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?

Answer 1

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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Answer 2

The spectroscopic binary would have a half-day orbital period.

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Answer from HIX Tutor

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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