Sun <==> Alpha Centauri gravity interactions

Some texts (notably one or two books I vaguely recall of Patrick
Moore's) often show projections of *brightest* and *closest* stars in
the several thousand years before and after the present time. I
distinctly recall that Barnard's star is one that will become the
closest star to the Sun in so many thousands of years from now at
around 3.5(?) odd light years and then it will start receding away
from us again after that time.

Firstly, how does one go about making such future positional guesses
and secondly, how long has Alpha Centauri been in close proximity to
the Sun? Is there any projections as to how long Alpha Centauri will
stay this close?

Could it be that Alpha Centauri (A+B+C) and the Sun are
gravitationally *locked* together and share a common proper motion
around the galaxy? I know we observe distinct radial velocity and
proper motions that Alpha Centauri has relative to the Sun, but they
are based on short term measurements in the current era... and I don't
expect you can simply *extrapolate* forwards/backwards in time simply
on the basis of their present values... or can you?

According to "Solstation" (my number one favourite site for local star
system research!):-
http://www.solstation.com/stars/alp-cent3.htm

the next nearest large star system to have any *significant*
interaction with both the Sun and Alpha Centauri(A+B+C) is Sirius
(A+B) - which is quite far removed at 8.6 LY away from the Sun and 9.5
LY away from from Alpa Cen.

This means the Sun and Alpha Centauri system are relatively isolated
in space, where it is conceivable that bodies orbiting far out around
each system are gravitationally perturbed in the manner in which I
illustrate he-

http://uk.geocities.com/aa_spaceagen....html#midrange

Its important I think to study our nearest triple star system in
greater depth (if only it rose above my horizon... but then I can't do
a lot with my tiny 8-inch Newtonian!). How much Hubble or other
space/ground-based telescope time is devoted to Alpha Centauri,
compared to all other stellar astronomy, I wonder...

cheers
Abdul Ahad

Abdul Ahad wrote:
Firstly, how does one go about making such future positional guesses
and secondly, how long has Alpha Centauri been in close proximity to
the Sun? Is there any projections as to how long Alpha Centauri will
stay this close?

The gravitational interactions between stars are pretty small. Unless
one star is predicted to pass very close indeed--say, less than a tenth
of a light-year or so--the impact on their orbit around the galactic
center is minimal. Testament to this is the relative stability of the
galactic disc. You can map the radial and proper velocities of the
star in three dimensions and get reasonably accurate results into the
fairly distant future (say, about a million years) for the nearest stars.

Could it be that Alpha Centauri (A+B+C) and the Sun are
gravitationally *locked* together and share a common proper motion
around the galaxy?

No. I forget the exact figures, but the relative velocity of the
alpha Centauri system is considerably more than permitted for a locked
system.

I know we observe distinct radial velocity and
proper motions that Alpha Centauri has relative to the Sun, but they
are based on short term measurements in the current era... and I don't
expect you can simply *extrapolate* forwards/backwards in time simply
on the basis of their present values... or can you?

You sure can, because the gravitational interactions between individual
stars separated by light-years are quite weak.

the next nearest large star system to have any *significant*
interaction with both the Sun and Alpha Centauri(A+B+C) is Sirius
(A+B) - which is quite far removed at 8.6 LY away from the Sun and 9.5
LY away from from Alpa Cen.

This means the Sun and Alpha Centauri system are relatively isolated
in space...

How do you figure? The Sun and alpha Centauri are 4.3 light-years apart,
or half the distance from here to Sirius. Since Sirius has a bit more
than twice the mass of the Sun, and is more massive than the entire alpha
Centauri system, I don't think you can consider the Sun and alpha Centauri
much more isolated from Sirius than they are from each other.

The essential paucity of gravitational interaction is why the "stellar
rape" hypothesis of the solar system's formation had such a short life
in the middle of the 20th century. It's just too darned unlikely for
stars to pass that close to one another. To give you an idea of how far
apart the stars are from one another, consider that the Sun and alpha
Centauri A are about the same size (1.4 million km across) and are
separated by about 42 *trillion* km. That is, the distance between them
is about 30 million times their diameters.

To put it another way, if the Sun is a golf ball in San Francisco, then
alpha Centauri is another one (or two golf balls and a marble) in Los
Angeles, and Sirius is a slightly larger racquetball, accompanied by an
incredibly dense BB pellet, in Boise. Picture that for a moment, and
ask yourself how likely it is that they will interact with one another.
And remember, they move in three dimensions, not two.

Its important I think...

Steady, Brian, steady...

Its important I think to study our nearest triple star system in
greater depth (if only it rose above my horizon... but then I can't do
a lot with my tiny 8-inch Newtonian!). How much Hubble or other
space/ground-based telescope time is devoted to Alpha Centauri,
compared to all other stellar astronomy, I wonder...

What you require is accurate astrometry, and this has all been done
previously--most recently by the Hipparcos mission.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

AA Institute wrote:

Could it be that Alpha Centauri (A+B+C) and the Sun are
gravitationally *locked* together and share a common proper motion
around the galaxy?

Brian's already answered this, but you don't have to take his word for
it. Your own page has the formulas you need to estimate the strength
of the gravitational interaction.

The gravitational force f between the sun and Alpha Centauri (assuming
I haven't goofed this up) is roughly

f = G M m / r^2

G = 6.7 * 10^-11 N m^2 / kg^2 Newton's Gravitational Constant
M = 2 * 10^30 kg mass of sun
m = 4 * 10^30 kg mass of Alpha Centauri
r = 4 * 10^16 m distance

f = 3.4 * 10^17 N

That looks like a lot, but it takes a lot of force to move a star. The
acceleration of the sun due to f is

a = f / M = 1.7 * 10^-13 m / s^2 = 0.00000000000017 m / s^2

Pretty small. If the sun were a car powered by the gravitational
attraction of Alpha Centauri, it would go from 0 to 60 (miles per hour)
in about 5 million years.

t = v / a

v = 60 mph = 27 m / s
a = 1.7 * 10^-13 m / s^2
t = 27 / (1.7 * 10^-13) s

Finally, if you substitute the Earth for Alpha Centauri,

m = 6 * 10^24 kg
f = 5.4 * 10^23 N

you find that the force between them is a million times stronger.

- Ernie http://home.comcast.net/~erniew

Wasn't it AA Institute who wrote:

Could it be that Alpha Centauri (A+B+C) and the Sun are
gravitationally *locked* together and share a common proper motion
around the galaxy?

To be gravitationally locked, their relative velocity would need to be
less than the escape velocity of one from the other. A quick calculation
shows the relevant escape velocity to be about 81 metres/second at this
distance. The radial component of the relative velocity is about 26400
metres per second, so they're not gravitationally locked.

--
Mike Williams
Gentleman of Leisure

(Brian Tung) wrote in message ...
Abdul Ahad wrote:
Firstly, how does one go about making such future positional guesses
and secondly, how long has Alpha Centauri been in close proximity to
the Sun? Is there any projections as to how long Alpha Centauri will
stay this close?

To put it another way, if the Sun is a golf ball in San Francisco, then
alpha Centauri is another one (or two golf balls and a marble) in Los
Angeles, and Sirius is a slightly larger racquetball, accompanied by an
incredibly dense BB pellet, in Boise. Picture that for a moment, and
ask yourself how likely it is that they will interact with one another.
And remember, they move in three dimensions, not two.

Your scale illustration is a good one, makes it easier to picture
distances in every day terms. Of course, the inverse square law
governing gravitational interactivity dictates that for a system such
as Sirius which is twice as far away from the Sun as Alpha Centauri,
the force of gravity will be only a quarter as strong (other things
like relative masses, being equal). So you'd expect the Sun and Alpha
Centauri to interact 4 times as strongly between one another, compared
to the strength with which each one interacts with the Sirius system.

So I would say, from a perspective of gravitational interactivity, the
Sirius system is relatively *far removed*... but you have every right
to disagree of course!

So if Alpha Centauri is not gravitationally *connected* with the Sun,
are you saying that its just another passing star system? Is there a
3D model available to show the projected distances separating Sun from
Alpha Centauri on a time-series basis like this:-

Epoch: Distance:
================================================== ============
Now - 1 million years ?
Now - 500,000 years ?
Now - 100,000 years ?
Now 4.3 LY
Now + 1 million years ?
Now + 500,000 years ?
Now + 100,000 years ?

Its important I think...

What you require is accurate astrometry, and this has all been done
previously--most recently by the Hipparcos mission.

What about extrasolar planet detection efforts around Alpha Centauri,
to your knowledge?

Thanks for sharing your thoughts.

Abdul Ahad

Abdul Ahad wrote:
So I would say, from a perspective of gravitational interactivity, the
Sirius system is relatively *far removed*... but you have every right
to disagree of course!

And I do. I still think you are entranced by this idea of the Sun and
alpha Centauri as being partners in space, when they very clearly are
not. Since the gravitational influence of Sirius on alpha Centauri is
just about half that of the Sun's, I wouldn't call that at all far
removed. Further removed, yes, but somebody has to be closest. That
doesn't say anything about whether we're bound to each other. And, as
it happens, we are not.

So if Alpha Centauri is not gravitationally *connected* with the Sun,
are you saying that its just another passing star system?

Yes. We've said that a number of times, now.

Is there a
3D model available to show the projected distances separating Sun from
Alpha Centauri on a time-series basis like this:-

Epoch: Distance:
================================================== ============
Now - 1 million years ?
Now - 500,000 years ?
Now - 100,000 years ?
Now 4.3 LY
Now + 1 million years ?
Now + 500,000 years ?
Now + 100,000 years ?

You can construct one very simply from available three-dimensional
velocity data. From the Doppler shift, one gets the velocity along the
line connecting us and alpha Centauri; from the proper motions, one
gets the velocity in the plane perpendicular to that line. Combine
that, and you can derive the values in the table above.

What about extrasolar planet detection efforts around Alpha Centauri,
to your knowledge?

To my knowledge, such efforts have been unsuccessful in detecting planets
around alpha Centauri A, B, or C. That doesn't mean that there aren't
any planets around any of those stars--only that if there are, they are
too small (or, just conceivably, in an orbital plane that is too close to
perpendicular to our line of sight) to have been detected yet.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Mike Williams wrote in message ...
Wasn't it AA Institute who wrote:

Could it be that Alpha Centauri (A+B+C) and the Sun are
gravitationally *locked* together and share a common proper motion
around the galaxy?

To be gravitationally locked, their relative velocity would need to be
less than the escape velocity of one from the other. A quick calculation
shows the relevant escape velocity to be about 81 metres/second at this
distance. The radial component of the relative velocity is about 26400
metres per second, so they're not gravitationally locked.

According to a formula I found in my spherical astronomy notes for
proper motion, the 'transverse velocity' (component of total velocity
projected *across* our line of sight) is given by:

v = 4.74 * (proper motion / parallax) km/sec, so for Alpha Centauri, v
= 4.74 * (3.7 / 0.74) = 23.7 km/sec = 5.0 AUs per year. Translating
the star's given radial velocity of -24.6 km/sec to AUs per year =
-5.5 AUs/year

So if the transverse velocity of Alpha Cen is 5.0 AUs/yr and the
radial velocity is -5.5 AUs/yr, does this mean that in 50,000 years
(272,000 AUs current distance / 5.5 AUs radial velocity) Alpha
Centauri is going to be very close to us?! Probably not, since due to
gravitational interaction with the Sun, Alpha Centauri might describe
a 'curved' trajectory as opposed to a linear one.

It would be so much easier to visualise the whole thing in a 3D
diagram.

Abdul

Ernie Wright wrote in message ...

a = f / M = 1.7 * 10^-13 m / s^2 = 0.00000000000017 m / s^2

Pretty small. If the sun were a car powered by the gravitational
attraction of Alpha Centauri, it would go from 0 to 60 (miles per hour)
in about 5 million years.


Ernie,

That is a seriously tiny acceleration and for a massive body like the
Sun, I'd expect that sort of result but thanks for putting some hard
numbers to illustrate it all - makes it so much easier to visualise.

However, in relation to my interstellar journey "blueprint" (or
proposal to a far future generation!) I am concerned with
gravitational accelerations of tiny comets (effectively infinitesimal
*particles* of negligible mass in comparison with the mass of a star)
which will be perturbed (gravitationally accelerated) from a fraction
of the total Sun-Alpha Centauri distance.

Of course, looking across the other side of the interstellar "pond" we
find Proxima Centauri (with just 12% of Sun's mass) sharing a definite
common proper motion with Alpha Centauri A+B, and its placed at a huge
range of 13,000 AUs from the primary pair.

Its all going to be a *conjecture* sort of result I think...! But the
beauty of the "Aster-Com" starship concept is you can turn back at any
time you run into vaccuums with regards to resource availability on
comets/planetoids towards Alpha Centauri!

I wonder if its possible to see a mirage ahead from the control room
of a water-starved starship... LOL!!!

Abdul

"AA Institute" wrote in message
m...
So if the transverse velocity of Alpha Cen is 5.0 AUs/yr and the
radial velocity is -5.5 AUs/yr, does this mean that in 50,000 years
(272,000 AUs current distance / 5.5 AUs radial velocity) Alpha
Centauri is going to be very close to us?! Probably not, since due to
gravitational interaction with the Sun, Alpha Centauri might describe
a 'curved' trajectory as opposed to a linear one.
I've not checked your figures but assuming them to be correct: since the
transverse velocity is of the same order as the radial velocity, then by the
time the radial velocity 'would' have closed the distance between Alpha
Centauri and the Sun, the transverse velocity would have carried it just as
far at right angles and it will end up a similar distance away. The closest
approach would then be about 0.7 times the current distance.

It would be so much easier to visualise the whole thing in a 3D diagram.
There are programs available for plotting just such things in 3D. I remember
mentioning Mathcad not too long ago! You can even allow a term for the
gravitational interaction between the stars and convince yourself that it
has little effect. I'd do it for you except I have more interesting projects
I would rather spend my time working on (no offence meant).

Also referring to memory, which, as I always remind everyone, is very dodgy,
I have a vague recollection that when the velocities of nearby stars are
compared, the stars essentially fall into two groups. Stars in our group
move pretty much in the same direction and speed as the Sun, while the other
group of stars travel in a direction and speed that is common to them and
different from ours. I believe there were other factors such as age and
composition that distinguished the two groups? I apologise if this is not
the case, however, like most things, I cannot remember my source.
Grim

Grimble Gromble wrote:

Also referring to memory, which, as I always remind everyone, is very dodgy,
I have a vague recollection that when the velocities of nearby stars are
compared, the stars essentially fall into two groups. Stars in our group
move pretty much in the same direction and speed as the Sun, while the other
group of stars travel in a direction and speed that is common to them and
different from ours. I believe there were other factors such as age and
composition that distinguished the two groups? I apologise if this is not
the case, however, like most things, I cannot remember my source.

You're probably thinking of the "Population I" _vs_ "Population II"
classification. The former stars, including our Sun, are part of the
galactic disk, having been born from its clouds of gas and dust, and
orbit the galactic centre pretty much in a plane. The latter group,
mostly older stars that are evolving out of the main sequence, form a
spherical 'halo' around the Galaxy, with orbits that tend to
intersect the disk at steep angles, and make up most of the globular
clusters. Arcturus (Alpha Boötis), a fairly nearby orange giant, is
one of the most prominent examples of a Population II star, and
because of the high inclination of its path through the galactic disk
it exhibits the largest proper motion of any first-magnitude star,
cutting across the 'stream' in which the Sun and its contemporaries
are moving.

--
Odysseus