Part I: Determining the distance between your eyes.

1. Place your thumb in front of your nose as far from your nose as you can. Draw a birds-eye view of your head from above with your arm & thumb stretched that way. On BB.

2. Place your thumb in front of your nose as far from your nose as you can. How far is that in cm? _______Mine was ~ 0.5 meters_____

3. Place the protractor right next to your right eye, while your arm is stretched out. Line up your right eye, the center of the protractor, the 90 degrees mark, your thumb, and an object at a distance (for example, the middle of the black board).

4. WITHOUT ROTATING the protractor move it to your left eye. Close your right eye. Your thumb should have moved WITH RESPECT TO THE DISTANT OBJECT. Did it move to the right of the object, or to the left? __To the right______

5. How far, in degrees, did your thumb move? ____7 degrees____________

Back to the diagram in part 1: Your eyes and thumb make an isosceles triangle. The apex angle of that triangle is called the parallax angle.

CORRECTION: HALF THE APEX ANGLE IS THE PARALLAX ANGLE.

You have just measured that angle. (The line from the right eye to the thumb intersects the faraway background object. The line from the left eye does not.)

 

 
 
 
 
 
 
 
 
 
 
 
 

7.Using trigonometry determine the distance between your pupils (optometrists call it your eye P.D.) ____

for half a triangle, 0.5 m x sin 3.5 deg = 0.03 m or 3 cm, So eye P.D. is 6 cm._____

8. Now, using the distance you found in 6, determine the distance to the person 3 rows away from you (look back if you are in rows A-C). _____

1 deg parallax __So X= 0.06 m/ sin(0.5deg)= 7 meters.

9. Can you use this method to determine the distance to the blackboard? NO. There is no background behind the BB.

Draw a diagram of the earth in its orbit around the sun in March and September, and a star that is very far from the sun, but is the same distance from earth in spring and fall. Draw a triangle for this situation, as on the board. On BB

Given that the apex angle of the triangle is 1.4 arcseconds, how far is the star in A.U.? __________

        Answer: 1.4 arcsec / 2 = 0.7 arcsec.

        Angle in degrees: 0.7 arcsec / (3600 arcsec/deg) = 1.94 x 10^-4 degrees.

        THEREFORE: X=1.5 x 10^11 m / sin (1.94 x 10^-4 degrees) = 4.4 x 10^16 m

Or:

In light years:

X= 4.4 x 10^16 m / (3 x 10^8 m/seconds x 3 x 10^7 seconds/year) = 4.9 (Light) Years

12. Why can’t we use this method to find the distance to all visible stars in the galaxy?

The accuracy of angle measurements without telescope is two arcseconds. The accuracy of measurements with optical telescopes is ~ few milli-arcseconds.

That means we can only measure distances of up to ~ a few1000 Light years

13. Why can’t we use this method to find the distance of objects half the way to the end of the visible universe? Background, as in 9.