Download 9/28/16 Wednesday Parallax Lab

Procedure
Let's test how the parallax of an object varies with distance. Follow these instructions and write your
answers on the answer sheet as you go along.
One partner takes the meter stick and places the pencil at the 50 cm mark, centering the pencil on the
meter stick. The other partner places the "zero" end of the meter stick against her/his chin, holding it out
horizontally. This partner then alternates opening and closing each eye, noting how the pencil moves
against specific background object s.
Have your partner move the pen half of the original distance (to 25 cm). When you alternate opening and
closing each eye does the pen appear to move more or less than before? Try to quantify how much more
or less (twice as much? half as much? three times as much? etc.).
Now, have your lab partner move the pen twice the original distance to you, to approximately the end of
the meter stick. When you alternate opening and closing each eye does the pen appear to move more or
less than before? Try to quantify how much more or less (twice as much? half as much? three times as
much? etc.).
The parallax of the pencil depends on the distance the pencil is from you -- the closer the object, the
larger the parallax. Thus, although it may have been hard to tell precisely, when the pencil was half the
original distance from you, it had twice the parallax; when it was double the original distance from you, it
had one-half the parallax.
Let's take a look at the approximate relationship between distance and parallax from a different viewpoint.
The distance d2 is twice the distance d1. Does it qualitatively appear that angle a2 is one-half of a1?
When the distance is large enough that the parallax angle is very small, the parallax angle is proportional
to the inverse of the distance (1/d). Conversely, if we can measure the parallax angle, we know that the
distance to the object is proportional to the inverse of that angle.
Name 1: ______________________________________
Name 2:______________________________________
01. Describe the way the pencil moved against background objects when it was in the middle of the
meter stick:
02. Calculate the distances to the following stars: Refer to the last page… d=1/p
Star Name
Arcturus (alpha Bootis)
Parallax (arc seconds)
0.090
Procyon (alpha Canis Minoris)
0.288
Hadar (beta Centauri)
0.0062
Rigel (beta Orionis)
0.0042
Sirius (alpha Canis Majoris)
0.379
Altair (alpha Aurigae)
0.194
Distance (parsecs)
03. You measure the parallax of the star Regulus to be one-half of the parallax of the star Denebola.
What do you immediately know about their relative distances from us? (Hint: compare Sirius and Altair in
the table just above.)
a.
That Regulus and Denebola are approximately the same distance from Earth.
b.
That Regulus is about half the distance from us that Denebola is.
c.
That Regulus is twice the distance from us.
d.
That Regulus is 8 light years away, and we cannot determine the distance to Denebola.
Name 1: ______________________________________
Name 2:______________________________________
Video of “What is a light year” - https://www.youtube.com/watch?v=j2uWp8WpGwY
Video of “What is a Parsec” - https://www.youtube.com/watch?v=x1up3thBSPc
The Method of Trigonometric Parallaxes
Nearby stars appear to move with respect to more distant background stars due to the motion of the
Earth around the Sun. This apparent motion (it is not "true" motion) is called Stellar Parallax.
In the picture above, the line of sight to the star in December is different from that in June, when the Earth
is on the other side of its orbit. As seen from the Earth, the nearby star appears to sweep through the
angle shown. Half of this angle, is the parallax, p.
Parallax Formula:
We saw before that the smaller the parallax, the larger the distance. We can express this as a simple
formula:
Where: p = parallax angle in arcseconds, d = distance in "Parsecs"
Writing our parallax formula in this way allows us to define a new "natural" unit for distances in astronomy:
the Parallax-Second or Parsec. "A star with a parallax of 1 arcsecond has a distance of 1 Parsec."
1 parsec (pc) is equivalent to: 3.26 Light Years = 3.086x1013 km
Examples of Parallax Distances:
The star alpha Centauri has a parallax of p=0.742-arcsec:
A star is measured to have a parallax of p=0.02-arcsec:
Name 1: ______________________________________
Name 2:______________________________________