Measurement of Length Triangulation and Parallax Method

Introduction

Measurement is the comparison of an unknown quantity with a known value. Measurement is a system of measuring. Measurement is always a numerical value. Measurements include length, mass, volume, temperature, etc. It is associated with geometry, trigonometry, algebra, etc. Units were given to the measured values. Fundamental units for length, mass, and time are m, kg, and sec. There are many methods for measuring length. But the distance between the stars and the distance between the objects in space are done by using triangulation and parallax methods.

What do you mean by the length triangulation method?

The distance between the stars is calculated by using the methods called triangulation and parallax. The concept of the requirement of three elements for the triangle is referred to by the triangulation method. This process is finding the three elements used in the calculation of the distance or location of the object in space. Not only it is used by astronomers but also it is used by surveyors and architects. If the location or distance of any object is not known, this triangulation method is used to find the location by considering the other two points of the triangle.

Two linear points are taken into consideration on the shore as a baseline of the triangle. The third point is the ship on the sea which is at an unknown distance. The line joining points A and C make an angle α with the baseline. Similarly, the line joining the points B and C makes an angle β with the baseline. These angles are made from the seashore to the ship on the sea. As we know the baseline distance and the two angles the distance between the ship and the seashore is calculated.

The distance between the ship from the seashore is given by,

$$\mathrm{d\:=\:l\:\frac{\sin\alpha\sin\beta}{\sin\:n(\alpha+\beta)}}$$

l denotes the distance between A and B.

Examples of length triangulation method

Generally, the triangular shapes are strong enough and rigid. So triangulation is used in constructing buildings and structures as it is the strongest form. This triangulation method is used in finding the distance of the ship from the seashore.

What is the parallax method?

Let us make your hand with one finger pointed out in front of your eye at a small distance from your face. Now close your left eye and see the finger with the right eye and vice versa. By continuously doing that the position of the finger looks different and looks like it jumps from one place to another. This is the parallax effect. There is an apparent shift between the vision of the image from two different points. The parallax method uses the principle of the triangulation method for the measurement of distance. Most astronomers use the parallax method they benefited from. While traveling through a vehicle we can see that the vehicle which is closer to us looks like it is moving fast. The vehicle that far away looks like they are moving slowly.

The parallax method uses the triangulation method to find the distance between the stars or the distance between the objects in space. The distance between the stars is measured in units of parsecs.

Let us consider the distant object observed from two points on the earth and the distance between the distant object and the baseline AB is d. Then the reciprocal of the parallax angle gives the distance. The unit of parallax angle is arcsec.

$$\mathrm{d\:=\:\frac{1}{\theta}\:parsecs}$$

Examples of parallax method

On the dashboard of the motorcycle, there is a needle-style speedometer. It shows the speed of the vehicle. It looks different for different people due to the position they see the meter. The person who drives notices some speed. But the same meter shows different readings for the person at the back because of the angle of sight.

Difference between length triangulation and the parallax method

The triangulation method measures the distance of the object by the accurate baseline on the earth. It is used in building construction and surveying. The parallax method uses the principle of the triangle to make use of the trigonometric relationship between the angle and the distance. It is used by astronomers to measure distance.

Solved examples

Example 1

The distance between Saturn and the satellite which is nearer to our earth is 1.5107 x 109 km according to the doppler effect and the angle subtended by Saturn is 77 x 10-3 radian according to the information from the observatory. Find the diameter of Saturn.

Given − $\mathrm{S\:=\:1.5107\:\times\:10^{9}km\:\varphi\:=\:77\times\:10^{-3}rad}$

Now the baseline is the diameter of Saturn so there are two points and the third point is on the satellite. Then the diameter of Saturn is

$$\mathrm{d\:=\:S\varphi}$$

$$\mathrm{d\:=\:1.15107\times\:10^{9}\:\times\:77\times\:10^{-3}rad}$$

$$\mathrm{d\:=\:116.3239\:\times\:10^{6}km}$$

Conclusion

In this tutorial, the length triangulation method and its examples were discussed. The parallax method and examples for the parallax method were also discussed. The differences between the triangulation method and the parallax method were also discussed.

FAQs

1. What is meant by Parasec?

Parsec is used for the unit of length that is used to represent a large distance. Especially for astronomical objects that are located beyond the solar system. It is the ratio between One astronomical distance unit to one arc second. The value of 1 parsec is around 3.26LY or 206 x 103.

2. What are the limitations of the parallax method?

• It is hard to find the distance if the parallax angle is less than 0.01arcsecs.

• One of the disadvantages of the parallax method is using trigonometry.

• The calculator is not always accurate.

3. What is the main approximation made in the parallax method?

The distance between the two points on the earth is very much smaller when comparing it with the distance of the planet from the point on the earth.

4. Can the parallax method be used for measuring the distance of far-away stars?

It is not possible to find the distance of the far-away stars. Because at very long distances the parallax angle is too small. it cannot be found accurately

5. What is stereoscopic parallax?

There is a phase shift if the image is seen from a different point of view. Similarly taking a photo image of the same object in different aspects of the references is known as stereoscopic parallax. The overlapping of adjacent photos is called stereo-pair.