My challenge is to both amateur and professional astronomers.

Amateur astronomers, those with money, have equipment that is first-class:
40 centimeter mirror telescopes, computer drive and image enhancement, CCD's, etc.

Some amateur astronomers have already imaged brown-dwarfs, and others have
recorded light intensity dips of exoplanets transiting their parent bodies.
Impressive achievements for amateur astronomers.
I know there are at least three amateur astronomers on habitablezone.com.

OK! Some additional facts.

(1) There are independent 'brown-dwarfs' out there that have been detected [those not orbiting a parent body].

(2) A brown-dwarf can be between 30 - 80 times the mass of Jupiter.

(3) A brown-dwarf can have a diameter between 3 - 4 times that of Jupiter.

(4) Spectra of brown-dwarfs HAVE been obtained...Thus...It is possible to try and obtain a cyclical Doppler-shift
graph of a brown-dwarf, assuming there is a planetary body orbiting the brown-dwarf.

(5) Pro-astronomers have achieved exoplanet detection sensitivity of (+ -) 2-3 meters/second using the Doppler-shift method.

(6) To detect a planet orbiting either an ordinary star, or a brown-dwarf, with a planetary orbital plane that can be viewed
'edge-on' [as opposed to viewing the orbital plane face-on] it must be assumed that the fusion star, or brown-dwarf, would
have a large transverse velocity and a small radial velocity....The ratio of the transverse velocity over the radial velocity would have to be LARGE. [It's best to draw a diagram to visualize this, relative to the observer]

(7) Theorists say that a terrestrial planet forming around a brown-dwarf is unlikely...They could be WRONG; at least
they admit that it's unlikely, NOT impossible...
[My opinion is that there are Earth-mass planets orbiting brown-dwarfs out there]

Taking all these facts together, couldn't it be possible that there is an Earth-mass planet [1/1000th the mass of the 'parent' brown-dwarf] orbiting one of those 'failed' stars?

For instance: An [hypothetical] independent brown-dwarf, of about 30 jovian masses, may have an Earth-mass planet
orbiting it at an orbital radius of perhaps 7 million kilometers [7.0 x 10^9 meters].

The brown-dwarf would have a (GM) value of about 6.3 x 10^18 m^3/s^2.
The Earth-mass planet would have an orbital velocity of about [ 6.3 x 10^18m^3/s^2/ 7.0 x 10^m]^-2
= 30,000 meters/second.
The orbital circumference would be about 44 million kilometers.
The orbital period would be close to 1.5 million seconds [17-18 days]

AND...The brown-dwarf would circle the mass-balance point [baricentric point?] between the two bodies [r = 7,000 kilometers] every 17-18 days.
Doppler-shift velocity = (+ -) 30 meters/second...That's within an detectable range.

BUT! Such an Earth-mass planet, assuming one is found orbiting a brown-dwarf so close, would be subject
to intense greenhouse heating. Remember that brown-dwarfs can radiate heat from the top of their clouds
at temperatures over 1,000 Kelvin. That would make a nearby Earth-mass planet's atmosphere oven hot.
No habitablezone that close.

Alright! Are there any astronomers out there willing to take the challenge?