From: henry@spsystems.net (Henry Spencer)
Newsgroups: sci.space.science
Subject: Re: Earth Mass+
Date: Tue, 30 Mar 1999 16:51:01 GMT

In article <7domdi$e5c$1@pith.uoregon.edu>,
Christopher Michael Jones <cjones@ix.cs.uoregon.edu> wrote:
>> >How much has the Earth's mass increased because of the infall
>> >of material and radiation over a year?
>> >What effect does this have on its motions?
>
>> None whatsoever.  Earth's mass is about six billion trillion tons.
>
>I wouldn't say none, haven't you heard of the Yarkovsky effect?
>It's very minor for the Earth, but it's not zero.

Likewise Poynting-Robertson effect, which points the other way.  But both
are small enough (as is the drag from the material infall) that they get
lost in the noise of things like perturbations from undiscovered
asteroids.  So their effect on Earth's motion is zero for all practical
purposes.

For those who aren't up on this stuff...  Both of these effects are due
to light pressure, and hence are significant only for bodies with a lot
of surface area per unit mass, i.e. small ones.

Yarkovsky effect happens with rotating bodies.  Sunlight heats the sunward
side more or less symmetrically, and that energy is lost again as radiant
heat.  But because the rotation carries warm surface along, the heat
emission is *not* symmetrical -- the surface is warmer at sunset than at
sunrise, so the sunset side is emitting more heat.  For a body which
rotates in the same direction as its orbital motion, the sunset side is
the rear side, and the excess heat emission accelerates the body slightly.
This is really major only for bodies on the order of 1m across, although
it has been observed that kilometer-sized asteroids are still affected
enough, over hundreds of millions of years, that it might be significant
in areas like the asteroid belt, where a small change in orbit can put an
asteroid into a resonance with Jupiter (which then causes larger changes).

Poynting-Robertson effect happens with anything.  Because the body is
moving, it experiences what the astronomers call aberration, in which the
velocity of its motion adds (more or less) to the velocity of the incoming
light, and so the sunlight is seen as coming from slightly ahead rather
than exactly from the side.  The loss of the energy by radiant heat is
more evenly distributed, so the net effect is a drag due to light
pressure.  This is major only for dust grains, and significant only up to
a size of a few centimeters.

(Bonus question for the alert student. :-)  Why "Poynting-Robertson", when
in fact it was Poynting who discovered the effect, and Robertson's work
came decades later and only refined it?  Answer in a few days, if nobody
else gets it.)
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)

From: henry@spsystems.net (Henry Spencer)
Newsgroups: sci.space.science
Subject: Poynting-Robertson effect (was Re: Earth Mass+)
Date: Fri, 2 Apr 1999 21:57:05 GMT

In article <37022454.38A9@pdnt.com>, Brian Davis  <bdavis@pdnt.com> wrote:
>> (Bonus question for the alert student. :-)
>> Why "Poynting-Robertson", when in fact it was Poynting who discovered
>> the effect, and Robertson's work came decades later and only refined
>> it?
>
>   I'm guessing here: because Robertson was the first to make sure it
>worked under relativitic theory (Poynting's derivation was classical)?

Close, but not quite.  That's the short version, which you'll find in the
books.  The full story is more obscure but also more interesting.

Poynting noted the existence of the effect in 1903, but with only a rough
sketch of the details.  Obviously, a rigourous quantitative derivation of
the exact size of the effect was his next step.

But it turns out that when you start looking at detail, P-R effect is more
complex than it looks, with subtle complications.  Over the next three
decades, there were half a dozen attempts at a full quantitative analysis,
including two by Poynting himself.  No two of them agreed, and all had
serious flaws.

Robertson's work in 1937 wasn't just the first relativistic treatment of
the effect.  It was the *very first* solid, widely-accepted quantitative
analysis of the effect, relativistic or not.  Which is why his name got
appended to Poynting's.
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)