A planetary nebula expanded in radius 0.2 arc seconds in 10 years. Doppler measurements show the nebula is expanding at a rate of 25 km/s. How far away is the nebula in parsecs? If the nebula now has a radius of 9 arc minutes, how long ago (in years) did the star explode? Part 1 of 3 We first need to determine what distance (in pc) the nebula expanded in parsecs during the time mentioned. Ad = V pc/s¹s So we first need to convert the rate into pc/s and the time into seconds: 1 pc Vpc/s Vkm/s 3.09 x 10¹3 km = ✓pc/s = T₂ T₂ = S Ad pc = pc/s (Tyr)(365 days/yr) (24 hrs/day) (3600 s/hr) S Ad = pc = V. Vpc/sTs pc

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Chapter1: Units, Trigonometry. And Vectors
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Hi! I only need help with Part 1 of 3. You can ignore the tutorial questions at the top.

A planetary nebula expanded in radius 0.2 arc seconds in 10 years. Doppler measurements show the nebula is expanding at a rate of 25 km/s.
How far away is the nebula in parsecs?
If the nebula now has a radius of 9 arc minutes, how long ago (in years) did the star explode?
Part 1 of 3
We first need to determine what distance (in pc) the nebula expanded in parsecs during the time mentioned.
Ad = V pc/s¹s
So we first need to convert the rate into pc/s and the time into seconds:
1 pc
Vpc/s Vkm/s 3.09 x 10¹3 km
✓pc/s =
T₂
T₂ =
S
Ad pc
Ad
=
pc
=
pc/s
(Tyr)(365 days/yr) (24 hrs/day) (3600 s/hr)
S
Vpc/s¹s
= V.
pc
Transcribed Image Text:A planetary nebula expanded in radius 0.2 arc seconds in 10 years. Doppler measurements show the nebula is expanding at a rate of 25 km/s. How far away is the nebula in parsecs? If the nebula now has a radius of 9 arc minutes, how long ago (in years) did the star explode? Part 1 of 3 We first need to determine what distance (in pc) the nebula expanded in parsecs during the time mentioned. Ad = V pc/s¹s So we first need to convert the rate into pc/s and the time into seconds: 1 pc Vpc/s Vkm/s 3.09 x 10¹3 km ✓pc/s = T₂ T₂ = S Ad pc Ad = pc = pc/s (Tyr)(365 days/yr) (24 hrs/day) (3600 s/hr) S Vpc/s¹s = V. pc
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Hi! Can you please help me with Part 2 of 3?

Part 2 of 3
Now
we can use the small angle formula to calculate the distance (in pc).
2.06 x 105
D
||
D = Ad-
0
as
рс
Transcribed Image Text:Part 2 of 3 Now we can use the small angle formula to calculate the distance (in pc). 2.06 x 105 D || D = Ad- 0 as рс
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