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 Bright light (Posted on 2015-04-09)
When the moon is full, it always looks brightest to us on Earth vs. any other phase since we see its full illuminated area. It’s the same for Mars and the other outer planets, as we see their “full” phase when they are also closest to the Earth, i.e. when they are aligned on the same side of the sun as the earth. Not so for Venus and Mercury. Because their orbital radii are smaller than Earth’s, they present less and less lit surface to an earth-based observer as they approach their closest distance to our planet. Therefore the position at which these two planets look the brightest from Earth is at some point where their orbital radius has some non-zero angle to that of Earth’s.

Develop the relationship on how bright Venus looks from the earth as a function of the angular difference in orbital positions, and solve for the angle where Venus looks the brightest from earth. Simplifying assumptions: the orbits are perfect circles in the same plane, and the orbital radius of Venus is 0.723 that of earth (a good avg. value).

 Submitted by Kenny M Rating: 4.0000 (1 votes) Solution: (Hide) Many online references give the answer as "about 40 degrees separation of orbits, when Venus presents about 27% of it's disk illuminated to the earth." One treatment of the math can be found here: http://articles.adsabs.harvard.edu//full/1999JALPO..42...18G/0000020.000.html

 Subject Author Date I fixed my model. Jer 2015-04-16 10:23:09 re: Interesting question. Charlie 2015-04-10 07:35:28 Interesting question. broll 2015-04-09 23:47:03 comparison with an actual case Charlie 2015-04-09 20:05:18 re(2): GSP Model disagrees with the previous posts Charlie 2015-04-09 17:14:21 re: GSP Model disagrees with the previous posts Charlie 2015-04-09 16:15:01 GSP Model disagrees with the previous posts Jer 2015-04-09 14:19:29 what I get Charlie 2015-04-09 13:03:18 my solution Daniel 2015-04-09 11:36:31

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