TAU and exploring the heliopause

[Paul F. Dietz]

It was mentioned that TAU will be able to explore the heliopause, the
region where the solar wind gives way to interstellar gas. While I
believe exploring the local interstellar medium is a great idea,
you don't need a HST-class telescope to do it. Nor does one need
nuclear powered ion engines. A recently proposed idea is to drop
a vehicle in an aeroshell through Venus's upper atmosphere to
put it onto a sun grazing orbit. At perihelion you fire a rocket
and get a nice big boost. The probe could then sail to Neptune
in 1.9 years, and could reach the heliopause not too long after.
A spacecraft with plasma measuring instruments and low data rates
would doubtlessly be much less expensive than a full blown astrometric
scope.

[Lew Mammel, Jr.]

> [ ... ] A recently proposed idea is to drop

> a vehicle in an aeroshell through Venus's upper atmosphere to
> put it onto a sun grazing orbit. At perihelion you fire a rocket
> and get a nice big boost. The probe could then sail to Neptune
> in 1.9 years, and could reach the heliopause not too long after.

At first I thought this was a fallacious extension of the gravitational
boost concept used by various planetary probes; the fallacy being that
the sun isn't moving in the solar system frame of reference, so there's
no boost to be had. However, I saw in the nick of time that this boost
is based on a different principle. Here's my analysis:

Starting from the earth's circular orbit, we send the craft into a sun
grazing orbit with an assumed net energy gain of zero. Note that without
a boost the craft would attain a distance of one AU from the sun. This is
because its semimajor axis must remain at 1 AU if the total energy is
unchanged, but now the sun is near one focus of its elongated orbit.

Now we ask, how big a boost does the craft need to achieve escape velocity?
The principle here is that the gain in kinetic energy is approximately
v * Dv, so for a fixed Dv (determined by our booster capability) we can
gain larger boosts in kinetic (and hence total) energy by blasting
near the sun, where v will be large. This apparent freebie is due to
the use of the kinetic energy gained by the rocket fuel in dropping
to lower potential.

To continue, in circular orbit near 1 AU we started with:

E = K + U = U - 1/2 U = - K

so to achieve solar escape we need to add kinetic energy equal to our
orginal kinetic energy. If we let v1 be our speed at perihelion and v0
be our speed at circular orbit near 1AU. I get:

v1 = v0 * ( 2AU/r1 - 1 ) ^ 1/2

based on the assumption of equal total energy. Then since we require

Dv * v1 = 1/2 * v0 ^ 2

We have the requirement:

Dv/v0 = ( 2AU/r1 - 1 ) ^ -1/2

So if we think we can stand to come within, say, .1 AU of the sun we
need Dv = .23 * v0 or about 15000 mph. I think this equation is nice
for a feasibility analysis of the concept. ( Assuming I got it right !)

By the way, I would think that you'd be able to achieve a sun grazing
orbit with increased kinetic energy by using a venusian gravity boost.

Lew Mammel, Jr.