Mercury Odd Orbital Behavior?

A friend of Chris Vancil wrote:
In the Nine Planets Site they mention that a person on Mercury would
see this odd behavior: "At some longitudes the observer would see the
Sun rise and then gradually increase in apparent size as it slowly
moved toward the zenith. At that point the Sun would stop, briefly
reverse course, and stop again before resuming its path toward the
horizon and decreasing in apparent size. All the while the stars would
be moving three times faster across the sky. Observers at other points
on Mercury's surface would see different but equally bizarre motions."

Why is this and what is the other "equally bizarre" behavior?

The apparent path of the Sun in the sky of any planet is actually the
combination of two separate motions of the planet. In the case of the
Earth, the most obvious one is its daily rotation. Once a day, the
Earth turns about once on its axis, from west to east. From the point
of view of someone standing on the Earth's surface, the Sun therefore
appears to cross the sky from east to west.

The Sun repeats its daily apparent motion once every 24 hours, on
average. However, the Earth does not rotate once on its axis in exactly
24 hours. Instead, the true rotational period is closer to 23 hours and
56 minutes. So how come the day seems to last 24 hours?

The reason for this is the second planetary motion in question, and that
is the revolution of the planet around the Sun. From the point of view
of an imaginary and highly heat-resistant observer on the Sun, the Earth
appears to revolve from east to west, and as a result, from the Earth,
the Sun also appears to revolve from west to east. (In case that seems
confusing, imagine going around a column in a clockwise direction while
always facing north. The column will appear to you to be revolving in
a clockwise direction around you.)

The Sun's daily apparent motion is therefore the sum of two separate and
also apparent motions: the east-to-west motion caused by the Earth's
rotation, and the much slower west-to-east motion caused by its orbital
motion around the Sun. How much slower? About 366 times slower, so
that the day is about 1/366 times longer than it would be if the Earth's
rotation were the only relevant motion. This brings the 23 hours and 56
minutes up to 24 hours, as expected.

But--remember that I mentioned that the Sun repeats its daily motion
every 24 hours *on average*. This is because although the Earth's period
of rotation doesn't change very much (varying by perhaps 1 part in 1
million throughout the year), its orbital motion does change noticeably.
Its orbit is elliptical, and Kepler's laws of planetary motion tell us
that the Earth therefore changes speeds as it goes around the Sun. When
the Earth is closer to the Sun, it speeds up, and the Sun's apparent
west-to-east motion increases. When it recedes from the Sun, it slows
down, and the Sun's west-to-east motion decreases.

The amount by which that motion acts against the daily rotation of the
Earth therefore is not a constant 4 minutes or so on top of the 23 hours
and 56 minutes, but instead varies smoothly throughout the year. There
are times of the year when the day, as measured by the Sun's return to
the meridian (the north-south line passing directly overhead us), is
more than 24 hours, and other times when it is less. Although the daily
difference is only a matter of seconds, these differences pile up, so
that on some days, the Sun may reach the meridian up to about 15 minutes
before or after the time that it "should," based on a constant orbital
motion. This variation is called "the equation of time," and it comes
up when trying to use sundials to compute the current time accurately,
for instance.

The Earth's orbit, however, is only slightly elliptical. Its distance
from the Sun varies only by a little more than 3 percent throughout the
year. The variation in the Sun's apparent motion doesn't change very
much as a result (about 6 percent, twice the variation in distance), and
its effect is never so great as to ever be *greater* than the rotational
motion (which, after all, is 366 times greater on average). Generally
speaking, we just don't notice.

That is *not* the case with Mercury. First of all, its orbit is much
more elliptical than the Earth's. Its distance from the Sun varies by
some 40 percent, and the Sun's apparent motion, as seen from Mercury,
therefore varies by almost a factor of 2.

More importantly, Mercury's rotation is not hundreds of times faster
than its orbital revolution, but only about 50 percent faster. That
means that if the Sun's apparent motion due to orbital motion were to
increase by 50 percent, it would be enough to counteract the apparent
motion of the Sun due to Mercury's rotation, and the Sun would actually
appear to stand still.

As a matter of fact, Mercury's orbital motion varies so much that it
sometimes is enough to make the Sun actually appear to move *backward*.
If you are standing in the right place on Mercury's surface, you can
actually see a double sunrise or sunset. In the latter case, you would
first see the Sun set. Then, as though it weren't sure of itself, it
would peep back up a short ways. Finally, making its mind up, it would
set back down.

Of course, because Mercury's rotational period is about 59 Earth days,
this whole process would take a long time from a human perspective. But
it would certainly qualify as "bizarre."

Hope that helps.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

I (Brian Tung) wrote:
The Earth's orbit, however, is only slightly elliptical. Its distance
from the Sun varies only by a little more than 3 percent throughout the
year. The variation in the Sun's apparent motion doesn't change very
much as a result (about 6 percent, twice the variation in distance)[*],
and its effect is never so great as to ever be *greater* than the
rotational motion (which, after all, is 366 times greater on average).
Generally speaking, we just don't notice.

That is *not* the case with Mercury. First of all, its orbit is much
more elliptical than the Earth's. Its distance from the Sun varies by
some 40 percent, and the Sun's apparent motion, as seen from Mercury,
therefore varies by almost a factor of 2[*].
[*] In both the cases, I mean the apparent motion *due solely to the
planet's orbital motion*. Sorry about any possible confusion.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

I (Brian Tung) wrote:
The Earth's orbit, however, is only slightly elliptical. Its distance
from the Sun varies only by a little more than 3 percent throughout the
year. The variation in the Sun's apparent motion doesn't change very
much as a result (about 6 percent, twice the variation in distance)[*],
and its effect is never so great as to ever be *greater* than the
rotational motion (which, after all, is 366 times greater on average).
Generally speaking, we just don't notice.

That is *not* the case with Mercury. First of all, its orbit is much
more elliptical than the Earth's. Its distance from the Sun varies by
some 40 percent, and the Sun's apparent motion, as seen from Mercury,
therefore varies by almost a factor of 2[*].
[*] In both the cases, I mean the apparent motion *due solely to the
planet's orbital motion*. Sorry about any possible confusion.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt