From: Henry Spencer <henry@zoo.toronto.edu>
Newsgroups: sci.space.science
Subject: Re: Satellites in Solar Orbit
Date: Sun, 31 Dec 1995 05:25:55 GMT

In article <4biaah$5ak@lace.colorado.edu> fcrary@rintintin.Colorado.EDU (Frank Crary) writes:
>>Is it not possible to swing by a planet so that the
>>spacecraft is heading directly towards the Sun?
>
>...quantity,
>0.5*A/a + sqrt(a*(1-e)/A)*cos(i)
>will be the same, before and after a flyby...

Sure that's right?  Roy's "Orbital Motion" says it's 1-e^2, not 1-e.

>Given this restriction, a single flyby wouldn't
>get you all that much closer to the Sun. I think
>the best you could do is drop the perihelion by,
>perhaps, a factor of two or three...

Not so; you just have to be sneaky.

The fundamental limitation here is that a/A can't go below 0.5 after a
single flyby (because the orbit must still intersect that of the flyby
planet, so aphelion radius cannot be less than A).  This creates a
problem, because you want to make e nearly 1, dropping the value of the
second term nearly to zero, which requires making the first term larger --
i.e. making a/A smaller -- to compensate.  For a Hohmann transfer from
Earth to Jupiter, a/A is *already* not much above 0.5, so it's hard to
drop it much. 

The sneakiness is, *don't use a Hohmann transfer*.

If your initial a/A is well over 0.5 -- with aphelion well outside
Jupiter's orbit -- then it's no problem to lower a/A somewhat.  As a
bonus, since the sqrt(1-e^2) factor nearly zeros out the second term
no matter what happens to i, you can select inclination freely.

JPL's Starprobe study in the early 1980s achieved a perihelion radius
of four solar radii (at an inclination of 90deg, chosen for best
science return) with a single Jupiter flyby.  It did require very high
launch energy (C3 of 133 km^2/s^2) or else an Earth gravity assist plus
a large midcourse burn (dropping C3 to 31.2 km^2/s^2).
-- 
Look, look, see Windows 95.  Buy, lemmings, buy!   |       Henry Spencer
Pay no attention to that cliff ahead...            |   henry@zoo.toronto.edu