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Given that Jupiter is 5 AU from our sun and a remote observer viewing our solar system from some other part of our galaxy looks at it. We assume that Jupiter's radius is $11 \times 6700$ km.

What would be the relative brightness (luminosity?) of Jupiter relative to our sun's?

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    $\begingroup$ You may want to clarify the point of the viewer. Title says remote galaxy, while the content suggests some where else in our galaxy. $\endgroup$ Commented Feb 13, 2015 at 15:14
  • $\begingroup$ just edited. I'm assuming that the distance if very very big, yet the remote viewer can detect the light $\endgroup$
    – vondip
    Commented Feb 13, 2015 at 15:28
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    $\begingroup$ Phase of the planet will make difference. Jupiter will only be fully lit when it's directly behind the sun, and not visible at all. $\endgroup$ Commented Feb 15, 2015 at 18:41

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The absolute visual magnitude of the Sun is about 4.8. (This is the Sun's brightness viewed from 10 parsecs).

The brightest visual magnitude for Jupiter is -2.7, when it is about 4 au from the Earth. Using the usual formula we can therefore calculate the absolute magnitude for Jupiter as 25.9. (Note that this is way brighter than the faintest objects seen for instance with the Hubble Space Telescope; but as Jupiter would be separated from the Sun by only 0.5 arcseconds, a telescope with even better angular resolution than the HST would be needed to pick it out of the glare from the Sun).

Thus to first order Jupiter is 21 visual magnitudes fainter than the Sun (a factor of 250 million) . The situation is slightly worse than this because as seen from outside the solar system, Jupiter could not be fully illuminated, because it must have an angular separation from the Sun to be visible at all. A half-illuminated Jupiter would be at least a magnitude fainter (actually a factor $\pi$ for a Lambertian reflector).

But all is not lost. If we we to switch to the infrared, the situation is far more favourable. The approximate ratio of Jupiter/Sun brightness improves from about $1.4 \times10^{-9}$ in the visible to about $2.8\times10^{-8}$ at a wavelength of 10 microns (Traub & Oppenheimer (2010). But this is still a 19 magnitude difference.

The technology to achieve these sorts of contrasts is not quite there yet, even if we were viewing from nearby stars. An example of what is currently possible can be seen with the discovery of a few Jupiter mass planet around the star GJ 504 by Kuzuhara et al. (2013). The star-planet contrast was about 15-16 magnitudes at near-infrared wavelengths of 1-4 microns and with a star-planet separation of 2.5 arcseconds (equivalent to Jupiter as seen from only 2 parcsecs).

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  • $\begingroup$ I got a bit lost with Traub & Oppenheimer's study. How did they come to the conclusion that Jupiter's brightness relative to our sun is 1.4×10^-9? Thanks ! $\endgroup$
    – vondip
    Commented Feb 14, 2015 at 5:44
  • $\begingroup$ @vondip It sounds about right. I arrived a $4\times10^{-9}$ using simple considerations. But as I pointed out, Jupiter would be $\sim 1$ mag fainter, because it could not be at "opposition" and this gives $1.6\times10^{-9}$. T+O indeed appear to have calculated a number at "maximum elongation" - i.e. it is half-lit by the Sun from the observers point of view. For "Lambertian" reflection this appears to reduce the flux by $\pi$, so is in excellent agreement with my calculation. $\endgroup$
    – ProfRob
    Commented Feb 14, 2015 at 9:43
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The absolute magnitude of Jupiter is at best +26 (give or take, depending on how you look at it). The absolute magnitude of the Sun is +4.8. There is a 21 magnitudes difference between them, or a ratio of 2.5 * 10^8 (250 million times brighter), which is huge.

From a 10 parsec distance (basically in our galactic neighborhood, where most visible stars are), the Sun and Jupiter would be approx 0.5 arcsec from each other at best, which is a very tiny angular distance, and there would also be the mentioned 250 mil brightness ratio (or more). It would be very difficult to tell Jupiter from the glare of the Sun with current technology.

At that distance, apparent magnitude and absolute magnitude are equal. So the Sun would be a +5 star (difficult to see with the naked eye, but doable in a dark sky), whereas Jupiter would be a +26 object, impossible to see except in a very large telescope (assuming it would be far from any star, which is NOT the case).

TLDR: Even from not far away, Jupiter would be quickly overwhelmed by Sun's glare, and would be pretty weak anyway.

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