Earth as a Baseline

It should be evident that the greater the baseline used the greater the distance that can be measured. Suppose that instead of measuring the distance across a river, you'd like to measure the distance to some object outside the Earth. What about using the Earth itself as a large baseline?

Now you stand on one side of the Earth and your friend stands on the other. You both look at the same object, say Jupiter, and by cell phone compare where the object is located against the background stars.

 
your views would look like this:
You and your friend would see the object in two DIFFERENT places. This shift is due to parallax .






Earth's Orbit as a Baseline

Within the Solar System we can use the diameter of the Earth as a long baseline to measure distances. But, it is still not big enough if we want to measure distances to the nearest stars. We do however have an even larger baseline that we can use: the Earth's Orbit.  Now we can measure the position of a nearby star on the sky using observations separated by six months.  Most stars are distant enough so that they won't appear to move - any star that does must be nearby.  So we measure the shift of the nearby star relative to the distant ones.

Let's look at the whole parallax cycle, that is, the effect of making parallax measurements continuously as the Earth orbits the Sun.

View the movie below. It consists of two parts. The first shows the parallax for a nearby star, the second for a more distant star. (Animation courtesy of R. Pogge, Ohio State University.)

 

In order to make finding large distances as easy as possible, astronomers invented a new unit of distance called the parsec (abbreviated "pc"). One parsec is the distance to an object that has a parallax of one arcsecond, using the Earth's orbit as the baseline. In terms of other units of length, 1pc = 3.26 lightyears = 3.08e13 km. The formula to convert parallax to parsecs is very simple, which makes it a very powerful and easy to use tool for calculating distances.  The smaller the parallax, the more distant the star:

The closest star to the earth (except the Sun) is associated with the brightest star in the southern constellation of Centaurus.  It is known as Proxima Centauri and it has a parallax of 0.77 arcsec.  Calculate the distance, in parsecs, of this star from the earth.

 9.

This distance is typical of the separation of stars in the Milky Way.  To the nearest order of magnitude, what, then, is this typical separation?

10.

Betelgeuse, (typically pronounced "beetle juice," but some people insist it should be " bet el geese") is the bright red star in the constellation Orion (top left in picture below).

copyright Matthew Spinelli

Its parallax is 0.0076 arcsec.  Calculate the distance, in parsecs, of this star from the Earth.

11.

In order to measure the large distances you found in questions nine and ten, what baselines must astronomers be using?

  12.

Is the parallax for Betelgeuse larger or smaller than that of Proxima Centauri?    What does that tell you about the general relationship between parallax and distance?

13.

If .005 arcsec is the smallest parallax we can measure, what would be the furthest distance we could measure?  This will tell you the limitation of the parallax method.  How does it compare to the size of our Milky Way Galaxy (about 30,000 pc)?  The Large Magellenic Cloud is one of the closest galaxies to us at 50 thousand parsecs away.  Is trigonometric parallax therefore useful in measuring distances to galaxies ?

14.

If a star is known to be 100pc away, what will its parallax be? Don’t forget your units!

15.

16. a) How would your ability to measure parallax (using the orbit as the baseline) change if you were taking measurements from Jupiter?  b) If you were taking measurements from Venus? c) How long would it take you to make the measurements?


If the Earth's orbit were very elliptical , what points of the orbit would you use to make the largest possible distance measurement?

17.

How is the concept of parallax related to the concept of retrograde motion we discussed in the previous lab?

18.