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Parallax method
Parallax method
- Large distance, such as the distance of a planet or a star from the Earth, cannot be measured directly with a metre scale, so a parallax method is used for it.
- Large distance, such as the distance of a planet or a star from the Earth, cannot be measured directly with a metre scale, so a parallax method is used for it.
- Let us do a simple experiment to understand what is parallax.
- Let us do a simple experiment to understand what is parallax.
- Hold your hand in front of you and look at it with your left eye closed and then with your right eye closed.
- Hold your hand in front of you and look at it with your left eye closed and then with your right eye closed.
- You will find that your hand appears to move against the background.
- You will find that your hand appears to move against the background.
- This effect is called parallax.
- This effect is called parallax.
-- Parallax is defined as the apparent change in position of an object due to a change in the position of the observer.
-- Parallax is defined as the apparent change in position of an object due to a change in the position of the observer.
Parallax method for determining distance
Parallax method for determining distance
- By measuring the parallax angle and knowing the distance between the eyes E1E2 as shown in Fig., we can determine the distance of the object from us, i.e., OP
- By measuring the parallax angle and knowing the distance between the eyes E1E2 as shown in Fig., we can determine the distance of the object from us, i.e., OP
As the distances of planets from the Earth are very large, we can not use two eyes method as discussed here. In order to make simultaneous observations of an astronomical object, we select two distant points on the Earth.
As the distances of planets from the Earth are very large, we can not use two eyes method as discussed here. In order to make simultaneous observations of an astronomical object, we select two distant points on the Earth.
Measurement of distances of planets
Measurement of distances of planets
- Consider two positions A and B on the surface of Earth, separated by a straight line at a distance b as shown in Fig.
- Consider two positions A and B on the surface of Earth, separated by a straight line at a distance b as shown in Fig.
- Two observers at these two points observe a distant planet S simultaneously.
- Two observers at these two points observe a distant planet S simultaneously.
- We measure the angle ASB between the two directions along which the planet is viewed at these two points.
- We measure the angle ASB between the two directions along which the planet is viewed at these two points.
- This angle, represented by symbol is the parallax angle.
- This angle, represented by symbol is the parallax angle.
- As the planet is far away, i.e., the distance of the planet from the Earth is very large in comparison to b, b/D << 1 and, therefore, is very small.
- As the planet is far away, i.e., the distance of the planet from the Earth is very large in comparison to b, b/D << 1 and, therefore, is very small.
- We can thus consider AB as the arc of length b of the circle and D its radius.
- We can thus consider AB as the arc of length b of the circle and D its radius.
- AB = b and AS = BS = D
- AB = b and AS = BS = D
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