How does the solar wind move?
I am confused about the solar wind and don't want to
mislead my students. On a web site about magnetic storms I read the following:
"This storm affects
the earth when it is on the western half of the sun, not when it is dead
center. This is because the solar wind follows a curved path between the sun
and the earth not a straight-line path."
Is the solar wind influenced by the magnetic field of the sun so it has a curved path to the earth? Or is this too much of a simplification?
What really happens?
Physics and astronomy get complicated at times. Will the interplanetary
magnetic field curve the path of the solar wind? Without peeking at the
observations, one can only say "it depends," and what it depends on is
the ratio between the density of particle energy (density n times average of
0.5 mv^2) and the magnetic field energy density (B^2/2 mu-zero).
This ratio is often called "beta" in plasma physics, and it's an important
quantity in experiments aimed at confining a plasma for nuclear fusion.
If beta is much less than 1, the magnetic field is the dominant factor
and particles meekly follow its field lines, making containment easy.
Practical fusion however requires a greater beta, and if beta exceeds 1,
the plasma starts pushing the magnetic field around. The way it does so
is by subtly segregating its charges, to create a charge density and
hence an electric field, and electric fields can allow a plasma to move
whichever way it wants.
Suppose the magnetic field is constant and equals B0 in the z
direction, and the plasma is moving along the x axis. Then an electric
field E0= -vB0 in the y direction will allow it to do so, canceling the magnetic force on any electric charge q, equal to qvB0 along -y. (It also works out with spiraling particles).
The same happens with the solar wind, where beta may be 5 or more.
As a result, the solar wind moves radially out, though it gets buffetted
a bit, and it's not clear by what.
Now what about the MAGNETIC field? There is a rule (for plasmas with
high beta, satisfying the "MHD condition"), that "particles that initially share a field line, continue doing so indefinitely" (there exist some extra "fine print" conditions, but we ignore them here).
What follows below is the original answer sent to the questioner. Later this was converted to a graphical exercise, Section S-6a Interplanetary Magnetic Field Lines, linked to section S-6. You can either link there or continue below (or both), as you choose.
Take a sheet of paper, put on it a small circle--that is the Sun viewed from far north of it, or rather, it is a circle in the corona, some level above the Sun, where the solar wind begins. On this scale, let's say the solar wind moves one inch (1") per day (or if you wish, 2 cm). Draw from the center 6 or 7 radial rays 13.3 degrees apart. Mark as "P" the point where the first ray--the one furthest clockwise--cuts the circle. We look at 6 ions located at P, and
therefore presumably on the same field line--let's number them 1, 2...6.
We have advance information that 1 will be released into the solar wind
today, 2, tomorrow, 3 the day after, and so on. Mark P with 1--that is
where ion no. 1 is today.
Next day, P is on the second ray. Point 1 has moved 1" outward, radially, and Point 2 is at the base of the new ray, ready to go. Next day: Point 1
is now 2" out on the first ray, point 2 is 1" out on the 2nd, point 3 at the base of the 3rd, ready to move. And so on.
Five days later, 1 is 5" out on the first ray, 2 is 4" out on the 2nd
3 is 3" out on the 3rd, etc., and 6 is at the base of the 6th ray.
However, all these points started on the same field line, so they are
still strung out along one line. CONNECT THE DOTS marking the outermost ions on the 6th day and you have a spiral line of the interplanetary field: if the ions started on the same line, they must still be on one.
The solar wind in all this has moved radially. But now and then the
sun releases bursts of high energy particles, say from flares. The
energy of these particles may be high enough to endanger astronauts
in interplanetary space--but their density is very low, so their beta is
also low. THEY therefore are guided by the magnetic field lines (rather
than deforming them to their own flow), and therefore they move spirally.
The solar wind takes about 5 days to cover 1 AU. Therefore, if the Earth
is to receive particles guided by an interplanetary field line when it
is on the first ray, the emission has to be at the base of ray 6--that
is, near the western limb. The high-energy particles take only an hour or
so to arrive, depending on their energy of course.
The shape of the orbit of Mars
I have read your articles about stargazers and I believed this is one of
the most interesting subjects in astronomy. Here is a question which came
up when I was reading 'Planetary evolution', could you please help, thanks.
Mars moves in an elliptical orbit around the Sun, what is the relative distance
of the Sun to this ellipse? Would it be at one end of the major axis of the
The eccentricity of the Mars orbit is 0.09337, the semi-major axis
of the orbit is A = 1.524 AU (1 AU is the mean Sun-Earth distance, about
150,000,000 km; AU stands for astronomical unit) and distances of
perigee (closest approach) and apogee (most distant) are B = 1.381 AU
and C = 1.666 AU (letters are just notation for here).
These are the numbers. What do they mean? I remember seeing long ago a
German physics text from the 1920s drawing the orbit of Mars. One side
of the line was a circle, one side was the orbit, and the varying
thickness of the line showed the difference between the two. It was
hard to see that difference!
Let us calculate the length and width of the ellipse. The length (through
the two foci--the line on which the Sun is located) is 2A = B + C = 3.048
or 3.047 AU. The displacement of the center from either focus is D = (C-B)/2 =
0.1425 AU and the width is 2G where
G2 = A2 – D2 G = 1.51732 AU 2G = 3.035 AU
I do not think you or I would be able to distinguish an oval with dimensions
(3.048, 3.035) from a true circle! The position of the Sun at one focus
is however notably asymmetrical, about 10% of the distance from the center
to the edge.
What if the Earth's axis were tilted 90° to the ecliptic?
I was recently looking at the webpage "Seasons of the Year" and I read about what would happen if the earth's axis were perpendicular to the ecliptic. I was just wondering if you could give me some insight on what would happen if the ecliptic was inclined at a 90-degree angle with respect to the celestial equator? Would this mean that earth's orbit would
travel along this "new ecliptic" while the north and south poles are
travelling along this "new ecliptic"?
The hypothetical case you describe does in fact exist: for some
unknown reason, the spin axis of the planet Uranus is almost exactly
in the ecliptic.
That means that at some time one pole (let me call it the north
pole, even though that "north" direction is almost perpendicular
to the northward direction from Earth) points at the Sun. Then the
northern hemisphere is in constant light and the other one in
constant darkness. Half an orbit later--42 years or so--the roles
are reversed. And halfway between those times, the planetary rotation
axis is perpendicular to the Sun's direction, making day and night
alternate in a way similar to what the Earth experiences at equinox.
I leave it as an exercise to you to figure out whether Uranus ever
receives sunlight the way Earth does at solstice.