Final answer:
The speed at which a star or gas cloud is moving towards or away from Earth can be determined by using the Doppler effect for light, where redshifted wavelengths indicate movement away, and blue shifted wavelengths indicate movement towards us. By using the observed and rest wavelengths in the Doppler effect formula, one can calculate the velocity of the object relative to Earth.
Step-by-step explanation:
To determine the speed at which the gas cloud or a star is moving toward or away from Earth using the observed shift in the H-alpha line wavelength, one can use the Doppler effect formula for light. The Doppler effect for light states that the observed wavelength (λ_obs) will differ from the emitted (or rest) wavelength (λ_0) based on the velocity (v) of the source relative to the observer, and the speed of light (c):
λ_obs / λ_0 = √((1 + v/c) / (1 - v/c))
Since the velocities involved are much less than the speed of light, a non-relativistic approximation can be applied, simplifying the formula to:
v/c ≈ (λ_obs - λ_0) / λ_0
If the observed line is redshifted (longer wavelength), the source is moving away, and for a blue shifted (shorter wavelength), the source is moving toward us. In the example given, the light is observed at 656.6 nm while it was emitted at 656.3 nm, suggesting a redshift. Therefore, the source is moving away from us, and we can calculate the velocity:
v ≈ c * (λ_obs - λ_0) / λ_0
v ≈ (3×10^8 m/s) * (656.6 nm - 656.3 nm) / (656.3 nm)
Solving this gives us the speed at which the gas cloud or the star is moving away from Earth. This can be compared to the Doppler shift that would be caused by a star or galaxy moving at various speeds that induce different wavelengths of emitted lines in their spectra.