# Case study on experiment 4 orbital velocity of the earth using stellar spectra

## Introduction

The orbital velocity of the earth can be calculated in reference to other objects in space such as stars. A spectrum of the object can be used because the Doppler shift of the earth’s movement can be measured. The earth is moves closer to objects during one half of its orbital path. This is recorded on the spectrum as red shifted light. On the half of its orbit it is moving away from the object and the spectrum measures this movement as blue-shifted light.

## Objective

This experiment uses the star named Arcturus to measure the spectrum shift during earth’ s orbit. The measurements are then used to calculate the velocity of the earth’s orbit using the spectral data from observing the earth’s relationship with Arcturus. The experiment involves using extrapolation in order to use millimeter measurements in order to measure shifts on the spectrum. At the end of the lab the calculated velocity of earth’s orbit will be compared to the standard reported velocity of earth’s orbit.

## Data and Calculations

The orbit of the earth was measured in reference to the spectrum of Arcturus at two six month intervals. The shifts were measured as carefully as possible in millimeters from the print out of the spectrum. These data were then converted into angstroms, the measurement of wavelengths by using the following conversion equation.
Conversion Factor (CF) = (4307. 91 – 4260. 48) angstroms / 112. 15 mm = 3. 9 angstroms/mm

## This equation is used to fill out Table 1.

vr = c
Where vr is the relative velocity

Δʎ is the Doppler shift
Δ˳ is the original wavelength corresponding to the reference lines
c is 300, 000 km/s, the speed of light
Table 1. Measurements and calculations based on Arcturus’ spectrum

vrr = 27. 8958
vrb = – 54. 6398
vEarth
= (vrr – vrb) / 2

= 41. 2678 km/s

## Conclusions and analysis.

In conclusion the velocity of earth calculated using the information from the measurement of the spectrum of Arcturus was 41 km/s. The average velocity of earth’s orbital velocity is 30 km/s. This is a difference of 41 km/s which considering the huge distances being calculated is relatively close to 30 km/s There is a certain technique to measuring the red shift and the blue shift from the spectrum print out yet the as there is only a difference of 11 km/s from today’s calculations and the reported average orbital velocity. This was a successful result to the experiment.