The Doppler effect, dark matter and the expanding universe

Overview

Recall questions on The Doppler effect, dark matter and the expanding universe.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State the Doppler relationship used for a source moving along the line of sight.

   Model answer

   Δλ/λ = v/c, where Δλ is the shift in wavelength, λ is the emitted wavelength and v is the radial velocity.

2. 2

   What is meant by the radial velocity of a star?

   Model answer

   The component of its velocity along the line joining it to an observer on the Earth.

3. 3

   How is a star's radial velocity found from its spectrum?

   Model answer

   The shift Δλ of a known spectral line from its laboratory wavelength λ is measured, and v = cΔλ/λ.

4. 4

   What does a redshift in a star's spectrum indicate?

   Model answer

   The star is moving away from the observer, so the observed wavelengths are longer than those emitted.

5. 5

   A line of laboratory wavelength 656 nm is observed at 656.9 nm. Calculate the radial velocity.

   Model answer

   v = cΔλ/λ = 3.00 × 10⁸ × 0.9 × 10⁻⁹ ÷ 6.56 × 10⁻⁷ = 4.1 × 10⁵ m s⁻¹ away from the observer.

6. 6

   How is an exoplanet detected from the radial velocity of its star?

   Model answer

   The star and planet orbit their common centre of mass, so the star's spectral lines shift periodically; the period of the variation gives the orbital period.

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