Positions of Mercury
Back in the '70s I assumed that whenever an inferior planet reaches maximum elongation (east or west) the radius vector of the planet is perpendicular to that of Earth. Logically, it seemed, the two radius vectors form a right angle whenever the angular distance of Mercury (or Venus) from the sun, as seen from Earth, is at its greatest. For example, if Mercury is at greatest western elongation when Earth is at heliocentric longitude 270 degrees, Mercury "must" be at heliocentric longitude 180 degrees; the separation amounting to a quarter of their orbits. To appear farthest from the sun, I imagined, the radius vector of Mercury couldn't be less than 90 degrees away from Earth's, since the planet wouldn't be fully elongated to one side of the sun.
As the diagram above makes clear, this reasoning was fallacious. Maximum elongation doesn't occur when the radius vectors form a right angle. It occurs when they form an acute angle. The separation of the two radius vectors, at farthest elongation, is far less than the "logical" 90 degrees. It's only about half that.
Why does reality, in this case, seem to defy logic? It's due to varying distances. When the radius vector of Mercury is perpendicular to Earth's, the planet is farther away from us than it is when at greatest elongation. When the planet is farther its angular distance from the sun appears less. Conversely, when it is nearer its angular separation is greater. If Mercury was much farther away its separation from the sun would be much smaller; if the distance were vast the two bodies would appear to merge. So it's not surprising the angular sun-Mercury distance appears greatest when the planet is closer to Earth, instead of when its radius vector is 90 degrees from ours.
Addendum I
When Mercury is at full elongation its radius vector is perpendicular to a line from Earth to Mercury. But that's irrelevant. A line from Earth to Mercury is not a radius vector (a line from planet to the sun).
Addendum II
This fall marks the 20th anniversary of the blog! It's great to see it's still extant and receiving more pageviews than ever. Thanks to all who contributed over the years!
posted by starman at 7:46 AM
7 Comments:
Congrats on the 20th anniversary of your blog!
Thank you--for the congrats and your input!
Can mercury appear most elongated if it's at aphelion when the radius Vectors are perpendicular?
Great question! Under those circumstances, Mercury is approaching aphelion when in its usual position for max. elongation. Since its distance from the sun is almost as far, my guess is that the angular distance is still greatest when at max. elongation i.e., before the radius vectors are perpendicular. It's likely, though, the angular difference is less than usual and the decrease in angular distance (following max. elongation) is slower since Mercury's increased distance from the sun compensates to an extent for its greater distance as seen from Earth.
November 20, 2025
Congratulations on your post! It gives excellent insights.
Thank you Neal!
November 22, 2025
The 20th anniversary of your blog is significant. It shows that you have stayed with it and showed dedication to your academic endeavors.
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