Parallax refers to the different views that you see from two different positions. Try this experiment. Hold the index finger of your left hand vertical, 20 cm in front of you. Hold the index finger of your right hand vertical, 40 cm in front of you. Now close your left eye and, using just your right eye, move the two fingers sideways until they line up. Now close your right eye and open the left. The closer finger has 'jumped' to the right of the further finger. Repeat a few times. Compared to a distant background, both fingers have both jumped to the right, but the closer one jumps farther. If you measure the angles through which they jump and the distance between your eyes, you can work out how far away the fingers are. For distant objects, the distance between our viewing positions must be greater than the distance between your eyes. Fortunately for astronomers, the Earth shifts our telescopes round the sun, so we can get a separation equal to the diameter of the orbit of the Earth (16 light minutes) if we wait six months, as shown in this diagram. In this sketch, which is not to scale, imagine an observer looking at objects A and B, standing at the pole of the Earth with his head towards us. Now he sees object A to be to the right of B. Six months ago, he saw it to be to the left of B. Now most stars are so far away from us that we cannot observe any relative motion in this way. However, for close stars it is possible. The next sketch shows the path of light from a close object and from a very distant star. From trigonometry, D = R/tanθ = R/θ where we have used the small angle approximation for θ measured in radians. A parsec is defined as the distance to an object that 'moves' (w.r.t. to the distant stars) by an angle of 1 second (1/3600 of a degree) when the Earth moves by the mean radius of its orbit. In terms of this sketch, if θ = one second, D = 1 parsec. Now all stars except the sun are more than one parsec distant, so to measure their distance by parallax, we need to be able to resolve angles of about 1 second or better.

Parallax refers to the different views that you see from two different positions. Try this experiment. Hold the index finger of your left hand vertical, 20 cm in front of you. Hold the index finger of your right hand vertical, 40 cm in front of you. Now close your left eye and, using just your right eye, move the two fingers sideways until they line up. Now close your right eye and open the left. The closer finger has 'jumped' to the right of the further finger. Repeat a few times. Compared to a distant background, both fingers have both jumped to the right, but the closer one jumps farther. If you measure the angles through which they jump and the distance between your eyes, you can work out how far away the fingers are. For distant objects, the distance between our viewing positions must be greater than the distance between your eyes. Fortunately for astronomers, the Earth shifts our telescopes round the sun, so we can get a separation equal to the diameter of the orbit of the Earth (16 light minutes) if we wait six months, as shown in this diagram.

In this sketch, which is not to scale, imagine an observer looking at objects A and B, standing at the pole of the Earth with his head towards us. Now he sees object A to be to the right of B. Six months ago, he saw it to be to the left of B. Now most stars are so far away from us that we cannot observe any relative motion in this way. However, for close stars it is possible. The next sketch shows the path of light from a close object and from a very distant star.

From trigonometry,
D = R/tanθ = R/θ
where we have used the small angle approximation for θ measured in radians. A parsec is defined as the distance to an object that 'moves' (w.r.t. to the distant stars) by an angle of 1 second (1/3600 of a degree) when the Earth moves by the mean radius of its orbit. In terms of this sketch, if θ = one second, D = 1 parsec. Now all stars except the sun are more than one parsec distant, so to measure their distance by parallax, we need to be able to resolve angles of about 1 second or better.

Linked Question 1

Parallex method is useful only if the star whose distance is to be measure should be closer to the earth and the reference star should be

very far away

very close

only pole star

any other star

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Linked Question 2

In above if we have three objects A, B and C such that you see only A & B from your left eye and A & C from your right eye. Angle formed by AB on your left eye equals that formed by AC on your right eye. Then AB will

always equal to AC

be equal to AC if your two eye and A form a right angled triangle

none of these

be equal to AC if your two eye and A form an isosceles triangle

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Linked Question 3

In the first experiment if we have two point objects A and B in place of your left and right fingers respectively then

none of these

your two eye and A will form a triangle area of which is be equal to the area of the triangle formed by A, B and your left eye

your two eyes and A and B will lie on a circle

your two eyes and A and B will always lie in a plane

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