An observer is moving in space toward a distant star at 50.0 km/s while the star is moving toward the observer at 180 km/s;the relative velocity being 230 km/s of approach.What relative change in frequency of the light from the star as seen by the observer? (The speed of light in space is 3.00 × 10⁵ km/s). A)0.077% increase B)0.077% decrease C)0.026% increase D)0.23% decrease E)0.23% increase

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Quizplus · Accepted Answer

The relative change in frequency, or Doppler shift, can be calculated using the formula for relativistic Doppler effect, which simplifies to $\Delta f / f = v / c$ for velocities much less than the speed of light. Here, $v = 230$ km/s is the relative velocity and $c = 3.00 \times 10^5$ km/s is the speed of light. Thus, $\Delta f / f = 230 / 300000 = 0.00077$, or a 0.077% increase in frequency.

An Observer Is Moving in Space Toward a Distant Star