Expert: Tom Whiting - 9/25/2006

Question
how can i find out whether an object is
a)in our solar system
b)outside our solar system but inside our galaxy
c)outside our galaxy
reasoning behind these staements

Answer
Hi Molly,
By "i"...I assume you mean "you".  Unless you are a professional astronomer working for a large observatory,
you can't.  Neither can I, or any other amateur astronomer
unless you have access to some pretty sophisticated
equipment.  That is why we hire and pay the professionals
to do that kind of work, then we simply read (and memorize)
their results and conclusions, in your astronomy textbook.
(No need to re-invent the wheel here). ;-)

But if you mean "i" as.....how do they, the professionals
do it...... well, one way is by motion across the sky over a
period of time, relative to the fixed stars.   Recall Kepler's 3rd law where any body in orbit around the sun, the period squared is proportional to the distance cubed.  So if an unknown body is slowly tracking  (read that....moving from night to night or even week to week, relative to the fixed stars), then all it takes is a series of several observations to determine it's orbital speed, it's period (the time it takes
to make one orbit around the sun) and thus the distance from the sun with Kepler's 3rd law.  Basically, the slower it's
moving, the farther from the sun it is.  Recall Mercury
takes only 88 days for one revolution, whereas Pluto
takes about 248 years for one revolution.

B.  Basically the same way, by measuring the motion, but
here the motion is so small, so we use another trick for the
closer stars that are beyond the Solar System but members
of the Milky Way Galaxy.  They  use "parallax"....hold one finger up at arm's length and close one eye, now switch eyes
back and forth looking at your finger against a more distant background wall.
Notice how your finger appears to "jump" when you switch
single eyes. This is because each eye is seeing the finger
at a different angle, and that small angle is called the
parallax angle. Once that angle is measured and known,
through mathematics called "trigonometry" we can calculate
the distance.  So how do they do it with unknown heavenly bodies?
They photograph the object tonight, and again, exactly 6 months (1/2 year) later when the Earth is on the other side of the sun.
The parallax shift is then measured on the photographic
plates....we know the diameter of the Earth's orbit, about
187 million miles and we know we have a right angle in
the triangle.  In trigonometry, if you have (know) either two sides and an angle, OR,  2 angles and a side, then you can
calculate any other angle or side length using trig.  That's how it's done for  your "b" objects.

C.  With something outside our galaxy, there would be
no motion sideways across the sky, at least in our short
lifetimes.  However there is a motion either toward us or
away from us (called approach velocity or recessional
velocity) that can be measured using the Doppler
Shift.  If a luminous object is moving toward you, it's light
will exhibit a blue shift (a shift of it's light toward the blue or
short wavelength end of the spectrum) , and if it's moving away, it's light will exhibit the opposite -  a red shift....in fact, since most objects are moving away as the Universal Space expands in size, this is called the Red Shift Effect.  This amount is measured by the professional astronomers using a spectroscope to find the amount of light wavelength shift, and that information, coupled with the Rate of Expansion of the Universe...called the Hubble Constant which is equal to about 70 Km/Second per megaparsec.....we can now calculate a reasonable distance,  and how far the object is from the Milky Way Galaxy.

So basically astronomers use a "distance ladder"...the
nearby Solar System objects are very accurately measured,
to within a few miles, sometimes even by bouncing radar
signals off of them which is super-accurate!  The parallax rung on the ladder has about a 10% error because it is not a direct measurement, and the Red shift rung on the ladder  could be as high as 30%.  Notice each successive step outward introduces a higher error, but it's the best we can do right now, so we have to live with it.  Besides, if something is out there 30 million lightyears, who cares if it's really 27 or 33 million lightyears...we ain't going there tomorrow anyway!  

There are also a few intermediate rungs on the distance
ladder that I haven't covered that can be used for
distance indicators...with varying degrees of built in error
between 10 and 30%.  A certain star varies in light on a
regular time basis, called a Cepheid Variable....and there
is a correlation between their variability and their brightness,
so astronomers simply time the peaks in variability, and
presto!  they have the distance because brightness ratio's
are related to distance.  (Basically the ratio is the absolute
magnitude compared to the apparent magnitude).
There is a "cluster variable" called an RR Lyrae star that
we can do the exact same thing with.

They do the same for Type Ia supernovae.....ideally, we
think that all Type Ia's have the same intrinsic brightness
at peak luminosity.....so by observing the apparent brightness at their peak, we can calculate a rough distance to that host galaxy.

So see, they aren't just "guessing" as we really use a known
system...it isn't perfect, but it's the best we can do right now,
until someone discovers, or invents....a better mousetrap.
I think the reasoning here, is pretty much self-explanatory in my explanations above.

Hope all this helps,
Clear skies,
Tom Whiting
Erie, PA