# Experiment 8: To measure the Proper Motion of Barnard's Star

### Objective :

To measure the Proper Motion of Barnard's Star.

### Introduction :

Most stars move slowly with respect to Sun in a direction which does not change significantly with time. The angular velocity of the star with respect to the Sun is called proper velocity. The largest known proper motion is that of Barnard's star which moves across the sky at a speed of $10.3"$ per year. Here you will measure the proper velocity of Bernard star using Stellarium.

### Procedure :

• Step 1: Pause the passage of time. (Press K)

• Step 2: Remove the Atmosphere and Ground. (Press A and G)

• Step 3: Set the Equatorial Grid. (Press E)

• Step 4: If the Grid is not horizontal and vertical, change the mount to equatorial. (Use Ctrl + M)

• Step 5: Locate Barnard's Star (Use F3).

• Step 6: Enable the Nebulas. (Press N)

• Step 7: Zoom in, till the field of view (FOV) is ~ 0.10 degrees. (Use Page up/down)

• Step 8: Select some star close to Barnard's Star and place it at the center. (Press space after selecting it)

• Step 9: Set the date and time. (Use F5)

• Step 10: Goto the configuration Menu. (Use F2)

• Step 11: In the Tools tab, set the screenshot directory and select 'Invert colors'.

• Step 12: Select Barnard's Star, but dont center on it.

• Step 13: Take the screen shot. (Use Ctrl + S)

• Step 14: Increase the year by 2, but dont change the date and time. (Use F5)

• Step 15: Ensure that the star selected earlier, is still at the center of the screen.

• Step 16: Take another screen shot.

• Step 17: Repeat these steps, till you have noted the change over a period of ~ 20 years.

• Step 18: Take a print out of all the images.

• Step 19: Using a ruler, find the Right Ascension $(\alpha)$ and Declination $(\delta)$ of Barnard's Star and the star fixed at the center. Convert both to degrees, using 24 hours == 360 degrees.

• Step 20: Find the position of Barnard's Star with respect to the fixed star. $(\Delta$ and $\Delta \alpha \times cos (\delta) )$

• Step 21: Plot $\Delta \delta$ versus time and fit a straight line to the data.

• Step 22: The slope found above, is the proper motion along the Declination $(\mu \delta)$ . It should be around 10338 mas/year.

• Step 23: Plot $\Delta \delta$ versus $\Delta \alpha \times cos (\delta)$ and fit a straight line to this.

• Step 24: The line found in the previous step is the path of the star in the vicinity of the fixed star. Use the slope found, to get the angle between the direction of motion and the axis of declination, using $Tan \theta$ = slope. $\theta$ should be around 356 degrees. (Measured counter clockwise).

• Step 25: The proper motion along the Right Ascension $(\mu \alpha)$ would be $sin (\theta) \times \mu \delta / cos (\theta)$ . It should be around -798 mas/year.