
The maths that made Voyager possible - nekojima
http://www.bbc.co.uk/news/science-environment-20033940
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lutusp
A quote: "Undeterred by the fact that some of the finest minds in history,
including Isaac Newton hadn't solved the three-body problem, Minovitch became
focused on cracking it."

This is misleading. The three-body problem is known to be insoluble in closed
form, but anyone cam model it numerically. The person being describes was one
of the first to do this, but the comparison with Newton is misleading.

Many kinds of problems are soluble through numerical modeling that aren't
remotely soluble in closed form, and it is important to distinguish between
the two kinds of solution.

On reading the article, it occurs to me that the author simply doesn't
understand the math well enough to grasp the difference between an analytical
and a numerical solution.

~~~
alphaBetaGamma
Moreover, "three body problem" is generally meant to mean the three bodies
with comparable mass, so they influence each others trajectory. But in this
case, Mass_sun >> Mass_planet >> Mass_probe, which greatly simplifies the
problem.

Nonetheless, kudos to the guy to understand that a gravitational slingshot is
possible, and proving it.

~~~
gizmo686
Theoretically, that doesn't simplify the problem at all. Practically, we can
say that Mass_probe=0, in which case we have a 2-body problem. We need to do
that even if we do find a closed form solution to the n-body problem (which
might be provably impossible), becuase in reality there is an infinite number
of bodys in the system.

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yanowitz
My biggest take away was that, and I can't believe I didn't know this already,
the Voyager probes relied on once-in-a-couple-centuries planetary alignments.
I wonder how long until propulsion technologies make that irrelevant.

~~~
T-hawk
Well, specifically only Voyager 2 did to reach Neptune. Voyager 1 slingshot
only Jupiter-to-Saturn, which is available much more often in a much larger
set of planetary positions. Pioneer 11 was essentially rerouted on the fly to
do that, and Cassini also flew a planned Jupiter-Saturn trajectory.

There's also a bit of a multiple endpoints situation in singling out the
4-out-of-4 giant planets scenario. That is indeed infrequent, but say a 3-out-
of-4 lineup with either Uranus or Neptune, or 4-out-of-5 with Uranus and Pluto
as the final two [dwarf] planets, also would have made for a fine and
successful mission.

OTOH, we could even argue that we were _un_ lucky that the giant planet
alignment occured for that 1977 launch window. If it occurred this decade
instead, we could send a much better spacecraft with the capabilities of
Cassini or Messenger or New Horizons.

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EvanMiller
There is more information on Michael Minovitch's website:

<http://www.gravityassist.com/>

He sounds rather bitter that his story has not made him more famous, and comes
off as something of a crank at that ("How Did Minovitch Discover (Create) His
New Theory Of Space Travel?"). I think Minovitch is basically an engineer at
heart, and is resentful that all of the attention seems to go to the
scientists, i.e. people who come up with the actual physical theories about
mass and energy and so forth.

Our culture does value scientists more than engineers. You could argue that
this is good because theories are universally applicable and represent
fundamental understanding, or that this is bad because many theories have
absolutely no applications and that it's the engineers who deliver value to
society. You could also argue that the amount of prestige that we heap on
scientists tends to go to their heads and they stop doing good work. But
whatever. Stay sharp, do what you're best at, and don't pay attention to other
people's benefits packages.

~~~
mturmon
Thanks for that link. Minovitch seems to still live in LA.

He also mentions his solution as addressing the three-body problem, so maybe
that's where the writer of the linked article got misled on that point. Too
bad the writer of TFA didn't check this out with an independent expert.

The group at JPL that Minovitch mentions is still intact
(<http://ssd.jpl.nasa.gov/>). They provide the highest-quality ephemeris
available anywhere (AFAIK) to all NASA missions.

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S4M
I had no idea before reading this article that it was hard to escape from the
attraction of the sun! It makes me wonder if we now have the capabilities to
build a rocket that can do it without the help of the attraction of the outer
planets.

Does somebody here who's knowledgeable on the subject have some reference?

~~~
grecy
I watched the Dawn spacecraft[1] launch, it uses an ion propulsion drive which
Wikipedia says can perform a velocity change of over 10 km/s over the mission.

My understanding is that if they left the ion drive on long enough, the craft
would continue to accelerate.

[1][http://en.wikipedia.org/wiki/Dawn_%28spacecraft%29#Propulsio...](http://en.wikipedia.org/wiki/Dawn_%28spacecraft%29#Propulsion_system)

~~~
uvdiv
It can be much better than that. The ion thrusters in Dawn have a specific
impulse of 3,100 seconds (30 km/s exhaust velocity). Later thrusters designed
for the Jupiter Icy Moons Orbiter achieved 9,600 seconds in a lab (94 km/s
e.v.) JIMO itself is designed for a delta-v of 40 km/s.

<https://en.wikipedia.org/wiki/High_Power_Electric_Propulsion>

<https://www.lpi.usra.edu/meetings/jimo2003/hartman.pdf>

delta-v is proportional to the specific impulse (or exhaust velocity), and
logarithmic in the propellant ratio. For instance, with a propellant ratio of
e = 2.7, you can get a delta-v equal to the exhaust velocity. For a delta-v
twice that, you need a propellant ratio of e^2 = 7.4. Obviously it's not
practical to go much faster the exhaust velocity; the propellant demand grows
exponentially.

<https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation>

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nodrama
I always wondered why would you send a probe around a planet... It seemed
dumb. But it seems that the probe would steal some energy from the planet's
speed <http://en.wikipedia.org/wiki/Gravity_assist>

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pmiller2
I was expecting something more like this:
<http://en.wikipedia.org/wiki/Binary_Golay_code>

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tdrgabi
unrelated to the article, sorry for hijacking but I'm very curios why people
like SparrowOS post things like that?

What do they have to gain from it?

~~~
tokenadult
You are asking about a top-level comment that many users will not see (because
it is autokilled on submission, presumably because the author has been
hellbanned for previous off-topic comments like that). Usually, I read HN with
"showdead" turned off in my user profile. Once in a while, I turn showdead
back on, only to be reminded why many comments and stories are killed on
submission.

