Or, a Summer Internship at NASA-Goddard

I'm spending the summer of 2002 in Washington, DC, along with every other intern on the face of the planet, except that I'm working at the Goddard Space Flight Center instead of with a Senator.   It's a long commute out to Greenbelt, MD, but I'm getting lots of good reading done on the way!   Anyway, I'm interested in dust in the solar corona.   My project is a review of the work done on the problem, so NASA will have all the information in one place when it's planning a mission to explore that hot region.   It's a project that has many tangents, and I've created this space to record some of the things I've learned during my time here.   An official journal is being kept on the SPS ( Society of Physics Students ) webpage, so check that out for more rigorous detail of my project.

 topics included:
poynting-robertson drag
the yarkovsky effect
brownian motion
magnetic effects

poynting-robertson drag
Our solar system is permeated by dust particles, which are constantly being bombarded by radiation from the Sun.   Poynting-Robertson drag occurs because a grain of dust will absorb energy preferentially from one direction (i.e., the Sun), but will re-emit the energy equally in all directions.   By slowing the particle down, the disparity of the radiation pressure causes the particle to slowly spiral into the sun, assuming it is a sphere in thermal equilibrium.

In general, the radiation pressure pushes on objects radially, providing an outward pressure.   But since the objects are moving in orbits around the Sun, there's also a small damping effect in the θ-direction.   One can visulaize this drag in two ways: first, in the reference frame of the dust particle.   From the point of view of the dust, the radial radiation will be coming towards it at a slight angle, because the dust is moving perpendicular to the radiation.   (The angle is very small because the radiation is moving at velocity  c while the dust grain's velocity,  v, is decidedly non-relativistic.)   The incoming radiation energy thus has a slight  θ-component, which serves to slow the particle down.   The loss of kinetic energy eventually causes the particle to spiral into the Sun.

Shifting to the reference frame of the solar system, the grain seems to absorb the sunlight entirely in the radial direction.   Instead, it is the  re-emission of energy that is uneven, because the particle is moving in the Sun's reference frame.   The anisotropic radiation serves to carry angular momentum away from the particle, thus slowing it down and decaying the orbit.

The flux of radiation from the Sun depends directly on its luminosity  Ls and inversely on the square of the grain's distance  R.   (It goes as  Ls/4πR2.)   Thus, the effect is greater for particles that are closer to the Sun, assuming all other parameters are the same.   For grains in highly elliptical orbits, Poynting-Robertson drag will be more pronounced near perihelion.   The phenomenon will therefore reduce the eccentricity of an orbit as well as its total energy.

The best explanation of Poynting-Robertson effect I found was in section titled "Dynamical Behavior of Dust in Space," from the  Comets and Meteors chapter of the trusty Physics and Chemistry of the Solar System, John S. Lewis, Academic Press: New York, 1997.

 The original papers:
Poynting, J. H. (1903).   Radiation in the Solar System: Its Effect on Temperature and Its Pressure on Small Bodies.    Royal Society of London Philosophical Transactions, Series A, 202, 525-552.

Robertson, H. P. (1937).   Dynamical Effects of Radiation in the Solar System.     Monthly Notices of the Royal Astronomical Society, 97, 423-438.

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the yarkovsky effect
(a small corollary to the poynting-robertson effect)
The basic explanation of Poynting-Robertson drag assumes a great deal about the particle: that it is spherical, not spinning, and in thermal equilibrium.   The spin of the grain, however, combined with thermal dis-equilibrium, can disturb the effectiveness of Poynting-Robertson drag.

For a medium-sized rocky object, anywhere from a few centimeters to a kilometer in size, thermal energy travels more slowly through the body and will result in uneven heating.   In such cases, the thermal profile will mimic that of larger asteroids or even planets.   That is, the temperature will be highest at the equator at noontime, and lowest nearer the poles and just before dawn.   For a prograde-rotating object, the warmer side of the body is the trailing one, i.e., it will radiate more energy behind it.   Such bodies may actually be accelerated by their radiation, pushing them further from the Sun.   On the other hand, retrograde-rotating objects will radiate more strongly on their leading side, slowing themselves down and compounding the effects of Poynting-Roberston drag.   The Yarkovsky effect is more pronounced for smaller bodies because of their smaller mass-to-surface-area ratio, which makes the small differential accelerations more effective.

 Source: the aforementioned Lewis text, Physics and Chemistry of the Solar System.

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brownian motion
Aside from being a clever name for the Brown University Ultimate team, Brownian motion is an interesting phenomenon that is relatively simple to explain.   It was first observed in 1827 by a botanist named Robert Brown (how lucky!), who noticed that grains of pollen suspended in solution were not stationary under the microscope, but jittered around as if they were alive.   The motion was observed even with old pollen grains, so it was not likely that the pollen was living and moving.   Einstein explained the what came to be known as Brownian motion in a 1905 paper, saying that the small particle was moved around by the bombardment of the molecules in which it was suspended.   If a small grain were suspended in water, the molecules would be moving about randomly, often bouncing off the particle.   Overall, the motions are random, so it is expected that the grain's random walk wouldn't take it very far.   But on short time scales, the grain might be seen to move about considerably.

 A java applet that demonstrates the phenomenon of Brownian motion:
by Dr. Jim Carlson at the University of Utah

Brownian motion was the first hard evidence for the existance of atoms; that's its significance.  Einstein hypothesized that it should exist before he knew of Brown's observations, and others used the phenomenon to learn about atoms.  In 1926, a professor at the University of Paris, Jean Baptiste Perrin, won the Nobel Prize for using Brownian motion to calculate Avagadro's number.  Recently, however, scientists have begun to speculate whether Brown observed the movement that bears his name or not.  In 1991, Daniel H. Deutsch submitted an abstract to the  bulletin of the American Physical Society in which he hypothesized that with Brown's microscope (which had a magnification power of 350x) and the size of grain he was studying, Brownian motion would have been on too small a scale for him to observe directly.  Perhaps the motions of the particles were simply evaporation or convection currents in the water droplet, or vibrations of the building in which it was housed.  Nevertheless, Brownain motion has been observed since, and perhaps would have taken much longer to identify without Brown's observations.  It's not going to loose the nomenclature of "Brownian" any time soon, that's for sure.

A good one-page summary of Brownian motion and speculation as to what Robert Brown observed (and a photo of Brown looking delightfully grumpy and academic) was published as "A Small Disturbance: Did experimental obstacles leave Brown motionless?" in  Scientific American, 265:3, 20, 1991.

 The original papers:
Einstein, A. (1905).   The Theory of The Brownian Movement.    Ann. der Physik, 17, 549.

Brown, R. (1927).   A Brief Account of Microscopical Observations, etc., London. [Not published.]

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magnetic effects
dust particles in the solar wind
The solar wind is a particle and magnetic field flux, eminating from the sun and composed mostly of protons, electrons, and ions.  These charged particles move outward from the Sun radially, spiraling around the magnetic field lines.  The magnetic field in the solar wind is, for the most part, one polarity in the Sun's northern hemisphere and the opposite in the southern, an effect of the Sun's own magnetic field.  At the magnetic equator, therefore, the two polarities meet and a strong current flows across the gradient, producing a plane at the equator of the solar wind that is essentially neutral.  The plane of the ecliptic, in which the Earth revolves, is nearly aligned with this "neutral sheet."  Since the sheet is not rigidly fixed, the Earth sometimes experiences one magnetic field polarity and sometimes the other.  As a result, the solar wind in the ecliptic has a "sector" structure that contains an average of six positive and negative regions.

Enter the dust particles.  These grains, orbiting around the Sun (or slowly spiraling into it under the effect of Poynting-Robertson drag, as the case may be) posess a small amount of positive electric charge.  The charge comes from the ionization of molecules on the grain surface, a result of UV bombardment.  The dust grains are, therefore, charged particles moving through a magnetic field, subject to Lorentz forces.  The radial magnetic field and orbiting dust grains result in a Lorentz force ( B x  qv) pointing out of the plane of the ecliptic.  The grains' trajectories will turn upward (assuming prograde orbits) in regions of positive magnetic field and downward in regions of negative.  In the ecliptic, where the sector structure exists, the overall motion of the particle in the  z-direction will be zero.  The effects of the positive and negative regions will cancel one another out, overall, but there will be a slight oscillation from the ecliptic plane.

Outside the ecliptic, however, there would be no cancelling of the Lorentz force.  If the northern hemisphere were producing a positive magnetic field, the dust grains' trajectories would would be pushed further north.  The southern hemisphere, with its negative magnetic field, would have the opposite effect.  As a result, the dust grain would move into a higher-inclination orbit.  Since the magnetic field polarity of the Sun flips with the eleven-year solar cycle, the Lorentz forces would flip as well, and the grain would move into a lower-inclination orbit for the subsequent eleven years.  Much of the dust, however, is in the plane of the ecliptic.  (According to one model in one paper I've read, anyway.)  Perhaps there is some imbalance of forces that would reduce the orbital inclinations over many cycles?  I don't know.  I'm speculating.  Most likely it's the same collisional damping/oblate gravitational field phenomenon that pushes satellites and ring systems into the orbital planes of the gas giants.  But it's an interesting thought, nonetheless.

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