(a) 0.01 parsecs;
(b) 0.1 parsecs; (c) 1 parsec; (d) 10 parsecs; (e) 100 parsecs.
(b) 0.1 parsecs; (c) 1 parsec; (d) 10 parsecs; (e) 100 parsecs.
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The answer is e. 100 parsecs.
The distance in parsecs is the reciprocal of the parallax angle in arc seconds.
Edit to Woody.
Have you been in a car and noticed how fast the nearby trees fly past your window but how slowly the objects on the horizon pass by? This is because if you draw a straight line between you and the tree from the point where you were to the point where you are, there is a larger angle than if you draw the same two lines to the distant objects, therefore the wider the arc of the angle the closer the object.
If this is unconvincing stick a finger in the air close to your face and with your other hand hold a finger in the air at arms length. Then keep switching eyes close first one eye then the other and notice how the finger closer to your face appears to move with relation to the more distant finger, the more distant finger moves (to a lesser extent) in relation to objects much further awy (say a picture on the wall or your computer monitor or TV).
This inverse relationship is the heart of parallax trigonometry. If you observe the angle between a nearby star and a distant star and notice how much that angle changes over six months, you have a known distance of 2 astronomical units (which you halve to get one AU, and twice the parallax angle again you halve it to get the parallax seconds. Now clearly the closer the star the larger the angle it will appear to move through. It is true we define 1 parsec to mean the distance a star must be to have a parallax angle of 1 arc second but the relationship is reciprocal because the closer it is the larger the angle. Thus a star with a parallax arc of 0.5 seconds of arc is 2 parsecs away.
The distance in parsecs is the reciprocal of the parallax angle in arc seconds.
Edit to Woody.
Have you been in a car and noticed how fast the nearby trees fly past your window but how slowly the objects on the horizon pass by? This is because if you draw a straight line between you and the tree from the point where you were to the point where you are, there is a larger angle than if you draw the same two lines to the distant objects, therefore the wider the arc of the angle the closer the object.
If this is unconvincing stick a finger in the air close to your face and with your other hand hold a finger in the air at arms length. Then keep switching eyes close first one eye then the other and notice how the finger closer to your face appears to move with relation to the more distant finger, the more distant finger moves (to a lesser extent) in relation to objects much further awy (say a picture on the wall or your computer monitor or TV).
This inverse relationship is the heart of parallax trigonometry. If you observe the angle between a nearby star and a distant star and notice how much that angle changes over six months, you have a known distance of 2 astronomical units (which you halve to get one AU, and twice the parallax angle again you halve it to get the parallax seconds. Now clearly the closer the star the larger the angle it will appear to move through. It is true we define 1 parsec to mean the distance a star must be to have a parallax angle of 1 arc second but the relationship is reciprocal because the closer it is the larger the angle. Thus a star with a parallax arc of 0.5 seconds of arc is 2 parsecs away.
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(e) 100 parsecs
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E is what I think now.. My brain was just fried when I said A.