Measurement of Length
We are already familiar with some direct methods for the measurement of length. For example, a metre scale is used for lengths from `10^(-3) m` to `10^2 m`. A vernier callipers is used for lengths to an accuracy of `10^(–4) m`. A screw gauge and a spherometer can be used to measure lengths as less as to `10^(–5) m`. To measure lengths beyond these ranges, we make use of some special indirect methods.
`text(Measurement of Large Distances :)`
Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a metre scale. An important method in such cases is the `text(parallax method)`.
When you hold a pencil in front of you against some specific point on the background (a wall) and look at the pencil first through your left eye A (closing the right eye) and then look at the pencil through your right eye B (closing the left eye), you would notice that the position of the pencil seems to change with respect to the point on the wall. This is called `text(parallax)`. The distance between the two points of observation is called the `text(basis)`. In this example, the basis is the distance between the eyes.
To measure the distance D of a far away planet S by the parallax method, we observe it from two different positions (observatories) A and B on the Earth, separated by distance AB = b at the same time as shown in Fig. We measure the angle between the two directions along which the planet is viewed at these two points. The ∠ASB in Fig. represented by symbol θ is called the `text(parallax angle)` or `text(parallactic angle)`.
As the planet is very far away `b/D` >> `1`, and therefore, `theta` is very small.
Then we approximately take AB as an arc of length b of a circle with centre at S and the distance D as the radius AS = BS so that AB = b = D θ where θ is in radians.
`D=b/theta`
Having determined D, we can employ a similar method to determine the size or angular diameter of the planet. If d is the diameter of the planet and α the angular size of the planet (the angle subtended by d at the earth), we have
`alpha=d/D`
The angle α can be measured from the same location on the earth. It is the angle between the two directions when two diametrically opposite points of the planet are viewed through the telescope. Since D is known, the diameter d of the planet can be determined using this equation.
`text(Range of Lengths :)`
The sizes of the objects we come across in the universe vary over a very wide range. These may vary from the size of the order of `10^(–14) m` of the tiny nucleus of an atom to the size of the order of `10^(26) m` of the extent of the observable universe.
We also use certain special length units for short and large lengths. These are
`1 text(fermi) =1f= 10^(-15)m`
`1 text(angstrom)=1overset@A=10^(-10)m`
`1 text(astronomical unit) = 1 AU` (average distance of the Sun from the Earth) `=1.496xx10^(11)m`
`1 text(light year) = 1 text(ly)= 9.46 × 10^(15) m` (distance that light travels with velocity of `3 × 10^8 ms^(–1)` in 1 year)
`1 text(parsec) = 3.08 × 10^(16) m` (Parsec is the distance at which average radius of earth’s orbit subtends an angle of 1 arc second)
`text(Measurement of Large Distances :)`
Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a metre scale. An important method in such cases is the `text(parallax method)`.
When you hold a pencil in front of you against some specific point on the background (a wall) and look at the pencil first through your left eye A (closing the right eye) and then look at the pencil through your right eye B (closing the left eye), you would notice that the position of the pencil seems to change with respect to the point on the wall. This is called `text(parallax)`. The distance between the two points of observation is called the `text(basis)`. In this example, the basis is the distance between the eyes.
To measure the distance D of a far away planet S by the parallax method, we observe it from two different positions (observatories) A and B on the Earth, separated by distance AB = b at the same time as shown in Fig. We measure the angle between the two directions along which the planet is viewed at these two points. The ∠ASB in Fig. represented by symbol θ is called the `text(parallax angle)` or `text(parallactic angle)`.
As the planet is very far away `b/D` >> `1`, and therefore, `theta` is very small.
Then we approximately take AB as an arc of length b of a circle with centre at S and the distance D as the radius AS = BS so that AB = b = D θ where θ is in radians.
`D=b/theta`
Having determined D, we can employ a similar method to determine the size or angular diameter of the planet. If d is the diameter of the planet and α the angular size of the planet (the angle subtended by d at the earth), we have
`alpha=d/D`
The angle α can be measured from the same location on the earth. It is the angle between the two directions when two diametrically opposite points of the planet are viewed through the telescope. Since D is known, the diameter d of the planet can be determined using this equation.
`text(Range of Lengths :)`
The sizes of the objects we come across in the universe vary over a very wide range. These may vary from the size of the order of `10^(–14) m` of the tiny nucleus of an atom to the size of the order of `10^(26) m` of the extent of the observable universe.
We also use certain special length units for short and large lengths. These are
`1 text(fermi) =1f= 10^(-15)m`
`1 text(angstrom)=1overset@A=10^(-10)m`
`1 text(astronomical unit) = 1 AU` (average distance of the Sun from the Earth) `=1.496xx10^(11)m`
`1 text(light year) = 1 text(ly)= 9.46 × 10^(15) m` (distance that light travels with velocity of `3 × 10^8 ms^(–1)` in 1 year)
`1 text(parsec) = 3.08 × 10^(16) m` (Parsec is the distance at which average radius of earth’s orbit subtends an angle of 1 arc second)