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Question: How do we calculate the angular velocity of precession ?...

How do we calculate the angular velocity of precession ?

Explanation

Solution

Angular velocity is defined as the angular displacement of a particle about its centre in unit time. Angular velocity can also be defined as the rate at which displacement is changing with respect to the time in circular motion. The SI unit of angular velocity is radians per second.

Complete step by step answer:
Precession is defined as the change in the orientation of the rotational axis of a rotating body. In other words, it can be said that if the axis of rotation of a body is itself rotating about a second axis, then it can be that the body precesses about the second axis.Now, we need to calculate the angular velocity of precession and find out whether the value is the same or not.The poles move along parallel circles, parallel to the orbital plane of the earth.This takes about 25800 years25800\,years to complete the circle. It is important to note that this is relative to the centre of the earth.

Now, as we know that the earth's axial tilt (obliquity) is currently about 23.4o{23.4^o}. So,
The radius of this circle ==polar radius ×sin⁡23.4o \times \sin {23.4^o}
Here, the line which joins that centre of the circle is normal to the ecliptic. This is known as the axis of revolution for its polar axis, for its precession motion.
So, the angle of precession == 360period\dfrac{{360}}{{period}}
Where, period is the period of revolution in years.

We know that the period of revolution in years is 25800 years25800\,years
The angle of precession =36025800 = \dfrac{{360}}{{25800}}
The angle of precession =0.01395oyear = \dfrac{{{{0.01395}^o}}}{{year}}
Now, to convert the degree in seconds we will multiply degree by 36003600
The angle of precession =(0.01395×3600)′′year = \dfrac{{{{\left( {0.01395 \times 3600} \right)}^{''}}}}{{year}}
The angle of precession =50.2′′year = \dfrac{{{{50.2}^{''}}}}{{year}}
Therefore, the final answer is 50.2′′year\dfrac{{{{50.2}^{''}}}}{{year}}.

Note: The term Great Year has two main meanings. It is defined by scientific astronomy as the period of one complete cycle of the equinoxes around the ecliptic. Now, this value comes out to be 25800 years25800\,years. More precisely, the value of this comes out to be 2577225772 years.