Скачать или смотреть NCERT Physics Class 11 Chapter 2.3 Measurement of Length | Parallax Method | Calculating One Parsec

Following topics are covered:

Parallax Method- Large Lengths using method of trigonometric parallaxes.

Parallax angles:
Parallax angle decreases as distance increases.
When viewed Earth, the red star appears to move first west (towards the right) then east (towards the left) with respect to the distant background stars.
The background stars must be so far away that their parallax motions are too small to be seen at this scale and can be neglected.
Trigonometric parallax of a star is inversely proportional to its distance from the Sun. A star 2 times farther away produces trigonometric parallax motions which are 2 times smaller. We can use this fact to produce a direct measurement of the star's distance.

What is a Radian?
Angle subtended by an arc at the center in radians is the ratio of arc length to radius.
1 radian is the angle for which the arc length is one radius.
The circumference is π diameters and 2π radii, so one complete revolution is 2π radians.
Traditionally a circle was divided into 360 degrees since that number has a convenient list of factors, and so one radian is 180/𝜋 degrees.

Parallax Calculations

Calculations in Parsecs
Parsec (pc) m is obtained by the use of parallax and trigonometry, and is defined as the distance at which 1 au subtends an angle of one arcsecond (1/3600 of a degree).
If parallax angle is half the distance would be double. If parallax angle is twice distance would be half.
In general d (in parsecs) = 1/𝑝 where p is in arcseconds.
1 Parsec is approximately equal to 3.26 light-years or 206,000 astronomical units (au), i.e. 30.9 trillion km.

Value of 1 Parsec

Numerical in Parsec
The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?

Measuring Small Distances (Oleic Acid Experiment)
Resolution of any microscope is proportional to the wavelength used.
Best we can do with a optical microscope is violet light (400nm).
An electron as a wave has a far smaller wavelength, in the range of picometres.

Normal Measurements
Normally measurement are in range of few hundred km to fraction of millimeters can be done with ordinary instruments.
Meter scale can measure in mm
Vernier callipers can measure in 10^(−4) (1/10th of mm)
Screw gauge and spherometer can measure with accuracy of 10^(−5) (1/100th of mm)




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NCERT Physics Class 11 Chapter 2.3 Measurement of Length | Parallax Method | Calculating One Parsec

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