DISTANCES TO NEARBY STARS
AND THEIR MOTIONS:
An Introductory Astronomy Lab
Stellar Parallaxes
The geometry of a stellar parallax is shown below. As the Earth orbits
the Sun, nearby stars will appear to shift in position relative to other,
more distant stars.
![[Geometry of a stellar parallax]](para.gif)
Question 1: How long do you have to wait for a star to undergo
its maximum parallactic displacement?
Question 2: How can the observation of stellar parallaxes in
general be used as evidence against a geocentric view of the cosmos?
Stellar parallaxes were predicted by the ancient Greek philosophers as
a consequence of heliocentricity, but were not detected until
the nineteenth century. Aristotle (and centuries later, even the astronomer
Tycho) actually used the lack of stellar parallax to argue the case in
favor of a stationary Earth.
Measuring astronomical distances
The angles involved are very small, typically less than 1 second or arc!
(Remember that 1 arc_second = 1/3600 of a degree).
To determine the distance to a star we can approximate the equation given
in the previous section with the small angle approximation:
d = r / p
where d is the distance to the star, p is the parallax angle
expressed in radians
(see diagram), and r is the baseline, in this case 1 Astronomical Unit
(A.U.) -- the radius of the Earth's orbit. Since there are 206,265 arc-seconds
per radian, the formula can be re-written as:
d (in AU) = 206,265 / p
with p measured in arc-seconds .
Or, if we define the distance of one parsec as 206,265 AU, we get:
d (in parsecs) = 1 / p
This is the distance unit astronomers use most frequently, and it is
equivalent to 3.26 light-years.
Question 3: How far, in parsecs, is an object that has a parallax p of
1 arc-second? How far is it, in light-years?
Question 4: How far, in parsecs, is an object that has a parallax p of
0.1 arc-seconds? How far is it, in light-years?
