan on asking another question about that later, once I know how luminous it is.
KEY_ABRADE
CC BY-SA 4.0
2022-01-30T20:54:10.710Z
The luminosity and luminous flux will vary by many, many orders of magnitude depending on the mass and age. For most brown dwarfs (except those at very young ages) the answer is essentially zero. How close to zero it is will depend on the very poorly modelled and almost entirely immeasurable V-band flux from a cold brown dwarf.
ProfRob
<luminosity><radiation><brown-dwarf><visible-light><electromagnetic-spectrum>
How luminous does a brown dwarf have to be to illuminate an Earth-sized planet with 0.5 lux at 2,000,000 kilometers away?
KEY_ABRADE
# How luminous does a brown dwarf have to be to illuminate an Earth-sized planet with 0.5 lux at 2,000,000 kilometers away?

(Asked by: username_0 on 2022-01-30)

A [brown dwarf](https://en.wikipedia.org/wiki/Brown_dwarf) is a [deuterium-fusing](https://en.wikipedia.org/wiki/Deuterium_fusion) substellar object, and, in the cases of the larger ones, a [lithium-fusing](https://en.wikipedia.org/wiki/Lithium_burning) one. They often emit electromagnetic radiation in frequencies that humans cannot see. However, the larger ones tend to emit visible light, if not much of it.

In this scenario, there's an Earth-sized body whose center is 2,000,000 kilometers from the center of a brown dwarf. Assume that the Earth-sized body is functionally identical to Earth in every way except for a lack of cloud cover.

**How luminous does the brown dwarf need to be in order to illuminate the Earth-sized body with 0.5 [lux](https://en.wikipedia.org/wiki/Lux#Illuminance)/0.5 [lumens](https://en.wikipedia.org/wiki/Lumen_(unit)) per square meter of visible light at [high noon](https://en.wikipedia.org/wiki/Noon#Solar_noon)?** Assume that the Earth-sized body has an atmosphere identical to Earth's, except without cloud cover capable of reflecting said visible light.

Note that I'm not referring to [radiant flux](https://en.wikipedia.org/wiki/Radiant_flux) per unit area here here; radiant flux per unit area is the total of *all* electromagnetic striking a certain area, whereas *I'm* referring to [*luminous* flux](https://en.wikipedia.org/wiki/Luminous_flux) - that is, the amount of *visible light* striking a certain area. Certainly, there'll more energy striking the Earth-sized body then what's visible, but, in this question, I'm only referring to visible light.

**Tags:** luminosity, radiation, brown-dwarf, visible-light, electromagnetic-spectrum
> **Comments:**
> **username_1**: Why does it have to be an Earth-sized planet? The rest of the question is ill-defined since the luminosity and temperature of a brown dwarf depend hugely on their age and mass.  
> **username_0**: @ProfRob Not sure, actually, but I figured that it would just make it easier for the person answering the question. As for the age and mass, I plan on asking another question about that later, once I know how luminous it is.  
> **username_1**: The luminosity and luminous flux will vary by many, many orders of magnitude depending on the mass and age. For most brown dwarfs (except those at very young ages) the answer is essentially zero. How close to zero it is will depend on the very poorly modelled and almost entirely immeasurable V-band flux from a cold brown dwarf.  

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## 0 answers

