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Introducing a third object into the Earth-Moon system

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Frank Scrooby

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Jul 7, 2004, 3:07:03 AM7/7/04
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Hi all

How massive an object could you introduce into the Earth-Moon without
hideously screwing everything up?

For purposes of a story I'd like to write I want a very dense object to
suddenly arrive in Earth orbit (about half-way between Earth and the Moon -
and no it is not a singularity - its nowhere near that dense!).

I am happy (more than happy) for it to trash any or all of Earth's
artificial satellites, de-orbit, impact, gravity sling, whatever.

I don't mind it having some environmental impact on Earth (like say an 1 mm
adjustment in tides) or the occasional (once monthly) stronger than usual
storm but on the whole I don't want it shredding the planet's atmosphere,
ripping up pieces of the crust or generally causing any extinction level
events.

So how big can this thing be? How many billions of tons?

And is half-way a convenient orbit?

Would it take this object one week to orbit the earth at this distance?

How long can this system remain stable with both the Earth and the Moon's
gravity wells affecting this object?

If there is an online resource where I can find these answers out please
point me in that direction.

Thanks and regards
Frank Scrooby


anon...@coolgroups.com

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Jul 7, 2004, 10:42:03 AM7/7/04
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From: "Frank Scrooby"

"
And is half-way a convenient orbit?

Would it take this object one week to orbit the earth at
this distance?
"

This contradicts the Third Law of Kepler!
A halfway orbit lasts 10 days. To get an orbit of 1 week,
you will need an orbit at about 40 % of the distance.

"
I don't mind it having some environmental impact on Earth
(like say an 1 mm adjustment in tides) or the occasional
(once monthly) stronger than usual storm but on the whole I
don't want it shredding the planet's atmosphere, ripping up
pieces of the crust or generally causing any extinction
level events.
"

The tides range up to 18 m.
I cannot decide whether the height of tide is proportional
to the mass of the body raising it or to the square root of
the mass. In any case I would expect that a body with the
density of Moon and, say, 140 km across would be in the
right range to cause tidal adjustments of up to 1 mm, if on
the orbit of Moon.

The tidal force increases with the inverse cube of distance,
and inverse square of orbital period. Thus a body 60 km
across with lunar density would be OK on the orbit with a
period of a week. Just how big did you want the density to be?

"
How long can this system remain stable with both the Earth
and the Moon's
gravity wells affecting this object?
"

And the gravity of the Sun, too.

Well, Jupiter, Saturn and Uranus have multiple big
sattellites. And these have presumably been stable for 4,5
milliards of years.

Hop David

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Jul 7, 2004, 1:39:20 PM7/7/04
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An L4 or L5 orbit is one of the more stable.
In such a configuration the object, moon and earth centers
would form the corners of an equilateral triangle. The object would be
about 400,000 kilometers from the earth and 400,000 kilometers from the moon
L4
/\
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
Earth---------------Moon
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\/
L3


If I recall correctly an L4 or L5 object shouldn't be more than 1/26 the
mass of the moon.

Google "Lagrange Points".

--
Hop David
http://clowder.net/hop/index.html

Hop David

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Jul 7, 2004, 2:05:58 PM7/7/04
to

Frank Scrooby wrote:
> Hi all
>
> How massive an object could you introduce into the Earth-Moon without
> hideously screwing everything up?
>
> For purposes of a story I'd like to write I want a very dense object to
> suddenly arrive in Earth orbit (about half-way between Earth and the Moon -
> and no it is not a singularity - its nowhere near that dense!).
>
> I am happy (more than happy) for it to trash any or all of Earth's
> artificial satellites, de-orbit, impact, gravity sling, whatever.
>
> I don't mind it having some environmental impact on Earth (like say an 1 mm
> adjustment in tides) or the occasional (once monthly) stronger than usual
> storm but on the whole I don't want it shredding the planet's atmosphere,
> ripping up pieces of the crust or generally causing any extinction level
> events.
>
> So how big can this thing be? How many billions of tons?
>
> And is half-way a convenient orbit?
>
> Would it take this object one week to orbit the earth at this distance?

Sorry, had read your post too hurriedly before my first reply.

For convenience lets use units Lunar Distance (LD) for length and Months
(a month is a good approximation of the Moon's orbital period).

If the distance is n LD then its period n^(3/2) months.

For example if it is half a lunar distance away, then it will orbit the
earth in (1/2)^(3/2) months. Which is .3535 months or about ten days.


There are some problems. If this object arrives from outside of the
solar system, then it will be traveling a parabolic (or maybe even
hyperbolic) trajectory. On its arrival it will be traveling at least 12
km/sec wrt to the earth. In which case it would not be trapped by
earth's gravity (escape velocity is 11.2 km/sec at earth's surface).
You need some way to slow the object down upon arrival if it's going to
hang around our neighborhood.

>
> How long can this system remain stable with both the Earth and the Moon's
> gravity wells affecting this object?

Some orbits are much less stable than others. If you use an L4 or L5
orbit as I described in my first reply, it will stay around for quite
awhile.

If the object was slowed down by grazing earth's atmosphere, then its
perigee would graze earth's atmosphere every circuit. In this case it
would probably fall to the earth before too long.

>
> If there is an online resource where I can find these answers out please
> point me in that direction.
>
> Thanks and regards
> Frank Scrooby
>
>

George W. Harris

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Jul 7, 2004, 2:23:58 PM7/7/04
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Hop David <hopspageHA...@tabletoptelephone.com> wrote:

:There are some problems. If this object arrives from outside of the

:solar system, then it will be traveling a parabolic (or maybe even
:hyperbolic) trajectory. On its arrival it will be traveling at least 12
:km/sec wrt to the earth. In which case it would not be trapped by
:earth's gravity (escape velocity is 11.2 km/sec at earth's surface).
:You need some way to slow the object down upon arrival if it's going to
:hang around our neighborhood.

Would a close pass to the moon, killing much
of the object's velocity, work? Perhaps the object
could end up in a highly eccentric orbit with a period a
fraction of the moon's (say 1/2 or 2/3). Could that
possibly be stable?

--
They say there's air in your lungs that's been there for years.

George W. Harris For actual email address, replace each 'u' with an 'i'.

Mike Williams

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Jul 7, 2004, 2:25:57 PM7/7/04
to
Wasn't it Frank Scrooby who wrote:
>Hi all
>
>How massive an object could you introduce into the Earth-Moon without
>hideously screwing everything up?
>
>For purposes of a story I'd like to write I want a very dense object to
>suddenly arrive in Earth orbit (about half-way between Earth and the Moon -
>and no it is not a singularity - its nowhere near that dense!).
>
>I am happy (more than happy) for it to trash any or all of Earth's
>artificial satellites, de-orbit, impact, gravity sling, whatever.
>
>I don't mind it having some environmental impact on Earth (like say an 1 mm
>adjustment in tides) or the occasional (once monthly) stronger than usual
>storm but on the whole I don't want it shredding the planet's atmosphere,
>ripping up pieces of the crust or generally causing any extinction level
>events.
>
>So how big can this thing be? How many billions of tons?

It's possible to calculate the size of an object that causes a 1mm
change in tidal range if you know a sensible value for the current tidal
range. (Tidal ranges seem to vary so much due to local geography that
it's hard to get a firm figure for a global value.)

Let's suppose that the current tidal range is 5 metres. The tidal force
is (to a first approximation) proportional to the mass and inversely
proportional to the cube of the distance. So for an object at half the
distance to have no more than 1/5000 of the tidal effect it would have
to have a mass of no more than 1/40000 of the Moon. That's about 2
million billion tons (1.8 * 10^18 kilograms).

I guess it's possible that some of your other requirements may impose a
small mass limit, it's just that that one can be objectively calculated.

--
Mike Williams
Gentleman of Leisure

Erik Max Francis

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Jul 7, 2004, 3:16:50 PM7/7/04
to
Hop David wrote:

> If I recall correctly an L4 or L5 object shouldn't be more than 1/26
> the
> mass of the moon.

No, the secondary body (the Moon in your example) needs to be less than
(about) 1/26 the mass of the primary body (the Earth in your example).
The mass of the object actually attempting to reside in the Trojan point
must be of negligible mass compared to the other two.

--
__ Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
/ \ San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
\__/ My life was better before I knew you.
-- Edith Wharton (to Morton Fullerton)

Hop David

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Jul 7, 2004, 8:07:03 PM7/7/04
to

Erik Max Francis wrote:
> Hop David wrote:
>
>
>>If I recall correctly an L4 or L5 object shouldn't be more than 1/26
>>the
>>mass of the moon.
>
>
> No, the secondary body (the Moon in your example) needs to be less than
> (about) 1/26 the mass of the primary body (the Earth in your example).
> The mass of the object actually attempting to reside in the Trojan point
> must be of negligible mass compared to the other two.
>

Thanks for the correctio.

Chuck Stewart

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Jul 7, 2004, 10:02:06 PM7/7/04
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On Wed, 07 Jul 2004 12:38:46 -0700, Erik Max Francis wrote:

> You're going to have a hard time coming up with some mechanism that
> provides that deltavee naturally.

There's one proven method for a body of astronomical mass, but it would
require another largish body and one of _those_ coincidences... have your
inbound body slam into a smaller body. In the example above your target
body, a rocky/iron object, is impacted by a large comet as it's
traversing the Earth/Moon system.

Iknow... cheesy... but it would work :)

--
Chuck Stewart
"Anime-style catgirls: Threat? Menace? Or just studying algebra?"

Phillip Thorne

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Jul 7, 2004, 11:26:33 PM7/7/04
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Frank Scrooby asked:

>> How massive an object could you introduce into the Earth-Moon without
>> hideously screwing everything up?

ObVidSF: In the 1984 "Transformers" story "The Ultimate Doom," Evil
Decepticon Leader Megatron brings his home planet of Cybertron into
cislunar space, specifically to harvest energy from its tide-driven
meteorologic influence (wave generators, etc.) on Earth -- not that
the term "tidal effect" was used, this being a toon for pre-teens.

(Cybertron's exact physical properties are unclear in the show. It
seems to be smaller than Luna, but it retains an oxygen atmosphere,
and human characters brought to its surface seem to experience
Earth-normal gravity. Given that it consists of numerous metallic
levels, possibly built atop an asteroidal core -- like an inverse
Zebrowski Macrolife habitat -- it may contain gravity generators.)

On Wed, 07 Jul 2004, Erik Max Francis <m...@alcyone.com> responded in
detail:
>[Tidal amplitudes in water]
>The real problem you have here is how the object gets captured.
>[...]


>You're going to have a hard time coming up with some mechanism that
>provides that deltavee naturally.

The problem of capture velocities is neatly solved (er, entirely
bypassed) by shipping the planet via Space Bridge, an artificial
temporary wormhole that apparently compensates for relative
velocities.

The plausibility of the Heroic Autobots' eventual solution, of
detonating Megatron's freighter of Energon Cubes to propel Cybertron
out of Earth orbit, does not bear close scrutiny. :)

/- Phillip Thorne ----------- The Non-Sequitur Express --------------------\
| org underbase ta thorne www.underbase.org It's the boundary |
| net comcast ta pethorne site, newsletter, blog conditions that |
\------------------------------------------------------- get you ----------/

Stan

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Jul 8, 2004, 2:01:21 AM7/8/04
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Erik Max Francis <m...@alcyone.com> wrote:

}Turning a passby into a
}capture requires an application of deltavee on the intruder -- even if
}the object were headed so that its perigee is right at the 200 000 km
}distance mark, when it gets there something is going to have to
}circularize its orbit, because otherwise it will just head out again.

}You're going to have a hard time coming up with some mechanism that
}provides that deltavee naturally.

Hmmm...what about a tangential grazing of the moon, taking out only the
very top of a ridge or peak? It would leave it in an elliptical orbit,
but it does seem plausible (however improbable).

Stan.

Erik Max Francis

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Jul 8, 2004, 2:03:04 AM7/8/04
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Stan wrote:

> Hmmm...what about a tangential grazing of the moon, taking out only
> the
> very top of a ridge or peak? It would leave it in an elliptical
> orbit,
> but it does seem plausible (however improbable).

To shed the required speed, you're probably talking about something much
more like a major crash rather than a graze.

--
__ Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
/ \ San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis

\__/ There are countless planets, like many island Earths ...
-- Konstantin Tsiolkovsky

Mad Bad Rabbit

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Jul 8, 2004, 2:31:56 AM7/8/04
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Erik Max Francis <m...@alcyone.com> wrote:

> You're going to have a hard time coming up with some mechanism that
> provides that deltavee naturally.

Of course if it's an artificial object, it can just fire up the
obscenely-huge antimatter drive and insert itself into cislunar
orbit (no doubt frying all our satellites and providing a lovely
worldwide aurora show at the same time.)


--
>;K

Frank Scrooby

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Jul 8, 2004, 4:43:28 AM7/8/04
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Hi all


"Mad Bad Rabbit" <madbad...@yahoo.com> wrote in message
news:yo2dnVYzFeX...@texas.net...


I am afraid that I have not provide enough information, and that the premise
I am trying to create is probably so horribly flawed as to be unworkable.

The object in question is highly artifical, some leftover ammunition from a
cosmic conflict that was over before our star was born. The beings who
created it are long gone, extinct possibly at their own hand. When you use
Objects like these as ammunition your wars tend to be ... well ... highly
fatal.

The object and its twin (which is somewhere very far away) are the
containers for a worm-hole. It is not captured into the Earth moon system so
much as it 'appears'. One second people are looking up at a nice ordinary
night sky and suddenly there this black splotch occluding stars. That is as
much hand-waving as I want to do. I want everything else to be HARD SCIENCE.

I want this insanely dense, unwelcomed visitor to behave exactly like a
planetoid of its mass would. And I want it screw up Earth's locale exactly
like a previously unnoticed satellite of its mass would.

I am quite happy to have it wrecking satellite orbits, smashing global
telecoms, causing the evacuation (and possible subsequent destruction) of
ISS, etc. Depending on where it might be it might even vacuum up the Van
Allen radiation belts ;-)

I am not happy about it causing massive changes in Earth's tide or such
like. A one meter increase in the daily high tides at a place not so far
from where I am right now will result in the routine and probably permanent
flooding on the CBD of a city (the main street is a meter below sea level,
the beach front is the only thing keeping the sea out). There are some
people who would probably welcome this sort of thing. Its great for urban
renewal, and Hollywood blockbusters. And what happens in Durban South Africa
will happen in dozens cities all around the world.

I don't want to write a disaster story, so I would like to keep the Object's
effects on Earth's eco-and weather-system to a minimum. This might mean
making the Object smaller than I have estimated below.

It does not need to be in a regular orbit. Something high eliptical (sp?)
would be fine

My initial estimate on its mass and apparent density (based on what I want
it to be made out of it) are:

+- 14.804 billion billion tons with a apparent density of 28 billion tons
per cubic meter.

It appears to be a sphere 1000 meters in diameter. It is 100% black, except
when something touches it and then there is a bright flash of multicolored
light for a millisecond or two during which the whole object is hidden from
view.

By comparison

(according to http://www.nineplanets.org/earth.html)

Earht's mass is +- 5972 billion billion tons making this sucker just 0.24 %
of Earth's mass (if I got all my numbers right). Earth density is a
relatively modest 5.52 grams per cubic centimeter, which translates into
5.52 tons per cubic meter (if I get all my numbers right again).

The Moon's mass is +- 73.5 billion billion tons (same source), making the
Object's mass nearly 20% that of the Moon's. The Moon's Density is only
3.34 grams per cubic centimeter which translates to 3.34 tons per cubic
meters (standard disclaimer).

>
>
> --
> >;K


Can this be made to work?

Erik Max Francis

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Jul 8, 2004, 4:50:42 AM7/8/04
to
Frank Scrooby wrote:

> The object and its twin (which is somewhere very far away) are the
> containers for a worm-hole. It is not captured into the Earth moon
> system so
> much as it 'appears'. One second people are looking up at a nice
> ordinary
> night sky and suddenly there this black splotch occluding stars. That
> is as
> much hand-waving as I want to do. I want everything else to be HARD
> SCIENCE.

If it's highly dense, then it's not going to be that large, which means
that in cislunar space it's not going to occlude many stars.

The rest I already responded to with numbers.

--
__ Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
/ \ San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis

\__/ It seems like Karma's making his rounds
-- Kina

Mike Williams

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Jul 8, 2004, 7:42:23 AM7/8/04
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Wasn't it Frank Scrooby who wrote:
>The Moon's mass is +- 73.5 billion billion tons (same source), making the
>Object's mass nearly 20% that of the Moon's.

If you only want the tides to rise by 1 millimetre, and you want it to
be 20% of the Moon's mass, then it can't come any nearer than 10 times
the distance of the Moon.

[Tide is proportional to m/d^3. 1mm is 0.0002 times the lunar tide. So
0.0002 = 0.2/10^3.]

With current technology, we probably wouldn't be able to detect it.

Bryan Derksen

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Jul 8, 2004, 11:59:58 AM7/8/04
to
On Thu, 8 Jul 2004 12:42:23 +0100, Mike Williams
<nos...@econym.demon.co.uk> wrote:
>If you only want the tides to rise by 1 millimetre, and you want it to
>be 20% of the Moon's mass, then it can't come any nearer than 10 times
>the distance of the Moon.
>
>[Tide is proportional to m/d^3. 1mm is 0.0002 times the lunar tide. So
> 0.0002 = 0.2/10^3.]
>
>With current technology, we probably wouldn't be able to detect it.

We'd eventually notice its gravitational effects. Even if its tidal
effects on Earth slipped our attention, I expect it'd cause minor
changes in the Moon's orbit that we'd be able to notice pretty
clearly. Probably take at least a few months to become apparent,
though.

Hop David

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Jul 8, 2004, 12:10:26 PM7/8/04
to

George W. Harris wrote:
> Hop David <hopspageHA...@tabletoptelephone.com> wrote:
>
> :There are some problems. If this object arrives from outside of the
> :solar system, then it will be traveling a parabolic (or maybe even
> :hyperbolic) trajectory. On its arrival it will be traveling at least 12
> :km/sec wrt to the earth. In which case it would not be trapped by
> :earth's gravity (escape velocity is 11.2 km/sec at earth's surface).
> :You need some way to slow the object down upon arrival if it's going to
> :hang around our neighborhood.
>
> Would a close pass to the moon, killing much
> of the object's velocity, work? Perhaps the object
> could end up in a highly eccentric orbit with a period a
> fraction of the moon's (say 1/2 or 2/3). Could that
> possibly be stable?
>

From the moon's point of view, Vinf on the inward arm of the hyperbola
is the same as Vinf on the outward arm. The delta vee is a direction change.

The minimum 12 km/sec velocity I mentioned was if the object was moving
parallel to the earth at perihelion. The earth is moving 30 km/sec wrt
sun and the object is moving the same direction at sqrt(2)*30 km/sec wrt
the sun (about 42 km/sec). Changing the object's direction would make
matters worse in this scenario.

I don't see a lunar gravity assist taking enough velocity to enable capture.

Hop David

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Jul 8, 2004, 12:31:45 PM7/8/04
to

Frank Scrooby wrote:

> I am afraid that I have not provide enough information, and that the premise
> I am trying to create is probably so horribly flawed as to be unworkable.
>
> The object in question is highly artifical, some leftover ammunition from a
> cosmic conflict that was over before our star was born. The beings who
> created it are long gone, extinct possibly at their own hand. When you use
> Objects like these as ammunition your wars tend to be ... well ... highly
> fatal.
>
> The object and its twin (which is somewhere very far away) are the
> containers for a worm-hole. It is not captured into the Earth moon system so
> much as it 'appears'. One second people are looking up at a nice ordinary
> night sky and suddenly there this black splotch occluding stars. That is as
> much hand-waving as I want to do. I want everything else to be HARD SCIENCE.

Have you read "Impact Parameter" by Geoffrey Landis? It's a short story
in a collection of short stories of the same name.

Has some similarities to your story.

Landis' wormhole bends space in a fashion that seems similar to a black
hole. So it has an intense gravity field.

Here is a "Flatland" model of a wormhole
http://clowder.net/hop/etc./wormhol2.html

Note that you can enter it from all directions in the plane, Something A
Square or Yendred would probably find disorienting. In the same
fashion you could enter a wormhole in our space from any direction. Once
inside the hole, light geodesics would be helixes. You might be able to
see multiple images of your self shrinking into infinity, something like
a hall of mirrors (I believe you'd get a similar effect at 1.5
Schwarzchild radii from a blackhole).

George W. Harris

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Jul 8, 2004, 2:43:16 PM7/8/04
to
Hop David <hopspageHA...@tabletoptelephone.com> wrote:

:
:

Hmmm. Wouldn't conservation of energy
pretty much guarantee that the object would be
traveling at 42 km/sec when it crossed Earth's orbit,
regardless of perihelion (given that it crosses Earth's
orbit at all)? So if perihelion were just inside Earth's
orbit and it passed just in front of the Earth on the
outward leg, that could provide a significant deltaV,
could it not?

Here's another idea; solar braking. If this
object is tremendously dense, it could skim the
surface of the sun without being destroyed, which
could kill significant velocity. I doubt tidal effects
from a close solar pass would provide significant
deltaV, though.

--
"Intelligence is too complex to capture in a single number." -Alfred Binet

Erik Max Francis

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Jul 8, 2004, 4:04:17 PM7/8/04
to
"George W. Harris" wrote:

> Hmmm. Wouldn't conservation of energy
> pretty much guarantee that the object would be
> traveling at 42 km/sec when it crossed Earth's orbit,
> regardless of perihelion (given that it crosses Earth's
> orbit at all)?

Yes, if it originated from elsewhere in the Solar System, or even
outside (in which case its speed would be greater). The original poster
clarified his scenario, though; he's actually talking about something
that materializes in cislunar space, rather than actually having to get
there.

--
__ Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
/ \ San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis

\__/ We have always been space travellers.
-- Carl Sagan

George W. Harris

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Jul 8, 2004, 4:18:44 PM7/8/04
to
Erik Max Francis <m...@alcyone.com> wrote:

:"George W. Harris" wrote:
:
:> Hmmm. Wouldn't conservation of energy
:> pretty much guarantee that the object would be
:> traveling at 42 km/sec when it crossed Earth's orbit,
:> regardless of perihelion (given that it crosses Earth's
:> orbit at all)?
:
:Yes, if it originated from elsewhere in the Solar System, or even
:outside (in which case its speed would be greater). The original poster
:clarified his scenario, though; he's actually talking about something
:that materializes in cislunar space, rather than actually having to get
:there.

Fie on the original poster. The problem of
Earth capturing an object that starts out in a
parabolic/hyperbolic orbit around the sun is
interesting in its own right.

--
When Ramanujan was my age, he had been dead for ten years. -after Tom Lehrer

Hop David

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Jul 8, 2004, 6:44:19 PM7/8/04
to

If it's traveling a parabolic orbit, yes. However there's a wide variety
of delta vee's wrt to the earth. You can use traffic as an analogy.

Northbound car 30 mph and a northbound car 42 mph rear, difference in
velocity 12 mph. (this would be like a prograde asteroid with 0 degrees
inclination with a 1 A.U. perhihelion coming near the earth, it's
trajectory would be parallel.)

If you're northbound at 30 mph and a westbound car broadsides you at 42
mph, it's velocity from your point of view is sqrt(30^2 +42^2) mph or
about 52 mph. (An object could pass earth's orbit at nearly 90 degrees
if it's perihelion is very close to the sun. It could also pass at right
angles if it's inclination is high).

If you have a head on collision with a southbound car, it's a 30+42 or a
72 mph impact. (0 degrees inclination, 1 A.U. perihelion, retrograde orbit)

So the ranges of delta vee of an object crossing earth's orbit on a
parabolic trajectory range from 12 km/sec to 72 km/sec.

Altering the direction of a parabolic orbit of an object 0 degrees
inclination, 1 A.U. perihelion and a prograde orbit would only increase
delta vee wrt the earth.

So if perihelion were just inside Earth's
> orbit and it passed just in front of the Earth on the
> outward leg, that could provide a significant deltaV,
> could it not?

As I mentioned earlier the delta vee of a gravity assist changes the
direction of the velocity vector but not it's magnitude (speed) wrt to
the assisting body. So the delta vee is a direction change, not a change
in speed. The moon's frame of reference is nearly the same as the
earth's, it is only traveling aobut 1 km/sec wrt Earth.

>
> Here's another idea; solar braking. If this
> object is tremendously dense, it could skim the
> surface of the sun without being destroyed, which
> could kill significant velocity. I doubt tidal effects
> from a close solar pass would provide significant
> deltaV, though.
>

The point it slows down at would be it's perihelion. In the sun grazing
scenario, the kindest orbit, delta vee wise, would be one with a 700,000
km perihelion (sun's radius) and a 150,000,000 (1 A.U.) aphelion. At
aphelion the object is traveling about 1 km/sec wrt the sun. Wrt the
earth it's 29, maybe 28 km/sec.

Hop David

unread,
Jul 8, 2004, 7:11:07 PM7/8/04
to

George W. Harris wrote:
> Erik Max Francis <m...@alcyone.com> wrote:
>
> :"George W. Harris" wrote:
> :
> :> Hmmm. Wouldn't conservation of energy
> :> pretty much guarantee that the object would be
> :> traveling at 42 km/sec when it crossed Earth's orbit,
> :> regardless of perihelion (given that it crosses Earth's
> :> orbit at all)?
> :
> :Yes, if it originated from elsewhere in the Solar System, or even
> :outside (in which case its speed would be greater). The original poster
> :clarified his scenario, though; he's actually talking about something
> :that materializes in cislunar space, rather than actually having to get
> :there.
>
> Fie on the original poster. The problem of
> Earth capturing an object that starts out in a
> parabolic/hyperbolic orbit around the sun is
> interesting in its own right.
>

It's something I enjoy playing with.

You might like this resource:
http://neo.jpl.nasa.gov/cgi-bin/neo_ca?sort=vrel

Even with not very eccentric, low inclination orbits, you can see a lot
of near approachers fly by pretty fast.

But even 1991 VG would not be captured by earth's gravity. Even if it
were falling from infinity with zero starting velocity, it's orbit about
the earth would be parabolic. But even this slow asteroid would zoom by
the earth with 1.18 km/sec hyperbolic excess velocity. Maybe if it
grazed the earth's atmosphere and had Lunar gravity assists, it could be
captured.

Deimos and Phobos look like captured asteroids. How Mars got these moons
with nice circular orbits is a mystery to me.

Hop David
http://clowder.net/hop/index.html

George W. Harris

unread,
Jul 8, 2004, 7:26:18 PM7/8/04
to
Hop David <hopspageHA...@tabletoptelephone.com> wrote:

: So if perihelion were just inside Earth's


:> orbit and it passed just in front of the Earth on the
:> outward leg, that could provide a significant deltaV,
:> could it not?
:
:As I mentioned earlier the delta vee of a gravity assist changes the
:direction of the velocity vector but not it's magnitude (speed) wrt to
:the assisting body. So the delta vee is a direction change, not a change
:in speed. The moon's frame of reference is nearly the same as the
:earth's, it is only traveling aobut 1 km/sec wrt Earth.

I'm slow but eventually catch on. So about
the only way the object could end up in Earth orbit
would be lithobraking, which introduces a host of
other problems (unless it's lunar lithobraking).

--
"The truths of mathematics describe a bright and clear universe,
exquisite and beautiful in its structure, in comparison with
which the physical world is turbid and confused."

-Eulogy for G.H.Hardy

Jordan Abel

unread,
Jul 8, 2004, 7:48:20 PM7/8/04
to
Hop David wrote:

> But even 1991 VG would not be captured by earth's gravity. Even if it
> were falling from infinity with zero starting velocity, it's orbit about
> the earth would be parabolic.

In the sense that a line is a degenerate parabola... if we assume that
the earth is the only gravitational influence (and a perfectly spherical
cow), an object falling from infinity with zero starting velocity would
tend to fall downwards in a straight line towards earth.

Hop David

unread,
Jul 8, 2004, 8:06:18 PM7/8/04
to

Vinf is 0 regardless whether a parabola is degenerate or upstanding.

Chuck Stewart

unread,
Jul 8, 2004, 9:04:55 PM7/8/04
to
On Thu, 08 Jul 2004 23:26:18 +0000, George W. Harris wrote:

> I'm slow but eventually catch on. So about
> the only way the object could end up in Earth orbit
> would be lithobraking, which introduces a host of
> other problems (unless it's lunar lithobraking).

I still say hit it with a comet while crossing cislunar space.
Juggle the parameters right and the comet goes poof while the
(badly impacted) object is braked enough to be captured into the
desired Earth orbit.

If the object is handwaved into existence near the Earth then
the order of unlikelytude of two objects colliding in cislunar
space is lowered somewhat.

Nothing to be done for the cheeseitude, tho.

Jordan Abel

unread,
Jul 8, 2004, 9:50:49 PM7/8/04
to
Hop David wrote:

> Vinf is 0 regardless whether a parabola is degenerate or upstanding.

yes, but if it's _starting_ there it's being accelerated towards earth,
not towards some other point

i could be wrong, though. infinities are tricky to work with.

Geoffrey A. Landis

unread,
Jul 8, 2004, 3:50:27 PM7/8/04
to
In <40ED76F1...@tabletoptelephone.com> Hop David wrote:

> Have you read "Impact Parameter" by Geoffrey Landis? It's a short
> story in a collection of short stories of the same name.

>...

Cool. It's nice to see that not only do people occasionally read my
stories, they even pay attention.

--
Geoffrey A. Landis
http://www.sff.net/people/geoffrey.landis

Frank Scrooby

unread,
Jul 9, 2004, 5:23:49 AM7/9/04
to
Hi all

"Hop David" <hopspageHA...@tabletoptelephone.com> wrote in message
news:40ED76F1...@tabletoptelephone.com...
>
>
<much snipped>

> Have you read "Impact Parameter" by Geoffrey Landis? It's a short story
> in a collection of short stories of the same name.
>

I dont' believe I have read Geoffrey's story. Is it published online or in
paper.


> Has some similarities to your story.
>

Ahh, crap I'm a plagarist!

> Landis' wormhole bends space in a fashion that seems similar to a black
> hole. So it has an intense gravity field.
>

The 'Object' I have imagined has a relatively intense gravity field for its
volume, but mostly only because its hideously dense. Also it isn't really
one object but two (you only ever see one 'opening' but they behave as if
their individual masses are combined). But with only 20% of the mass of the
Moon its not really going to be a massive threat to interplanetary space,
not in the order of a real singularity.

> Here is a "Flatland" model of a wormhole
> http://clowder.net/hop/etc./wormhol2.html
>
> Note that you can enter it from all directions in the plane, Something A

This is a feature of my Object. I can not believe this. I thought I was
being completely original.

I am dreadful sorry, Geoffrey. I did not intend to plagarize. I promise.


> Square or Yendred would probably find disorienting. In the same
> fashion you could enter a wormhole in our space from any direction. Once
> inside the hole, light geodesics would be helixes. You might be able to
> see multiple images of your self shrinking into infinity, something like
> a hall of mirrors (I believe you'd get a similar effect at 1.5
> Schwarzchild radii from a blackhole).

I had decided that humans who utilize the wormhole (and that is the main
thrust of the story I want to write - there is something much more
interesting and tempting than a left-over, decaying, 10-billion old,
forgotten munition that now acts as an instanteous interstellar transport
system at the other end of the wormhole) will not experience at all anything
when going through the wormhole. I.e. They see the approaching 'event
horizon' of the object. It passes directly through their ship, and their
space suits. If they don't blink, faint, or haven't pinched their eyes shut
in prayer they will even see the moment of contact between their eyes and
the Object, and then they see the destination. They will have absolutely no
awareness of any time having passed in between those moment. This is not
like sleep, or being unconscious or even blinking. It is like not having
missed any time at all. People who try counting during the passage will find
themselves finishing saying the last number they were counting at the moment
of contact. Stuff like that. Computers and atomic clocks, especially those
that synchronize themselves with equipment back in Earth's solar system will
record the loss of a couple of 100ths of a millisecond, if they are that
precise.

Geoffrey A. Landis

unread,
Jul 9, 2004, 12:07:15 PM7/9/04
to
Hop David" <hopspageHA...@tabletoptelephone.com> wrot:> <much
snipped>
>
>> Have you read "Impact Parameter" by Geoffrey Landis? It's a short
>> story in a collection of short stories of the same name.


In <ppGdnRggZM6...@is.co.za> Frank Scrooby replied:


> I dont' believe I have read Geoffrey's story. Is it published online
> or in paper.

It's in my collection (which is hardcover only, alas. I haven't gotten
a paperback deal on it yet; it's hard to sell collections in mass market.)

The short-story is independently available from fictionwise:
http://www.fictionwise.com/servlet/mw?authorid=28&template=author.htm&
action=view

>> Has some similarities to your story.

>> Landis' wormhole bends space in a fashion that seems similar to a
>> black hole. So it has an intense gravity field.


Frank Scrooby continued:


> Ahh, crap I'm a plagarist!

Well, it's not plagiarizing to independently come up with a similar idea.

I had the thought of gravitational lensing from a workhole from the
original Morris and Thorne paper, where the wormhole external metric is
identical to a Schwartzschild metric-- i.e., from the outside it looks
like a black hole. Later, after I learned a lot more about wormholes, I
discovered that the external metric can be any of many different
possibilities, even negative mass solutions.

In any case, my plot was entirely about the reaction of astronomers on
Earth, and if you're talking about people travelling through the
wormhole to explore, you'll be looking at a different plot entirely.

Hop David

unread,
Jul 9, 2004, 2:53:07 PM7/9/04
to

I see what you mean..

In an ideal two body scenario where the bodies are completely motionless
wrt to one another they'd approach each other along a straight line.

But more practically speaking, straight geodesics don't exist. Our space
isn't flat with masses like the planets, stars, galaxies etc. bending
space. "Falling from infinity" is certainly an imprecise and inaccurate
term to describe NEOs as most asteroids don't go further than 6 A.U.
from the earth.

Even so, those using orbital mechanics will use Vinf for hyperbolic
excess velocity. Vinf is a very good approximation for velocity wrt
earth once outside Earth's Sphere Of Influence (SOI). Prussing & Conway
define the radius of a planet's Sphere Of Influence as (Mp/Ms)^(2/5) * Rsp

Mp = Mass of planet
Ms = Mass of Sun
Rsp = distance between planet and sun.

Using this definition, Earth's SOI has a radius about 925,000 kilometers

In a flat space an object at this distance traveling .077 km/sec wrt
earth would have a perigee in low earth orbit and it's apogee would be
right back to 925,000 km, the very edge of Earth's SOI.

Jordan Abel

unread,
Jul 9, 2004, 3:39:51 PM7/9/04
to
Geoffrey A. Landis wrote:

> original Morris and Thorne paper, where the wormhole external metric is
> identical to a Schwartzschild metric-- i.e., from the outside it looks
> like a black hole.

If it looks like a black hole, how does anyone on the outside know it's
not a black hole? other than to accidentally (who's going to go into a
black hole on purpose?) fall in and then come back to tell about it,
that is.

James Nicoll

unread,
Jul 9, 2004, 3:42:31 PM7/9/04
to
In article <20040709120...@newsread.grc.nasa.gov>,

Geoffrey A. Landis <Geoffrey_...@sff.net> wrote:
>
>It's in my collection (which is hardcover only, alas. I haven't gotten
>a paperback deal on it yet; it's hard to sell collections in mass market.)

Happily, it is worth getting in hardcover.
--
"The keywords for tonight are Caution and Flammable."
Elvis, _Bubba Ho Tep_

LukeCampbell

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Jul 9, 2004, 4:13:27 PM7/9/04
to

If the wormhole has the Schwartzschild metric down past the event
horizon, then you don't come back after falling in - ever. If you are
lucky, the wormhole on the other side does not have an event horizon and
you can get out. Otherwise, you are stuck.

If the Schwartzschild metric stops before the event horizon, it does not
look like a black hole.

Note that I have not read the story by Landis, so I cannot comment on
specific things that happen in the story or the author's representation
of this system.

Luke

--
To email me, take out the trash.

pervect

unread,
Jul 9, 2004, 5:06:01 PM7/9/04
to
On Thu, 8 Jul 2004 10:43:28 +0200, "Frank Scrooby" <X...@Xer.com> wrote:


>I am not happy about it causing massive changes in Earth's tide or such
>like. A one meter increase in the daily high tides at a place not so far
>from where I am right now will result in the routine and probably permanent
>flooding on the CBD of a city (the main street is a meter below sea level,
>the beach front is the only thing keeping the sea out). There are some
>people who would probably welcome this sort of thing. Its great for urban
>renewal, and Hollywood blockbusters. And what happens in Durban South Africa
>will happen in dozens cities all around the world.

Tidal responses are very complex, but some insight can be gained by
looking at the simpler 'driving terms'.

Tidal acceleration is directly proportional to mass, and inversely
proportional to distance^3

So if your object has .2 of the mass of the moon, but is twice as
close, it will produce a tidal acceleration of about 1.6 that of the
moon.

That would probably qualify as a major disruption.

If you keep it at the same distance as the moon, with a mass of 20% of
the moon, it would have a tidal acceleration of about 20% of that of
the moon. Presumably the response would be around 20% as well, but
that's very approximate, as I mentioend the earth's tidal response is
rather tricky.

Assuming intelligent guidance, a convenient place to stick it would be
at one of the stable Lagrange points as someone else has mentioned.
I'm not sure about long term (astronomical) stability, but over the
short term it should be OK here.

If you want to have the body approach closer than the moon, you'll
have to decrease its mass, or live with the higher tidal effects.

I believe there are several orbital simulators available on the web,
you might start your search at

http://www.burtleburtle.net/bob/physics/solar.html

this would allow you to numerically simulate how the body would act
and what effect it would have on the orbits of the earth and moon.


jimirwin

unread,
Jul 9, 2004, 8:51:21 PM7/9/04
to
pervect wrote in rec.arts.sf.science:

>
> I believe there are several orbital simulators available on the web,
> you might start your search at
>
> http://www.burtleburtle.net/bob/physics/solar.html
>
> this would allow you to numerically simulate how the body would act
> and what effect it would have on the orbits of the earth and moon.
>
>

I ran the Solex program, which is supposedly one of the most accurate
integrators. I put an object instantaneously at about 40% the distance
to the moon, with an approximately circular orbit, and varying masses.

I was surprised that the earth-moon-wormhole system remained relatively
stable (with respect to the earth) for several years even with a
wormhole mass equal to 100% of the moon's mass. The moon's orbital
period became shorter by about 40 hours, and the year became longer by
about 4 hours, but neither the moon nor the wormhole escaped the system,
although the moon's orbit was becoming quite noticably more eccentric at
the end of 4 years.

At 10% of the moon's mass, the moon's orbital period decreased by about
6 hours. The year was about a half hour longer.

At 1% of the moon's mass, the moon's orbital period remained
approximately the same, but I'm sure there would still be long term
effects. I only ran this simulation for a couple of months.

--
Jim Irwin
http://www.holoscenes.com

Jordan Abel

unread,
Jul 10, 2004, 4:46:09 PM7/10/04
to
jimirwin wrote:
> I was surprised that the earth-moon-wormhole system remained relatively
> stable (with respect to the earth) for several years even with a
> wormhole mass equal to 100% of the moon's mass. The moon's orbital
> period became shorter by about 40 hours, and the year became longer by
> about 4 hours, but neither the moon nor the wormhole escaped the system,
> although the moon's orbit was becoming quite noticably more eccentric at
> the end of 4 years.

Did you try putting it in with the same initial velocity as the velocity
of the CM of the earth-moon system? [that might be more neutral to the
length of the year, and possibly also to the length of the month, than
one that's not moving]

jimirwin

unread,
Jul 10, 2004, 5:52:19 PM7/10/04
to
Jordan Abel wrote in rec.arts.sf.science:

> Did you try putting it in with the same initial velocity as the velocity
> of the CM of the earth-moon system? [that might be more neutral to the
> length of the year, and possibly also to the length of the month, than
> one that's not moving]
>
>

No, because if it had the same velocity as the CM of the earth-moon system,
it would quickly plummet to the earth rather than orbit. It takes a little
more than a day to fall to earth under those initial conditions. I chose
an initial velocity that resulted in an approximately circular orbit around
earth, in the plane of the ecliptic, in the same angular direction as the
moon's orbit. Because I placed it initially to the outside of earth's
orbit, it gave the system a little more energy and made the year longer.
If I had placed it to the inside of earth's orbit, it would have made the
year shorter. No matter where it starts, if it's massive, it's going to
perturb the system in some manner, either by changing the plane or the
eccentricity of the earth's orbit, or some combination of those.

Geoffrey A. Landis

unread,
Jul 10, 2004, 4:47:47 PM7/10/04
to
Geoffrey A. Landis wrote:

>>> ...original Morris and Thorne paper, where the wormhole external
>>> metric
>>> is identical to a Schwartzschild metric-- i.e., from the outside it
>>> looks like a black hole.

Jordan Abel replied:

>> If it looks like a black hole, how does anyone on the outside know
>> it's not a black hole? other than to accidentally (who's going to go
>> into a black hole on purpose?) fall in and then come back to tell
>> about it, that is.

LukeCampbell elucidated:

> If the wormhole has the Schwartzschild metric down past the event
> horizon, then you don't come back after falling in - ever. If you are
> lucky, the wormhole on the other side does not have an event horizon
> and you can get out. Otherwise, you are stuck.
>
> If the Schwartzschild metric stops before the event horizon, it does
> not look like a black hole.

The Morris-Thorne wormhole has the Schwarzschild metric in to a distance
r larger than the event horizon, has a shell of exotic matter comprising
the wormhole throat, and then has a Schwartzschild metric metric on the
other side.

Joseph Hertzlinger

unread,
Jul 11, 2004, 1:35:20 PM7/11/04
to
On Wed, 07 Jul 2004 12:16:50 -0700, Erik Max Francis <m...@alcyone.com>
wrote:

> Hop David wrote:
>
>> If I recall correctly an L4 or L5 object shouldn't be more than 1/26
>> the
>> mass of the moon.
>
> No, the secondary body (the Moon in your example) needs to be less than
> (about) 1/26 the mass of the primary body (the Earth in your example).
> The mass of the object actually attempting to reside in the Trojan point
> must be of negligible mass compared to the other two.

In order to be stable, the masses of the three bodies must obey the formula:

27*(m_1*m_2 + m_2*m_3 + m_3*m_1) < (m_1 + m_2 + m_3)^2

If I did the arithmetic correctly, in a system where two of the bodies
have masses of 1 and 1/81, the third must have a mass of either
greater than 25.281 or less than 0.27.

--
http://hertzlinger.blogspot.com

Erik Max Francis

unread,
Jul 11, 2004, 4:47:32 PM7/11/04
to
Joseph Hertzlinger wrote:

> In order to be stable, the masses of the three bodies must obey the
> formula:
>
> 27*(m_1*m_2 + m_2*m_3 + m_3*m_1) < (m_1 + m_2 + m_3)^2
>
> If I did the arithmetic correctly, in a system where two of the bodies
> have masses of 1 and 1/81, the third must have a mass of either
> greater than 25.281 or less than 0.27.

The stability criterion is usually given as (_Orbital Motion_, A.E. Roy,
p. 139):

mu = (1/2) - (23/108)^(1/2),

where mu is the mass of the secondary body expressed in units of the
primary body; that's 0.03852, or 1/25.96.

I'm not sure where you get your stability criterion (involving all three
bodies) from; for one thing, it gives seemingly absurd results (at least
by your solution, I didn't solve it myself), such as a Trojan point
being stable where the test body is more than 25 times massive than the
primary -- that's considerably more massive than Neptune!

--
__ Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
/ \ San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis

\__/ Forever we / Infinitely
-- Sandra St. Victor

Aaron Denney

unread,
Jul 11, 2004, 5:03:09 PM7/11/04
to
On 2004-07-11, Erik Max Francis <m...@alcyone.com> wrote:
> Joseph Hertzlinger wrote:
>
>> In order to be stable, the masses of the three bodies must obey the
>> formula:
>>
>> 27*(m_1*m_2 + m_2*m_3 + m_3*m_1) < (m_1 + m_2 + m_3)^2
>>
>> If I did the arithmetic correctly, in a system where two of the bodies
>> have masses of 1 and 1/81, the third must have a mass of either
>> greater than 25.281 or less than 0.27.
>
> The stability criterion is usually given as (_Orbital Motion_, A.E. Roy,
> p. 139):
>
> mu = (1/2) - (23/108)^(1/2),
>
> where mu is the mass of the secondary body expressed in units of the
> primary body; that's 0.03852, or 1/25.96.
>
> I'm not sure where you get your stability criterion (involving all three
> bodies) from; for one thing, it gives seemingly absurd results (at least
> by your solution, I didn't solve it myself), such as a Trojan point
> being stable where the test body is more than 25 times massive than the
> primary -- that's considerably more massive than Neptune!

Well, in that case, the trojan point is the primary, the primary is the
secondary, and the secondary is the trojan point.

--
Aaron Denney
-><-

Erik Max Francis

unread,
Jul 11, 2004, 5:05:46 PM7/11/04
to
Aaron Denney wrote:

> Well, in that case, the trojan point is the primary, the primary is
> the
> secondary, and the secondary is the trojan point.

His lesser stability limit still puts the test body at much more massive
than the secondary body (1/81 vs. 0.27), which isn't stable at all, so
there's clearly something wrong with the equation he's using. (I've
never seen an equation like that, so I suspect this is just a
misapplication of something.)

Joseph Hertzlinger

unread,
Jul 11, 2004, 5:53:34 PM7/11/04
to
On Sun, 11 Jul 2004 13:47:32 -0700, Erik Max Francis <m...@alcyone.com> wrote:

> Joseph Hertzlinger wrote:
>
>> In order to be stable, the masses of the three bodies must obey the
>> formula:
>>
>> 27*(m_1*m_2 + m_2*m_3 + m_3*m_1) < (m_1 + m_2 + m_3)^2
>>
>> If I did the arithmetic correctly, in a system where two of the bodies
>> have masses of 1 and 1/81, the third must have a mass of either
>> greater than 25.281 or less than 0.27.

Actually, the 0.27 should have been 0.027.

> The stability criterion is usually given as (_Orbital Motion_, A.E. Roy,
> p. 139):
>
> mu = (1/2) - (23/108)^(1/2),
>
> where mu is the mass of the secondary body expressed in units of the
> primary body; that's 0.03852, or 1/25.96.
>
> I'm not sure where you get your stability criterion (involving all three
> bodies) from; for one thing, it gives seemingly absurd results (at least
> by your solution, I didn't solve it myself), such as a Trojan point
> being stable where the test body is more than 25 times massive than the
> primary -- that's considerably more massive than Neptune!

I got it from an article in Volume 5 of of "What's Happening in the
Mathematical Sciences" by Barry Cipra. In the limiting case where m_3
goes to zero, it becomes the usual formula.

--
http://hertzlinger.blogspot.com