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# Venus and the earth are about the same size. However, viewed from Venus, the earth at its best would appear six times brighter than Venus ever appears to the Earth. This is despite the fact that the earth is farther away from the sun! How can you explain this paradox?

Question #24969. Asked by Nude Dude. (Dec 08 02 2:42 PM)

sequoianoir

I was about to say that I was not sure there is a paradox because I didn't believe it was true.
I'd be very interested to see the evidence myself.
However I have come up with a possible theory.

The ALBEDO (reflectivity) of the Earth is 0.39
Venus has an albedo of 0.59
This means 39% of sun light directed towards the planet's surface is reflected by the Earth , 59% by Venus.
Since Venus is much closer to the Sun more light actually hits the surface than does the Earth (calculated by some inverse square law re distance).
Looking at the Solar system from outside , say in a space craft half a light year away, Venus would actually appear over 2 and a half times brighter than the Earth.
This being the case, if it is true, then it must be down to the conditions under which it is possible to look at Venus from the Earth and vice-versa.
The only thing that springs to mind is that you cannot view Venus 'at night'
Being nearer to the Sun than the Earth, you have the problem (as you asked in another question) of it setting shortly after the Sun and only viewed in the 'morning' or 'evening'.
The magnitude (apparent brightness) of an object overhead is much better than one viewed near to the horizon and better still the darker it is.
On Venus the Earth would be an 'outer planet' and this would be possible.

 Dec 08 02, 7:55 PM
sequoianoir

Having had a little longer to consider this, I have decided that my original thoughts could not explain a six times difference.
Then I thought about my answer to the question regarding the 'non linear' brightness of different phases of the moon.
On Venus it is possible to view the full face of the planet Earth fully illuminated by the Sun (from behind the observer) with a 'viewing' distance that is the difference between the two planets orbits radii.
Earth = 93,000,000 miles, Venus = 67,000,000 miles (approx)
Observer on Venus is 26 million miles from fully illuminated Earth.
Whilst reversing the viewing position gives the same distance, the REAR of the plant Venus is lit by the Sun and the front is in darkness.
As Venus goes around the Sun, it goes through viewing phases, just like the Moon around the Earth. When it is 90 degrees lit (first/last quarter) only 10 percent light is directed towards Earth.
When it is fully lit (full moon) 'Full' Venus is the opposite side of the Sun to the Earth. This means the veiwing distance is the 2 plants radii ADDED together. 93 + 67 = 150 million miles.
Although Venus 'shines' 2.5 times more than the Earth, at that distance it would be apparently look 6 times dimmer !

 Dec 08 02, 11:41 PM
Nude Dude

This is the correct answer - As Venus revolves within the earth's orbit, its sunlit hemisphere is presented to the earth in varying amounts. It shows its full phase at the time of superior conjunction, the quarter phase on the average near the elongations, and the new phase at the inferior conjunction. Paradoxically, Venus is at its brightest not when it is nearest the earth (its new phase), but in its crescent phase (about 5 weeks before and after the new phase). On the other hand, the earth, being farther away from the sun than Venus, presents all of its illuminated hemisphere toward Venus when the two planets are closest.

 Dec 09 02, 1:00 AM

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