In a spectroscopic binary, if a pair shows a combined set of lines tonight, but a maximum split two nights later, what must its orbital period be?
Eight days.
Consider the splitting of the lines as two sine waves that are 180 degrees out of phase because Star B is moving in a red shift away from Earth and Star A is moving in a blue shift toward Earth.
Spectral lines together in the initial state.
1/4 period: Star B reaches its maximum red shift (trough), and Star A reaches its maximum blue shift (imagine it as a sine wave peak).
Half-period: The spectral lines have reunited.
Maximum red shift (trough) for Star A and maximum blue shift (crest) for Star B during a 3/4 period; reversal of 1/4 period.
Complete period: A return to the starting point for a new cycle.
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The spectroscopic binary would have a half-day orbital period.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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