Re: Poynting-Robertson effect

[Leigh Palmer <palmer@sfu.ca>]

> OK, if none of you other fish will bite, I will.

Thanks, Chip; you're a sport!

> In what sense does sunlight "speed up" a planet?  I assume this means it
> increases the planet's velocity, and not, say, its rotation rate.  If so,
> is the planet's orbital angular momentum conserved in the process?

Because light travels at a finite speed, a planet receives the thrust of
the light from a direction which does not coincide with the source of the
light. The Earth, for example, moves in its orbit at about 10**-4 c, and
the sunlight appears to come from a body which is 20.5 arc seconds
displaced from the Sun. It is as if you are walking in a rain which is
falling dead vertical. If you walk the rain does not seem to come from
straight overhead; it comes from a point way above and a little in front
of you. As a result you have rain hitting you in the face at a steeper
angle the faster you move, and regardless of the direction in which you
move.

This effect, which has been known for starlight for more than two
centuries, makes stars appear to be shifted from their actual positions.
It is called the "aberration of starlight" and a discussion of it can be
found in any good astronomy textbook.

Now the Sun's gravity makes planets move in roughly circular orbits around
the Sun. That gravitational force is strictly central; it appears to point
directly to the center of the Sun. That is because the gravitational force
does not in any sense have to propagate; it is a property of the space
itself. Thus the speed of light does not limit it. The planets move
perpendicular to the direction from which gravity seems to come. Sunlight
appears to come from a point a little ahead of the center of the Sun. The
result is that the pressure of sunlight works to decrease the orbiting
Earth's energy, and that, perversely, means it speeds up as the orbit
shrinks!

The force due to sunlight "raining in Earth's face" exerts a component of
force in the direction opposing Earth's orbital motion. This effect, which
is not measurable for planets, is important for interplanetary dust grains
It explains why grains below a certain size have disappeared from the
solar system. They have all been swept into the Sun. It is called the
Poynting-Robertson effect.

> Does the sun do this to all the planets?

Yes. The strength of the effect is proportional to the inverse first power
of the size of the object invoved. It is a surface-to-volume effect. My
titilating you with planets was a device to start discussion, a rhetorical
device. Please forgive the excess. I think that teachers should know about
the Poynting-Robertson effect if they are to teach their students about
radiation pressure. Talking about this effect beats the hell out of
"demonstrating" it with a Crooks radiometer as is so often dome. The
explanation of how the Crooks radiometer actually works should not involve
mention of radiation pressure at all. It is a bit too advanced for
introductory courses in my opinion; I have to go back and look it up
whenever anyone asks (and I can't do it just now).

Leigh