A planetary nebula expanded in radius 0.3 arc seconds in 30 years.  Doppler measurements show the nebula is expanding at a rate of 35 km/s.  How far away is the nebula in parsecs? First, determine what distance the nebular expanded in parsecs during the time mentioned.  Δd = vpc/sTs So we first need to convert the rate into pc/s and the time into seconds: vpc/s = vkm/s (1 pc / 3.09 x 1013km) vpc/s = ? Ts = (Tyr)(365 days/yr)(24 hrs/day)(3600 s/hr) Ts = ? s Δd= vpc/sTs Therefore, Δd = ? pc

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Chapter1: Units, Trigonometry. And Vectors
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A planetary nebula expanded in radius 0.3 arc seconds in 30 years.  Doppler measurements show the nebula is expanding at a rate of 35 km/s.  How far away is the nebula in parsecs?

First, determine what distance the nebular expanded in parsecs during the time mentioned.  Δd = vpc/sTs

So we first need to convert the rate into pc/s and the time into seconds:
vpc/s = vkm/s (1 pc / 3.09 x 1013km)
vpc/s = ?
Ts = (Tyr)(365 days/yr)(24 hrs/day)(3600 s/hr)
T= ? s
Δd= vpc/sTs
Therefore, Δd = ? pc
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