How do we know the distance between the moon and the earth or the moon and the sun? How did we measure the mass and the diameter of the earth? Length measurement, measurement of mass and time are not always simple and straightforward. We will try and answer these questions below. Furthermore, we will learn about the various ways for the measurement of length, mass and time.

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## Measurement of Length

### Measurement Of Large Distances

Distances like the distance of the Sun from the Earth or the distance of, say Alpha Centauri from Earth is measured indirectly by the Parallax method. Parallax is the shift in the position of an object with the shift in the position of the observer.

Let the angle subtended by the arc-ab at O be = P. Imagine a circle that has its centre at O and passes through A and B. Then from the definition of an angle, we can write

P = [length of arc ‘AB’]/[radius of the circle (OA or OB)]

If we know any two variables in the above equation, we can find the third one. Imagine the point a and b are two diametrically opposite points on Earth and O is Alpha Centauri. We can measure the distance between a and b (known as the basis) and also the angle aOb – the parallax angle or the parallactic angle. As a result, we can find the distance to the star.

### Measurement of Very Small Distance

Very small distances like the diameter of a molecule are done indirectly by taking advantage of equations that include these parameters. Let’s take the example of the Oleic acid (C_{18}H_{34}O_{2}) molecule. It is a fairly big molecule with a size of approximately 10^{-9 }m. Firstly, we make a very dilute solution of Oleic acid in alcohol.

Secondly, we sprinkle a very small quantity of lycopodium powder (highly hydrophobic) on the surface of the water. After this, we add one drop of the Oleic acid – alcohol solution to the lycopodium-water mixture. The drop spreads into a large film. The container that has the lycopodium-water mixture is made very large. The Oleic acid-alcohol solution will form a thin film on the surface. As this film spreads, its thickness will approach the size of one molecule.

The ratio of the volume of the drop (volume of a sphere) to the area of the film produced (area of a circle) from the drop will give the thickness of the film and hence the size of the molecule.

Size of the Oleic Acid molecule = [Volume of the drop]/[area of the film]

## Measurement of Mass

The mass of an object is defined by Newton’s Laws. It is the resistance offered by an object to acceleration. In SI system we use kilogram to measure mass. But large quantities of matter like the mass of a mountain or the Earth or stars or the entire Universe is measured indirectly by using Newton’s Law of gravitation or other such equations. The law says that two bodies of mass M_{1} and M_{2} (say) attract each other with a Force F given by

**F = GM _{1}M_{2}/R**

^{2 }……. where R is the separation between the two.

As a result, the value of mass obtained from this equation is sometimes called the Gravitational mass. We measure small masses like that of an electron or a proton by observing their acceleration. We use an electromagnetic force of known value to accelerate these particles in a device known as the mass spectrometer. The lighter particles accelerate easily while as the heavier particles are pretty, let us say lazy to move around.

## Measurement of Time

We need a clock to measure time. By a clock, we mean any natural or man-made phenomenon that is repetitive and regular in nature. Galileo used his heartbeat to measure the time period of a simple pendulum and laid the foundation of Classical mechanics. We can say that he literally put his heart into Physics. Today we have very accurate timekeeping devices or clocks like the atomic clocks.

The time interval required for 9192631770 vibrations of the radiation corresponding to the transition between two hyperfine states of the cesium-133 atom is one second.

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## Solved Examples For You

Which of the following principle helps in the measurement of the mass of the planets?

a) Einstein’s Theory of Relativity b) Newton’s Law of Gravitation

c) Newton’s Law of Cooling d) Parallax Method

Solution: b) Newton’s Law of Gravitation

Newton’s law of gravitation states that every mass in the universe attracts every other mass with a force given by the equation of the Universal Law of Gravitation.

F = GM_{1}M_{2}/R^{2}

Here, F is the force of Gravitation, M_{1 }and M_{2 }are the masses of any two objects. R is the distance of separation between the centres of the two masses. G is the Universal Gravitational constant. Therefore, if we put one of the masses equal to one unit, we can measure the other mass from the above equation.

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