(455) Doppler effect in astrophysics [IB Physics SL/HL]

Doppler Effect in Astronomy

  • The Doppler effect describes the change in wavelength of light emitted from a moving source relative to an observer.

  • Redshift: Occurs when a source moves away from the observer, causing light to appear redder (longer wavelengths).

  • Blueshift: Occurs when a source moves toward the observer, causing light to appear bluer (shorter wavelengths).

Key Concepts

  • Light emitted moves in concentric circles, getting bunched up at the front when the source is moving away.

  • Wavelengths involved in visible light:

    • Red: ~600 nm (higher wavelength)

    • Blue: ~400 nm (lower wavelength)

Non-relativistic Speeds

  • Doppler effect applies when the speed of the source (star or galaxy) is much less than the speed of light (non-relativistic speeds).

  • At relativistic speeds, additional complexities arise, requiring adjustments for relativistic effects.

Mathematical Relationship

  • The equation from the data booklet:

    • ( \frac{\Delta f}{f} \approx \frac{\Delta \lambda}{\lambda} \approx \frac{V}{C} )

  • Where:

    • ( \Delta f ): Change in observed frequency

    • ( f ): Emitted frequency

    • ( \Delta \lambda ): Change in observed wavelength

    • ( \lambda ): Emitted wavelength

    • ( V ): Speed of the source

    • ( C ): Speed of light

  • Example simplifies calculations by facilitating ratio comparisons.

Example Calculation

  • Example:

    • Emitted wavelength: 80 nm

    • Received wavelength: 86 nm

  • Observations:

    • Wavelength increase indicates redshift; the galaxy is moving away.

Calculation Steps

  1. Determine ( \Delta \lambda ):

    • ( \Delta \lambda = 86 , \text{nm} - 80 , \text{nm} = 6 , \text{nm} )

  2. Apply the equation:

    • ( \frac{\Delta \lambda}{\lambda} = \frac{6}{80} = 0.075 \approx \frac{V}{C} )

    • Result: ( V = 0.075C ) or 7.5% the speed of light

Summary

  • The Doppler effect allows astronomers to determine the movement of celestial objects through redshift/blueshift observations.

  • Key applications involve calculating velocities of galaxies relative to Earth based on wavelength shifts.