From: mechalas@gn.ecn.purdue.edu (John P. Mechalas)
Subject: Re: Pioneer Venus Out of Fuel, Orbit Deteroriating
Organization: Purdue University Engineering Computer Network
Date: Wed, 7 Oct 92 17:45:21 GMT

In article <1992Oct7.143222.15439@ll.mit.edu> nates@ll.mit.edu ( Nate Smith) writes:
>In article <1992Oct7.004757.24245@gn.ecn.purdue.edu> mechalas@gn.ecn.purdue.edu (John P. Mechalas) writes:
>>Yes, but the radius to the spacecraft changes because of the drag forces.
>>   When a s/c enters the atmosphere, the drag force cause the semi-major axis
>>to decrease by 4 * pi * Drag / n^2 per orbit (assuming a nominally cirular
>>orbit).  The altitude of the s/c also decreases.  Since orbital velocity is
>>inversely proportional to the semi-major axis and the radius, as those
>>terms decrease, the velocity must increase.  Orbital energy is defined as
>>being inversely proportional to the semi-major axis as well, so energy 
>>increases, too.  The result is a more energetic, and more elliptic orbit.
>>   It is very counter-intuitive, as is a lot of orbital mechanics.  :)
>
>well, i'd like to add my 2 cents.
>for the purpose of this argument, do we consider the atmospheric drag to be
>negligible at a certain distance away from Venus?  suppose we do.  then we
>would need to know if the apoapsis is "outside" of the atmosphere.  if so,
>then the drag effect will almost entirely be observed in the apoapsis height,
>as the semi-major axis shrinks.  when all the orbit has fallen into the
>atmosphere, for drag purposes, then the periapsis height will be affected,
>but not in the way we would picture it.  the argument of periapsis is the
>angle between the periapsis point on the orbit and the ascending node, where
>the satellite rises through the equatorial plane of the planet.  this would
>be racing ahead of the satellite, in a mathematical sense, so that by the
>time the satellite reaches the old point of periapsis, that point will have
>advanced around the orbit to a new location.  think of it as "the slowing
>down here reduces the height on the other side", sort of.

I was assuming the entire orbit was in the atmosphere, so drag was a present
effect over the orbit period.  I don't know the specifics of the orbiter
in question...I was just referring to the question about the counter-intuituve
results of drag on spacecraft.

>but if the satellite only briefly dips into the atmosphere, then the effect
>will be as Shari described it: circularization.  of course, by the time the
>apoapsis has been brought into a height equivalent to the original periapsis
>height, the whole orbit will be subject to drag forces.

Hence the term "aerocapture".  :)  It would be an interesting problem to 
determine the "crossover" point where drag goes from "aerocapture" to
the other case.  Meaning, how long in the atmosphere is too long?

>another point:  the semi-major axis reduces, the energy is inversely
>proportional to the semi-major axis, but it is NEGATIVE.  so its magnitude
>will increase, yes, but the satellite LOSES energy.

You are right of course...I did mean to say "magnitude of energy" in my
original post (honest! :).  Either way, though, it's that increase in
magnitude that tends to be a surprise...at least it was to me when I first
learned it.  *smile*

-- 
John Mechalas                                          "I'm not an actor, but
mechalas@gn.ecn.purdue.edu                                 I play one on TV."
Aero Engineering, Purdue University                     #include disclaimer.h
Newsgroups: sci.space