Orbital Velocity of the Earth Using Stellar Spectra - Essay Example

By looking at the Earth’s orbit from the above its orbit appears to be much more elliptical.

1. Determination of the rotational velocity of the Earth

        In this calculation, it was significant to measure the Full-Width at Half-Minimum (FWHM) Of the lines. This value was later used in determining effective shift resulting from the rotational motion

Effective shift= FWHM/ 2.35

As observed from the spectrum, FWHM is approximately 0.5 nm. Thus,

Effective shift= 0.5 nm/ 2.35 = 0.2128 nm

The Doppler formula gives the velocity as

Velocity= 0.2128/ 492 * (300000 km/sec)

V= 129.74 km/sec

2. Radical Velocity of the Stars

    The next step involved measuring the radial velocity of the star Arcturus in the solar neighbourhood. The star Arcturus is relatively close to the Sun hence its temperature is slightly different from that of the sun. Zooming into the small regions of the spectrum of individual stars, similar absorption lines are observed. The little offset in wavelength is a result of the movement of Arcturus. 

     The spectra lines from the sun appear at a wavelength of about 882.4 nm. In the spectra of Arcturus, they appear at a wavelength of about 882.55 nm.

Shift= 882.55- 882.4 = 0.15 nm

Radical velocity=  * (300000 km/ sec) = 51 km/ sec

3. Earth’s orbital radius

     Since we have obtained the value of the earth’s velocity as 129.74 km/sec, and the period of its orbit is known to be one year, we can calculate the earth’s radius (in astronomical units) using the formula. 

The maximum shift would be given by

Shift= (radical velocity/speed of light) * rest wavelength= (466 * 656)/ 300000= 0.001 nm

5. The apparent color of the Arcturus changes with the radial velocity. If the object is close to the observer only a single edge of shifting to the other but if the object is far away it will appear as a small dot of light. In case the observer is moving quickly, the interference of wavelengths will result in the spreading of individual lines, a condition known as rotational broadening (Richmond 2).