Sun <==> Alpha Centauri gravity interactions

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

Dave's reply is correct. One further point is that you can have
epochs in fractions of a year (1950.5, 2004.0, etc.). The positions
on a chart are accurate and can be compared (internally and
externally) only if the epoch is given. For crude studies the epoch
isn't that important (the changes are tiny). Astronomers have gone
way beyond that.

Any reference frame can be used (usually a star, or maybe the galactic
center) so long as the epoch for each position is known. There are
plenty of old photographic plates stored in observatories going back
about 100 years that are still useful for modern studies. I used such
plates at Allegheny Obs. in Pittsburgh back in the 1960s to measure
parallaxes of stars (distances). Most of the stars were faint with
strange catalog names. The brightest one was Tau Ceti..

Good question, BP!

Saul Levy


On Fri, 10 Sep 2004 20:55:30 -0700, "BP"
wrote:

All right this is an something that is bothering me...Every period, new
Epochs are published for star charts. What is it 50 years? I have a chart
that was from 2000.0. If I remember correctly the obsolete one was 1950.
So, I am assuming that this is a trend. Every 50 years, a new epoch.

1.) Is there some object within this galaxy that we can use as a relative
point that moves minimally enough to use as a "relative object" to which we
can attach our reference frame? Or is motion just measured relative to
neighbors? Or is everything just placed by position on the celestial sphere
on these newer editions(epochs)?

2.) Are measurements made in the past (far by our standard, short in other
frameworks) good enough to include with our more precise instruments to form
observations about motion?

BP

Space motion (plus galactic motion) is used to determine how close
stars will get to each other. Of course you can extrapolate from
present values. Astronomers do it all the time. Very close stars can
only take thousands of years to reach closest approach. Most stars
are much farther away and take much longer (if it occurs at all).
There is plenty of proper motion data going back 50-100 years which is
enough time to pin down the space motion of the nearer objects.

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

Wasn't it AA Institute who wrote:
Mike Williams wrote in message news:Q9MYRBANsrQBFwP
...
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

Are you certain that your values for "proper motion" and "parallax" have
the correct units for the equation you're using? I use a more direct
method and get a vastly different answer.

I started with the fact that the proper motion is RA: -7.54775
acsecs/year, Dec: +0.48180 arcsecs/year and the distance is 4.3 light
years.

A light year is 9.46e15 metres.
-7.54775 arcsecs/year of RA is -0.000549399 radians/year
0.48180 arcsecs/year of Dec is 2.33583e-06 radians/year
(Note a complete circle is 24h of RA but 360d of Dec)

The transverse motions are Distance * sin(Angle), giving
-2.23484e+13 and 9.5017e+10 metres/year. Divide by the number of seconds
in a year and combine the two velocities by Pythagoras and I get the
transverse motion to be 710 km/sec = 150 AU/year.

--
Mike Williams
Gentleman of Leisure

"Grimble Gromble" wrote in message ...
"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.

Thanks Grim, silly me for not seeing the wood for the trees...
So the closest approach point for Alpha Centauri (around 3 LY) is
still yet to come? Hoooorrrraaayyy!!!

This could be the ideal interstellar *launch window* for the Aster-Com
starship. A future generation of Earth might face the challenging
choice of either taking this window of opportunity or declining the
offer in anticipation of another star passing by the Sun. But that's
gonna be a long, long time coming...

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).

That's fair comment. Hey, what's the big deal with a 50,000 year
voyage inside some hollowed out gigantic boulder rolling across in the
deep, dark ocean of space toward some unknown destination
pre-programmed by your great great great grand parents? It sucks...

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.

No probs, really appreciate your thoughts.

One final question: interstellar navigation - how can I do it whilst
drifting in this great interstellar ocean where the shores reach out
to near eternity in every direction?

"In the extreme circumstance where no new bodies are found for meeting
projected resource requirements, the ship can turnaround and back
track towards previously charted bodies using emergency reserves. With
no magnetic fields, no bright planets, no "GPS" for relative
referencing, the minute positional shifts of nearby stars may be the
only method of interstellar navigation in the surrounding darkness of
3D space."

How can I precisely chart the *absolute* positions and ship-relative
velocities of icy comets encountered on a forward pass... then try to
re-intercept them on a reverse pass, having turned my ship around?

Abdul

(Brian Tung) wrote in message ...

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

Thanks Brian, that's awfully clear now.

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.


I've heard it once mentioned that a planet orbiting one of the stars
of a binary system can receive large doses of radiation from two stars
as opposed to one and that 'flaring' between the two suns of the
system could be common place.

Take our Sun for instance and the recent high levels of solar activity
we've seen, sending massive amounts of charged particles toward the
Earth. Now imagine if Alpha Centauri B was orbiting somewehere around
where Uranus or Neptune is in our solar system, how much of an effect
would the additional radiation from this secondary sun add to our
every day lives?

If solar type flaring occurs on Alpha Centauri A and B, I wonder if
the gravitational interactivity between the two stars would increase
this flaring disproportionately. In other words, if the two stars were
isolated and not confined in a binary setup then (radiation from A +
radiation from B) would be less than that where the two stars are
gravitationally bound as in the case of Alpha Centauri? Is it
possible that the invisible gravitational flux lines (if that's the
right way to put it?) could induce too much flaring and cause harm to
any life evolving around a planet orbiting either star?

If such flaring caused *minute* variability to the overall
brightnesses of each star, surely that would vary across the 80 year
orbital period of the system and we should perhaps see an increase
towards the periastron passage time when the stars are closest
together? I wonder if such tiny variations could in fact be tracked by
photometric equipment carried on space telescopes in orbit around
Earth like the Canadian MOST mission. etc...

Thanks,
Abdul

"AA Institute" wrote in message
om...
Take our Sun for instance and the recent high levels of solar activity
we've seen, sending massive amounts of charged particles toward the
Earth. ...
My god; it's shooting at us!
Grim

"AA Institute" wrote in message
om...
How can I precisely chart the *absolute* positions and ship-relative
velocities of icy comets encountered on a forward pass... then try to
re-intercept them on a reverse pass, having turned my ship around?
That isn't necessary. Just plant a small transmitter on the comet; that will
give you directional information. If the transmissions and receptions are
accurately timed (pulsars make excellent clocks available to all) then the
distance to the comet can be easily calculated.
Grim