
The Moon is the Earth’s only natural satellite . It is located 240,000 miles
from Earth .

There are two (2) methods for determining the Moon’s distance from the Earth .

One of them uses parallax . (The other method was discussed in an earlier chapter on the Moon .)
: - The apparent motion of an object due to the motion of
the observer .

When using the Earth’s diameter as the baseline , the Moon is observed from opposite sides of the Earth .

A line is drawn directly to the Moon from both sides of the Earth.

The resulting triangle is then cut in half .

Using trigonometry the distance to the Moon is then calculated .
331


This is a three (3) step process.
1) Measure the angle .
2) Measure the length of one side of the triangle .
3) Use the tangent to find the distance to the Moon

The Earth’s diameter is large enough, and provides enough of a parallactic shift , to measure adequately the distance to the Moon .

But stars , however, are found at very great distances out in space , and the
Earth’s diameter is too small to serve as their baseline .

We instead use the diameter of the Earth’s orbit as the baseline .

By observing a star at opposite times of the year , we can increase the parallactic baseline to 2 AUs .
332


These 2 AUs are the diameter of the Earth’s orbit , which equals
186,000,000 miles . (below, left)

From June to December , we see the same star shift in space as the Earth orbits the Sun . (below right)

And since this distance is 23,250x larger than the Earth’s diameter ,
then the diameter of
Earth’s orbit
provides an adequate baseline to measure the distances of stars .

If the star had been closer to the Earth , then its parallactic shift would have
been even greater . (below, left)

And had the same star been farther away from Earth , then its parallactic shift would have been less . (below, right)

So parallax serves as an excellent distance indicator of stars because the closer a star is to the Earth , then the greater the parallactic shift the star exhibits, and the farther away a star is from the Earth , then the less the parallactic shift it exhibits .
333

*****************WS#1****************

Even with a baseline as broad as 2 AUs , many stars are too far away to reveal any parallactic shift at all .

Even with the closest stars to the Sun , the parallactic shift is less than
334

1 arcsecond .

But if a star did exhibit exactly 1 arcsecond of parallactic shift , then the distance to that star would be known as 1 parsec . (below, left)
(For future reference, 1 arcsecond is written as 1”, and 1 parsec is
written as 1 pc.)

One (1) pc is equal to 3.26 LY , and there is not a single star which exists within
3.26 LYs or 1 pc of the Sun .

Since all stars within the Universe are farther away than 1 pc , then their parallactic shifts will all be less than 1 arcsecond .

The closest star system is Alpha Centauri , and it is located at 4.3 LY , or 1.3 pc
from the Sun .

At 1.3 pc of distance , Alpha Centauri will exhibit exactly
0.76”
of parallactic shift . (below, right)

What happens to the parallactic angle if the star were closer than 1 arcsecond ?

For example , imagine that a star were only 1/2 pc away from the Sun ?

In that case , its parallactic shift would be 2 arcseconds . (below, left)
335


However, if the star were located at a farther distance than 1 pc away from
the Sun , then the angle will close up and becomes smaller .

For example , a star located at distance of 2 pc from the Sun shows a parallactic shift of only 1/2 arcsecond . (below, center)

So at twice the distance , the angle is only half as much. (below, right)

In the (3) examples given thus far , a trend should be apparent .

The parallactic shift exhibited by a star is always the inverse of the distance ratio .

Imagine that (5) random stars exhibit the parallax shown below .

The stars’ parallaxes can be represented either as a decimal or as a fraction .

Using only this information , the stars’ distances
can be derived . (below, left)

Notice the relationship which exists between a star’s fractional parallax and its distance .
336


They are all reciprocals of each other . (below right)

Just like a teeter-totter , when one is up , the other is down .

But as long as only one of the two numbers is known , then the other number can be instantly found .
*****************WS#2****************

The Alpha Centauri star system is the closest star system to the Earth .

When looking at it from a distance , then Alpha Centauri looks like one single star . (below, left)

Upon closer examination , however, we see that there are really 3 stars there.
(below, right)
337


The largest star within the system is also called “ Alpha Centauri ”.

It is the brightest star within the constellation of “ Centaurus ”.

The second largest star within the system is called “ Beta Centauri ”, and it is the second brightest star in the constellation of “ Centaurus ”.

The last star, “ Proxima Centauri ”, is the smallest star within the system .

Proxima Centauri is the star which actually comes the closest to the Earth .

Sometimes, Alpha Centauri is closer to the Earth than is Proxima Centauri .

But when traveling past the Earth , then Proxima Centauri is the star which actually comes the closest to Earth of them all . (below, middle)

Since Alpha Centauri is 1.3 pc away from the Sun , then its parallactic shift is only
0.76”
. (below, left)
338


Beyond the Alpha Centauri system lies Barnard’s Star , the second closest star to the Sun . (below, left)

At a distance of 6 LY , Barnard’s Star is 1.8 pc away and shows only 0.55” of parallactic shift . (below, right)

The farther we look into space , the greater the volume of space we observe .

Imagine a cube of space which is 8 pc on each of its 3 sides . (below, left)

If the Earth were positioned at the exact center of this cube , then we would only be looking 4 pc (13 LY) in any one direction . (below, middle)

Within 4 pc of Earth , we would find about 30 stars in each of 6 different directions ( up, down, left, right, front, back ) from Earth . (below, center)
339

*****************WS#3****************

As the Earth orbits the Sun, some stars show parallactic shift .

But even for Alpha Centauri , this shift is less than 1 arcsecond (0.76”).
(below, left)

Since Alpha Centauri is the closest star , then it shows the greatest amount of parallactic shift .
340


But the parallactic shift for every other star in the Universe will be less .
(below, right)

The light from any star should appear only as a pinpoint of light when viewed from Earth , however, it never does . (below, left)

The main hindrance to viewing stars from a ground-based telescope is that the turbulence in the atmosphere will blur and smear the star’s light
.

Instead of appearing merely as a pinpoint of light , the star’s light is instead spread and smeared over a much wider circle . (below, middle)

This circle over which a star’s light is spread is referred to as its “ seeing disk ”.
(below, right)

The smaller the seeing disk is, the more highly resolved the star will be.
(below, left)
341


But the larger the seeing disk is, then the blurrier the star will appear to be.
(below, right)

Due entirely to turbulence in the atmosphere , even the best ground-based telescopes cannot resolve the star’s seeing disk to less than the 1” smear .
(below, left)

Since the greatest amount of parallactic shift is always 0.76” or less , then telescopes cannot detect the star’s parallax
. (below, right)

The star’s parallax would always occur entirely within the (1) arcsecond smear and therefore be undetectable motion . (below)
342


When astronomers use special equipment , however, then the seeing disk can be reduced to only 0.03
” or less . (below, left)

Since the seeing disk is now smaller than the parallactic shift , then the parallactic shift can be detected from Earth . (below, right)

These 0.03
” of parallactic shift corresponds to about 30 pc of distance , and
30 pc = 100 LY .

Imagine a cubic volume of space which is 60 pc on each of (3) sides .
(below, left)

If the Earth were positioned at the exact center of this cube , then we would be looking 30 pc (100 LY) in any direction . (below, middle)
343


Within 30 pc of Earth , we would find about thousands of stars in each of
6 different directions ( up, down, left, right, front, back ) from Earth .
(below, right)

Thanks to technology , we can now overcome the atmospheric limitations , and the parallax of thousands of stars can be seen within 100 LY of the Earth .
*****************WS#4****************

When stellar parallax is observed , it is not because the star is really moving .

Instead, this apparent motion is caused by the Earth’s orbit around the Sun .

While stars do not orbit the Sun , they do however move through space as they orbit the galactic center .

This real motion is called “proper motion” , and is totally independent of the motion of the Earth as it orbits the Sun .

When a star’s motion is observed , the parallactic component of the total motion must be subtracted , and what is left is the star’s true motion , or its proper motion .
344


For example , a star is seen to move from one side of the sky to the other .
(below, left).

But in which direction was the star really moving ? Did it move as shown below ?
Not necessarily!

All stars will appear to be projected onto the celestial sphere . This can make them appear to be closer to the Earth than they actually are .

The true location of the star may be much farther away . (below, right)

So while the star may appear from Earth that it traveled as shown in the photo (below left), its true motion was as shown in the photo (below middle).

This motion is the star’s actual motion , also called its “ proper motion ”.
(below, right)
345


Some of the star’s proper motion can be resolved into its lateral motion .
 The star’s lateral motion is always at a right angle to our line of sight .

This motion is called the star’s “ transverse motion
” and is the motion as seen from Earth across the celestial sphere . (below, left)

But some of the star’s proper motion was also towards the Earth .

This motion is known as the star’s “ radial motion ” and is the component of the star’s proper motion either towards or away from Earth . (below, right)

Radial motion can be determined by the Doppler Effect .

So in trying to determine a star’s true actual motion , we must first establish both its transverse and radial motions .
346


While many stars exhibit proper motion , it is
Barnard’s Star
which exhibits the most .

Watch the motion of
Barnard’s Star
in the blink comparator with 2 photos taken 22 years apart. (below, left & middle)
 During those 22 years between when the two photos were taken,
Barnard’s Star moved a total of 227” . (below, right)

This translates to 10.3”/year of proper motion.

The motion of Alpha Centauri can be seen in the photos below.
347


Its proper motion is shown at 31 km/sec (below, left).

Its radial motion is shown as 20 km/sec (below, middle).

And finally , its transverse motion is shown as 24 km/sec in a direction perpendicular to our line of sight (below, right).
*****************WS#5****************
*****************TEST****************
348