# Experiment 6: Extracting position of a star

### Objective :

To extract coordinates of a star assuming a telescope in equatorial mount. You will also learn the concept of sidereal time.

### Introduction :

A telescope has two degrees of rotation which allow us to point it in any direction in the sky. In the case of equatorial mount, one of the axis is taken parallel to the axis of rotation of the Earth. This is called the polar or the hour axis. The other axis, perpendicular to the hour axis, is called the declination axis as shown in the figure below:

Fig. : The two axis of rotation of a telescope in equatorial mount. One of the axis, the hour axis, is taken parallel to the Earth's axis of rotation. The other declination axis is perpendicular to the hour axis.

While viewing any object in the sky it is necessary to keep the telescope point towards that object for an extended period of time. In order to do so one needs to continuously rotate the telescope to compensate for the Earth's rotation. In the equatorial mount this is easily accomplished since we simply need to rotate it about the hour axis at the same rate as the rotation of the Earth, but in the opposite direction. Since one of the axes is chosen to be the axis of rotation of Earth, the declination of an object can be directly obtained. It corresponds to the amount of rotation about the declination axis and can be directly read off from the declination dial of the telescope. In order to obtain the Right Ascension we first need to choose a reference for the azimuthal angle and locate the position of vernal equinox with respect to this reference. The reference is conveniently chosen to be the direction where the meridian intersects the equatorial plane towards south, as shown in the figure below.

Fig. : The schematic illustration of equatorial mount. Here the observer is located at the center. The great circle NZS is the observer's meridian. The hour angle of a source 'P' is measured clockwise from the reference point (Ref) on the celestial equatorial plane. Here $\Gamma$ shows the position of the vernal equinox. The angle between the vernal equinox and the source 'P' is the right ascension $\alpha$ .

Let $\Gamma$ denote the angle to the vernal equinox and 'h' the hour angle of the source with respect to the reference, defined above. The hour angle corresponds to clockwise rotation about the hour axis and is read off from the hour angle dial of the telescope. Due to rotation of Earth both of these would increase at a steady rate. The hour angle of the vernal equinox, $\Gamma$ , is also called the sidereal time. The stars as well as the vernal equinox return to their original positions after one sidereal day. A sidereal day is slightly shorter than the solar day. It is roughly equal to 23 hours, 56 minutes and 4.091 seconds (Wiki). For our observations it is convenient to use the sidereal time. The right ascension $\alpha$ is given by,

$\Gamma = h + \alpha$

In practise it is convenient to determine the location of the vernal equinox by first finding the 'h' of an easily recognizable star and using the catalogues to determine its $\alpha$ . The hour angle of the vernal equinox is then given by the above equation.

Next we may observe the hour angle of the star whose coordinates are to be determined. Let's call this star X. In order to extract the RA or $\alpha$ for this star we need the sideral time $\Gamma$ corresponding to the time of this observation.This is computed by adding the sidereal time elapsed between the observation of the reference star and star X.

Description of the experiment : This virtual experiment will be performed using Stellarium. We shall use the declination, hour angle and the time readings provided by the software and ignore all other readings.

• Step 1: Start by getting some familiarity with the sidereal time and sidereal day. Note that as you advance the view by one sidereal day all the stars return back to the original positions. This is in contrast to what is observed if we advance by one solar day where the positions of the stars are shifted. Also get some familiarity with how the hour angle changes with position on the sky. Check if it agrees with the definition given above.

• Step 2: Select some reference bright star whose RA and Dec are known. Locate its hour angle at some fixed time. It is helpful to take a view of the image at any particular time so that the time and hour angle reading may be taken simultaneously. You may freeze the time in Stellarium to the time chosen for observation. This may be done by pressing the key 7. The time may be restarted by pressing K. You may check these controls by using the help provided. at a particular time. Now note both the hour angle and the corresponding time.

• Step 3: Using the known RA for this star determine the hour angle of the vernal equinox.

• Step 4: Now select the star X whose coordinates are to be observed. Read off the hour angle and corresponding time of this star. Repeat this for one more time.

• Step 5: Determine the sidereal time elapsed between the observation of the reference star and the star X. Note that if the time elapsed between the two observations is small the difference between the sidereal and solar time is negligible and may not make any difference.

• Step 6: Using this sidereal time find the RA of star X for both the times. Check that you get the same RA for both the cases. Compare the RA with that provided by Stellarium.

• Step 7: For consistency repeat the experiment for one more observation of the reference star. Check the consistency of your results.