Chapter03 questions answers - 1 3 Stepping Out practice...

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3 Stepping Out practice with calculations: the parallax equation p 1 d = d in AU, p in seconds of arc 1. If p = 0.01”, what is d? 1/0.01 = 100 pc 2. If p = 0.025”, what is d? 1/0.025 = 40. pc 3. If p = 0.082”, what is d? 1/0.082 = 12 pc 4. If p = 0.125”, what is d? 1/0.125 = 8.00 pc 5. If d = 144 pc, what is p? p = 1/d = 0.00694 seconds of arc 6. If d = 550 pc, what is p? p = 1/d = 0.0018 seconds of arc 7. If p = 0.037” ± 0.001”, what is d? As asked, we would normally quote an upper limit to the distance based on p = 0.036" and a lower limit to the distance based on p = 0.038" (these are referred to as the ± 1 sigma error bars and are understood as such): d = 1/p = 1/0.036" = 27.78 pc = 28 pc d = 1/p = 1/0.037" = 27.03 pc = 27 pc d = 1/p = 1/0.037" = 26.31 pc = 26 pc To two-digit accuracy, we would say d = 27 ± 1 pc (27 plus or minus 1). We know by convention that this 'error bar' of 1 pc indicates the one-sigma (68%) confidence level. 8. If p = 0.167” ± 0.003”, what is d? d = 1/p = 1/0.164" = 6.098 pc = 6.10 pc d = 1/p = 1/0.167" = 5.988 pc = 5.99 pc d = 1/p = 1/0.170" = 5.882 pc = 5.88 pc To three-digit accuracy, we would say d = 5.99 ± 0.11 pc. 1
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9. If p = 0.083” ± 0.008”, within what limits do we know d at the 99% confidence level? The 99% confidence level is the three-sigma range rather than the one-sigma range, so we need to calculate distances for 0.083", 0.083" + 3(0.008") and 0.083" - 3(0.008"): d = 1/p = 1/0.059" = 16.95 pc = 17 pc d = 1/p = 1/0.083" = 12.05 pc = 12 pc d = 1/p = 1/0.107" = 9.346 pc = 9.3 pc So we are 99% confident that the distance to this star lies within the range from 9.3 to 17 pc.
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  • Fall '10
  • STASSUN
  • Astronomy, Astronomical unit, Proxima Centauri, Parsec

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