PARALLAX ANGLE ( HOW TO MEASURE AND IT'S UNIT)

PARALLAX METHOD

Parallax is the change in position of an object seen from two different line of sight , and is measured by angle of inclination (p) between those two lines of sight. The angle of inclination (p) is known as parallax angle.

                                                         Parallax Method Diagram fig no 1

Some other example of parallax : 

                                                       You can do an experiment related to parallax method with your thumb. Stretch your arm and examine the relative position of your thumb with one eye closed. Now closed that eye and open another eye and look at your thumb. What do you notice?

Then your thumb will appear to move in front of the backward.

                            Thumb experiment related to parallax method fig. no 2

HOW TO MEASURE ?

We know that the earth revolves around the sun in  the elliptical orbit. Suppose the earth is at A position in June. Six month later, the earth will remain at B position in December [ because the earth takes about an year to travel around the sun ]. These two places are such place that we are going to observe a star (S).  A and B are two opposite position of earth.

                                                                      Figure no 3

C be the any mid point lie on arc AB. Suppose the earth moves from A to C. During this motion, the earth will move along arc AC. We observe star (s) from A and C and form angle at the star that angle is called parallax angle (p). It means the earth covers the angular distance along arc AC. The distance between the earth and sun is also known as astronomical unit (AU). The distance from earth to the sun is equal to about 149597870700 m ( approximately 150 million) i.e. 1 AU = 149597870700 m.

To measure the parallax angle, first we have to measure angular distance. In the field of astronomy, the scientist generally use angular measurements to describe the apparent size of a celestial body and the apparent distance between celestial bodies in space. 

                                                   Apparent size of a celestial body                                      

                                     Apparent distance between between two celestial body

But this angle is very small. An angular measurements are generally expressed in term of degree ( ° ).
we know one complete circle is of 360°. one degree is divided into 60 minutes of arc, and one minute into 60 second of arc.

           1 degree = 60 minutes of arc (arc minute)

           1 minute = 60 seconds of arc (arc second)

    

           1 degree = 60 * 60 = 360 arc second

 It is same as that of time i.e. 1 hour is divided into 60 minutes, and 1 minute into 60 second.

Therefore the unit of angular measurement is degree / arc second / arc minute. Parallax angle is nothing angular measurement. Therefore the unit of parallax angle (p) is degree / arc second / arc minute.
From figure no 1 ,

By using trigonometry we can find parallax angle

In triangle
                           

      parallax angle (p) = b / D 

                                  p = 1 AU / D

                                  p = 1 / D

                            

Why radian is not the unit of parallax angle ?

Let us discuss about it. First we have to understand what is exactly radian? Let draw a circle. Let point O be it's center and length R it's radius. Now let me take this length R and place it at the point P vertically. Now all I do is push it onto the circumference of the circle. length of this black part is still R it has just become curved. Curved length start from point P to Q. Now draw radius from center O to Q. Let observed the fig. we conclude that the arc PQ is equal to the radius of the circle (R) and two radii joining the center and the end point of that arc PQ. At the center of the circle arc PQ form an angle and that angle is 1 radian. That's the concept of radian Actually there is radius everywhere around this angle. Hence it is called as radian.

But this type of condition for radian is not obeyed during angular measurement of celestial bodies. in angular measurement of celestial bodies arc is not equal to radius. therefore the radian is not used as the unit of parallax angle (p).