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There are various things to measure around us. In terms of shape and size, it can be as small as an atom and as big as the universe or a planet. But if we have to measure the distance between two objects either small or large, there are different units used for different objects. We can measure the distance between two atoms with a different unit and a different unit is used for massive planets.
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Length and Distance
We can measure the lengths of objects using specified units. The units can be small or large depending upon the objects or distances we are measuring.
Length and Distance
To understand lengths and how to measure distances, we can take an example of two persons standing at a distance of 20 m. If an observer asks them about the length of the distance between them they can tell that they are standing 20 m apart. This 20 m shows the distance between them. And m is the unit.
Units and Measurements: NCERT Notes
Distance
To define distance in simple terms, we can say how far the object or person has moved. It is a Scalar quantity, measuring the total/complete path travelled by an object. Distance can never be negative or zero. It will always have a positive value.
Distance
Measurement of Distances
We can measure distance in various units, it can be cm, m or km. Cm or centimetre is a CGS system of units.
SI unit of Distance
According to the International system of Units, meter is the SI unit of distance. It is used to measure distances and it’s more like a standard unit.
We can use a meter as a base unit along with some equations and can derive some other units of various physical quantities like volume, area, acceleration, speed.
Metric Unit of Distance
- CGS and MKS units of the system form the metric units of distance.
- CGS system = centimetre, gram, seconds
- MKS system = meter, kilogram, seconds
- The table below shows metric units of Distance:
| UNIT | SYMBOL |
|---|---|
| millimetre | mm |
| centimetre | cm |
| decimetre | dm |
| metre | m |
| kilometre | km |
Distance Conversion
For different conversion of units, the table is given below:
| Units → ↓ | Millimeter(mm) | Centimeter(cm) | Meter(m) | Kilometers(km) |
|---|---|---|---|---|
| 1 Millimeter(mm) | 1 | 0.1 | 0.001 | 0.000001 |
| 1 Centimeter(cm) | 10 | 1 | 0.01 | 0.00001 |
| 1 Decimeter(m) | 100 | 10 | 0.1 | 0.0001 |
| 1 Meter(m) | 1,000 | 100 | 1 | 0.001 |
| 1 Kilometer(km) | 1,000,000 | 100,000 | 1000 | 1 |
| 1 inch(in) | 25.4 | 2.54 | 0.0254 | 0.0000254 |
Measurement of Large Distances
Metre scales can be used only for small distances. But we cannot measure long distances such as planet to planet or planet to star distances using a metre scale. We need a larger scale to measure it.
Measurement of Large Distances
For measuring large distances we use units like light year, parsec, astronomical units etc. The Astronomical Unit is used to denote the mean distance between earth and the sun. The mean distance between the planet earth and sun is approx. 1.496 × 1013cm or we can say 93 million miles.
Measurement of Large Distances
Light year is also such a unit to measure the distance. Light year is the distance travelled by light in a year. 1 light year = 9.46 × 1017 cm.
Parsec or pc is the mean radius of earth’s orbit that subtends an angle of one second of arc. It is the unit of distance used in astronomy. Parsec is used to represent distances to stars and galaxies.
1 parsec = 3.26 light years = 296,265 Astronomical Unit
Some Other Units to Measure Distance
10 meters = 1 decameter
10 decameters = 1 hectometer(hm)
10 decameters = 100 meters
10 hectometers = 1 kilometer
10 hectometers = 1000 meters
Parallax Method
To measure large distances we use the parallax method. This method is useful to measure the large distances of two distant objects by knowing the angles and some small distances between objects.
Parallax Method
We can understand this method by taking a simple real life example, Suppose an object is kept in a table in front of you. Now all you have to do is see the object with one eye closed or you can put your hand before the eye.
After this, you have to do the same activity with your other eye. You will observe a change in position of the object kept on the table. This is called a Parallax. We can use the parallax method to measure the distance of a far away planet.
The parallax method formula,
| D = ab/Θ |
Where D= distance between observer A, B and the planet S,
AB= arc of length b of a circle,
Θ= parallax angle or parallactic angle
If we have know Θ and AB we can use this formula to calculate the distance,D.
Example based on Unit of Distance
If we observe the moon from two distant places of earth, say, A and B. The angle Θ subtended at the moon by the two observers is 1°54’’. You have to find the distance of the moon from the earth. Given that, the diameter of Earth is 1.276 ×10? m. (Solved Example, NCERT)
Solution: To solve this problem, first we have to change Θ means changing angle from degree into radians(rad) ,
Θ = 1°54’’ = 114’
= (114 × 60 )’’ × (4.85 × 10-6) rad (Since, 1’’ =4.85 × 10-6 rad )
= 3.32 × 10-2 rad
and ,b = AB = 1.276 ×10-6 m
Hence, using parallax equation,
D = b / Θ
= 1.276 ×107 / 3.32 × 10-2
Therefore, we have earth-moon distance = 3.84 ×108 m.
Sample Questions
Ques. What is the largest unit of distances we use? (1 mark)
Ans. Parsec (pc) is the largest unit of distance which we use to measure astronomical objects. It is used to measure the distances between the celestial objects outside the solar system.
Ques. What is the smallest known unit of distance? (1 mark)
Ans. We use Planck’s length as the smallest unit of distance. It is equal to 1.616255(18)×10−35 m. Plank’s Length is denoted by lP
Ques. Convert 15 kilometers into centimeters? (2 marks)
Ans. We know, 1 km = 100,000
15 kms = 100,000× 15 = 15,00,000 cms
Ques. Which unit of distance is used to measure distances between planets and sun? (2 marks)
Ans. Parsec or pc is used to represent the distance between planets, stars and galaxies. 1 Parsec is equal to approx. 3.26 light years(ly) and is also equal to 296,265 Astronomical units (AU).
Ques. Define Light year. (1 mark)
Ans. Light year is the distance travelled by light in a year.
1 light year = 9.46 × 1017 cm = 9.46 × 1012 km
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