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Which of these is the best method to measure the distance to a star? calculate the variations in the position of the star due to movement of Earth in its orbit measure the red shift of emitted light and use it in calculations use doppler effect to calculate the shift in light traveling from star to Earth in summer use doppler effect to calculate the shift in light traveling from star to Earth in winter

Physics
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Doppler shift, the key point in the latter three answers, tells us relative velocity, not distance. Interestingly enough, Edwin Hubble found that the relative velocity of a celestial body is directly proportional to its distance from us, so we could use this...... but I assume in the context of the question that measuring parallax, which is the first answer, is what they're looking for.
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